Higher twist corrections to Bjorken sum rule
International Nuclear Information System (INIS)
Some higher twist corrections to the Bjorken sum rule are estimated in the framework of a quark-diquark model of the nucleon. The parameters of the model have been previously fixed by fitting the measured higher twist corrections to the unpolarized structure function F2(x,Q2). The resulting corrections to the Bjorken sum rule turn out to be negligible. (author). 15 refs, 1 fig
Corrections to the Bjorken and Voloshin sum rules
International Nuclear Information System (INIS)
We calculate near zero recoil the order αs corrections to the Bjorken and Voloshin sum rules that bound the B→D(*)scr(l)bar ν form factors. These bounds are derived by relating the result of inserting a complete set of physical states in a time-ordered product of weak currents to the operator product expansion. The sum rules sum over physical states with excitation energies less than a scale Δ. We find that the corrections to the Bjorken bound are moderate, while the Voloshin bound receives sizable corrections enhanced by Δ/ΛQCD. With some assumptions, we find that the slope parameter for the form factor hA1 in B→D*scr(l)bar ν decay satisfies 0.4 approx-lt ρA12 approx-lt 1.3. copyright 1997 The American Physical Society
Modelling power corrections to the Bjorken sum rule for the neutrino structure function F1
International Nuclear Information System (INIS)
Direct measurements of the structure functions Fνp1 and Fνn1 at a neutrino factory would allow for an accurate extraction of αs from the Q2-dependence of the Bjorken sum rule, complementing that based on the Gross-Llewellyn-Smith sum rule for F3. We estimate the power (1/Q2-) corrections to the Bjorken sum rule in the instanton vacuum model. For the reduced matrix element of the flavour-nonsinglet twist-4 operator u-barG-tildeμνγνγ5u - (u → d) we obtain a value of 0.18 GeV2, in good agreement with the QCD sum rule calculations of Braun and Kolesnichenko. Our result allows one to reduce the theoretical error in the determination of αs
The nucleon axial isoscalar coupling constant and the Bjorken sum rule
International Nuclear Information System (INIS)
The nucleon coupling constant with the axial isoscalar current entering the Bjorken sum rule for the deep inelastic scattering of polarized electrons on a polarized target is calculated in nonperturbative QCD. The result, gsub(A)sup(s) approximately 0.5, is about a factor of two smaller as compared to that of the SU(6) symmetric quark model
Bjorken unpolarized and polarized sum rules comparative analysis of large-N_F expansions
Broadhurst, D J
2002-01-01
Analytical all-orders results are presented for the one-renormalon-chain contributions to the Bjorken unpolarized sum rule for the F_1 structure function of nu N deep-inelastic scattering in the large-N_F limit. The feasibility of estimating higher order perturbative QCD corrections, by the process of naive nonabelianization (NNA), is studied, in anticipation of measurement of this sum rule at a Neutrino Factory. A comparison is made with similar estimates obtained for the Bjorken polarized sum rule. Application of the NNA procedure to correlators of quark vector and scalar currents, in the euclidean region, is compared with recent analytical results for the O(alpha_s^4 N_F^2) terms.
Low x Behaviour of the Isovector Nucleon Polarized Structure Function and the Bjorken Sum Rule
Buccella, F; Santorelli, P
1997-01-01
The combination g_1^p(x) - g_1^n(x) is derived from SLAC data on polarized proton and deuteron targets, evaluated at Q^2 = 10 GeV^2, and compared with the results of SMC experiment. The agreement is satisfactory except for the points at the three lowest x, which have an important role in the SMC evaluation of the l.h.s. of the Bjorken sum rule.
Low x Behavior of the Isovector Nucleon Polarized Structure Function and the Bjorken Sum Rule
Buccella, Franco; Pisanti, Ofelia; Santorelli, Pietro
The combination gp1(x)-gn_1(x) is derived from SLAC data on polarized proton and deuteron targets, evaluated at Q2=10 GeV2, and compared with the results of SMC experiment. The agreement is satisfactory except for the points at the three lowest x, which have an important role in the SMC evaluation on the L.H.S. of the Bjorken sum rule.
Measurement of the neutron spin structure function---Test of the Bjorken sum rule
International Nuclear Information System (INIS)
As experiment to measure the neutron spin-dependent structure function g1n (x) over a range in x from 0.04 to 0.7 and with Q2 > 1 (GeV/c)2 is presented. The experiment consists of scattering a longitudinally polarized electron beam from the Stanford Linear Accelerator off a polarized 3He target and detecting scattered electrons in two magnetic spectrometers. The experiment will provide a critical test of the Bjorken sum rule and valuable information in understanding the nucleon spin structure and the violation of the Ellis-Jaffe sum rule. 3 figs., 1 tab
QCD effects to Bjorken unpolarized sum rule for νN deep-inelastic scattering
International Nuclear Information System (INIS)
The possibility of the first measurement of Bjorken unpolarized sum rule for F1 structure function of νN deep-inelastic scattering at neutrino factories is commented. The brief summary of various theoretical contributions to this sum rule is given. Using the next-to-leading set of parton distributions functions, we simulate the expected Q2-behaviour and emphasize that its measurement can allow us to determine the value of the QCD strong coupling constant αs with reasonable theoretical uncertainty, dominated by the ambiguity in the existing estimates of the twist-4 non-perturbative 1/Q2-effect
Yaouanc, A Le; Raynal, J -C
2015-01-01
We underline that the Bakamjian-Thomas relativistic quark model is the only known theoretical scheme, describing hadrons with a fixed number of constituents, that yields covariant Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules of the heavy quark limit of QCD (Bjorken-Uraltsev sum rules). In the heavy quark limit, it has been demonstrated that a formalism, based on Lorentz group representations in a Hilbert space, implies this class of sum rules. On the other hand, it has been recently shown that a Lorentz group representation in a Hilbert space underlies the Bakamjian-Thomas class of relativistic quark models in the heavy quark limit. Therefore, due to completeness in this space, the model satisfies the whole tower of Bjorken-Uraltsev sum rules. To illustrate in practice this feature we provide some examples. In particular, we demonstrate explicitly Bjorken and Uraltsev sum rules within the Bakamjian-Thomas framework, and also an interesting sum rule that involves only heavy mes...
The spin-dependent structure function of the proton g(1)(p) and a test of the Bjorken sum rule
Czech Academy of Sciences Publication Activity Database
Alekseev, M.; Alexakhin, V. Yu.; Alexandrov, Yu.; Alexeev, G. D.; Amoroso, A.; Austregisilio, A.; Badelek, B.; Balestra, F.; Ball, J.; Barth, J.; Baum, G.; Bedfer, Y.; Bernhard, J.; Bertini, R.; Bettinelli, M.; Birsa, R.; Bisplinghoff, J.; Bordalo, P.; Bradamante, F.; Bravar, A.; Bressan, A.; Brona, G.; Burtin, E.; Bussa, M.; Chaberny, D.; Chiosso, M.; Chung, S.U.; Cicuttin, A.; Colantoni, M.; Cotic, D.; Crespo, M.; Dalla Torre, S.; Das, S.; Dasgupta, S. S.; Denisov, O.; Dhara, L.; Diaz, V.; Donskov, S.; Doshita, N.; Duic, V.; Dünnweber, W.; Efremov, A.V.; El Alaoui, A.; Eversheim, P.; Eyrich, W.; Faessler, M.; Ferrero, A.; Filin, A.; Finger, M.; Finger jr., M.; Fischer, H.; Franco, C.; Friedrich, J.; Garfagnini, R.; Gautheron, F.; Gavrichtchouk, O.; Gazda, R.; Gerassimov, S.; Geyer, R.; Giorgi, M.; Gnesi, I.; Gobbo, B.; Goertz, S.; Grabmüller, S.; Grasso, A.; Grube, B.; Gushterski, R.; Guskov, A.; Haas, F.; von Harrach, D.; Hasegawa, T.; Heinsius, F.; Hermann, R.; Herrmann, F.; Hess, C.; Hinterberger, F.; Horikawa, N.; Höppner, Ch.; d'Hose, N.; Ilgner, C.; Ishimoto, S.; Ivanov, O.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jasinski, P.; Jegou, G.; Joosten, R.; Kabuss, E.; Käfer, W.; Kang, D.; Ketzer, B.; Khaustov, G.; Khokhlov, Y.; Kisselev, Y.; Klein, F.; Klimaszewski, K.; Koblitz, S.; Koivuniemi, J.; Kolosov, V.; Kondo, K.; Königsmann, K.; Konopka, R.; Konorov, I.; Konstantinov, V.; Korzenev, A.; Kotzinian, A.; Kouznetsov, O.; Kowalik, K.; Krämer, M.; Kral, A.; Kroumchtein, Z.; Kuhn, R.; Kunne, F.; Kurek, K.; Lauser, L.; Le Goff, J.; Lednev, A.; Lehmann, A.; Levorato, S.; Lichtenstadt, J.; Liska, T.; Maggiora, A.; Maggiora, M.; Magnon, A.; Mallot, G.; Mann, A.; Marchand, C.; Marroncle, J.; Martin, A.; Marzec, J.; Massmann, F.; Matsuda, T.; Meyer, W.; Michigami, T.; Mikhailov, Y.; Moinester, M.; Mutter, A.; Nagaytsev, A.; Nagel, T.; Nassalski, J.; Negrini, S.; Nerling, F.; Neubert, S.; Neyret, D.; Nikolaenko, V.; Nunes, A.S.; Olshevsky, A.; Ostrick, M.; Padee, A.; Panknin, R.; Panzieri, D.; Parsamyan, B.; Paul, S.; Pawlukiewicz-Kaminska, B.; Perevalova, E.; Pesaro, G.; Peshekhonov, D.; Piragino, G.; Platchkov, S.; Pochodzalla, J.; Polak, J.; Polyakov, V.; Pontecorvo, G.; Pretz, J.; Quintans, C.; Rajotte, J.; Ramos, S.; Rapatsky, V.; Reicherz, G.; Richter, A.; Robinet, F.; Rocco, E.; Rondio, E.; Ryabchikov, D.; Samoylenko, V.; Sandacz, A.; Santos, H.; Sapozhnikov, M.; Sarkar, S.; Savin, I.; Sbrizzai, G.; Schiavon, P.; Schill, C.; Schlütter, T.; Schmitt, L.; Schopferer, S.; Schröder, W.; Shevchenko, O.; Siebert, H.; Silva, L.; Sinha, L.; Sissakian, A.; Slunecka, M.; Smirnov, G.; Sosio, S.; Sozzi, F.; Srnka, Aleš; Stolarski, M.; Sulc, M.; Sulej, R.; Takekawa, S.; Tessaro, S.; Tessarotto, F.; Teufel, A.; Tkatchev, L.; Uhl, S.; Uman, I.; Virius, M.; Vlassov, N.; Vossen, A.; Weitzel, Q.; Windmolders, R.; Wislicki, W.; Wollny, H.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zhao, J.; Zhuravlev, N.; Zvyagin, A.
2010-01-01
Roč. 690, č. 5 (2010), s. 466-472. ISSN 0370-2693 R&D Projects: GA MŠk ME 492 Institutional research plan: CEZ:AV0Z20650511 Keywords : deep inelastic scattering * structure function * QCD analysis * Bjorken sum rule Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 5.255, year: 2010
International Nuclear Information System (INIS)
The next-next-to-leading order QCD corrections to the Gross-Llewellyn Smith sum rule for deep inelastic neutrino-nucleon scattering and to the Bjorken sum rule for polarized electron-nucleon scattering have been computed. This involved the proper treatment of γ5 inside the loop integrals with dimensional regularization. It is found that the difference between the two sum rules are entirely due to a class of 6 three loop graphs and is of the order of 1% of the leading QCD term. Hence the Q2 behavior of both sum rules should be the same if the physics is described adequately by the lower order terms of perturbative QCD. (author). 12 refs.; 2 figs.; 4 tabs
Baikov, P A; Chetyrkin, K G; Kühn, J H
2010-04-01
We compute, for the first time, the order alpha(s)(4) contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta(3) in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha(s)(4). PMID:20481875
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order αs4 in a General Gauge Theory
International Nuclear Information System (INIS)
We compute, for the first time, the order αs4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop β function in quenched QED. In particular, the appearance of an irrational contribution proportional to ζ3 in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order αs4.
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
2010-01-01
We compute, for the first time, the order alpha_s^4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (non-singlet) Adler function for the case of a generic colour gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta-function in quenched QED. In particular, the appearance of an irrational contribution ...
The spin structure function g1p of the proton and a test of the Bjorken sum rule
Adolph, C.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badełek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Burtin, E.; Capozza, L.; Chang, W.-C.; Chiosso, M.; Choi, I.; Chung, S. U.; Cicuttin, A.; Crespo, M. L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O. Yu.; Dhara, L.; Donskov, S. V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P. D.; Eyrich, W.; Ferrero, A.; Finger, M.; Finger, M.; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F. H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; -Yu Hsieh, C.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jörg, P.; Joosten, R.; Kabuß, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G. K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V. I.; Novy, J.; Nowak, W.-D.; Nunes, A. S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pesek, M.; Peshekhonov, D. V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N. S.; Ryabchikov, D. I.; Rychter, A.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O. Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-02-01
New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p (x) by about a factor of two in the region x ≲ 0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS (x ,Q2) yields as ratio of the axial and vector coupling constants |gA /gV | = 1.22 ± 0.05 (stat.) ± 0.10 (syst.), which validates the sum rule to an accuracy of about 9%.
The spin structure function g1p of the proton and a test of the Bjorken sum rule
Directory of Open Access Journals (Sweden)
C. Adolph
2016-02-01
Full Text Available New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p(x by about a factor of two in the region x≲0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS(x,Q2 yields as ratio of the axial and vector coupling constants |gA/gV|=1.22±0.05 (stat.±0.10 (syst., which validates the sum rule to an accuracy of about 9%.
The Spin Structure Function $g_1^{\\rm p}$ of the Proton and a Test of the Bjorken Sum Rule
Adolph, C.; Alexeev, M.G.; Alexeev, G.D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badelek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E.R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Buchele, M.; Burtin, E.; Capozza, L.; Chang, W.C.; Chiosso, M.; Choi, I.; Chung, S.U.; Cicuttin, A.; Crespo, M.L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S.S.; Dasgupta, S.; Denisov, O.Yu.; Dhara, L.; Donskov, S.V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Ferrero, A.; Finger, M.; M. Finger jr; Fischer, H.; Franco, C.; von Hohenesche, N. du Fresne; Friedrich, J.M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmuller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F.H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.Yu; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jorg, P.; Joosten, R.; Kabuss, E.; Ketzer, B.; Khaustov, G.V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J.H.; Kolosov, V.N.; Kondo, K.; Konigsmann, K.; Konorov, I.; Konstantinov, V.F.; Kotzinian, A.M.; Kouznetsov, O.; Kramer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z.V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R.P.; Lednev, A.A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V.I.; Novy, J.; Nowak, W.D.; Nunes, A.S.; Olshevsky, A.G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.C.; Pereira, F.; Pesek, M.; Peshekhonov, D.V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V.A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N.S.; Ryabchikov, D.I.; Rychter, A.; Samoylenko, V.D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I.A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schonning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O.Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Wolbeek, J. ter; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-01-01
New results for the double spin asymmetry $A_1^{\\rm p}$ and the proton longitudinal spin structure function $g_1^{\\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\\rm p}(x)$ by about a factor of two in the region $x\\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\\Delta \\Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\\rm p}$. The uncertainty of $\\Delta \\Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\\rm...
Cvetič, Gorazd; Kataev, A. L.
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the non-singlet part of the $e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering $C_{ns}^{Bjp}$, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is a two-fold series in terms of powers of the conformal anomaly and of $SU(N_c)$ coupling $\\alpha_s$. Explicit expressions are obtaine...
Cvetič, Gorazd
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\\{\\beta\\}$-expanded perturbation coefficients at $O(\\alpha_s^4)$ level in $\\overline{\\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\\{\\beta\\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are pres...
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
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Djawotho, Pibero [College of William and Mary, Williamsburg, VA (United States)
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
Anomalous commutator corrections to sum rules
International Nuclear Information System (INIS)
In this paper we consider the contributions of anomalous commutators to various QCD sum rules. Using a combination of the Bjorken-Johnson-Low limit with the operator product expansion the results are presented in terms of the vacuum condensates of gauge-invariant operators. It is demonstrated that the anomalous contributions are non-negligible and reconcile various apparently contradictory calculations
Statistical Inspired Parton Distributions and the Violation of QPM Sum Rules
Buccella, F; Miele, G; Pisanti, O; Santorelli, P; Tancredi, N
1996-01-01
A quantum statistical parametrization of parton distributions has been considered. In this framework, the exclusion Pauli principle connects the violation of the Gottfried sum rule with the Ellis and Jaffe one, and implies a defect in the Bjorken sum rule. However, in terms of standard parametrizations of the polarized distributions a good description of the data is obtained once a large gluon polarization is provided. Interestingly, in this description there is no violation of the Bjorken sum rule.
Spinrath, Martin
2016-01-01
There is a wide class of models which give a dynamical description of the origin of flavour in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing angles and the Dirac CP phase with each other and/or on the other hand neutrino masses and Majorana phases with each other. We will briefly sketch how this happens and discuss briefly the impact of renormalisation group corrections to the mass sum rules.
Adler Function, DIS sum rules and Crewther Relations
International Nuclear Information System (INIS)
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(αs4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(αs4) contribution to the singlet part of the Adler function.
Adler Function, DIS sum rules and Crewther Relations
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
2010-01-01
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) con...
Study of spin sum rules (and the strong coupling constant at large distances)
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur
2009-12-01
We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.
International Nuclear Information System (INIS)
An approach to gluonium based on QCD sum rules is given. The basic idea underlying the sum rules is that asymptotic freedom is violated first by interaction of quarks and gluons with vacuum fields. Formation of resonances is a phenomenological manifestation of this interaction. The emphasis is given to a new mass scale implied by the sum rules
Sum rules in photonuclear physics
International Nuclear Information System (INIS)
After a survey of experimental data the nuclear compton scattering and the derivation of the dipole- and GGT-sum rules are discussed. The calculation that have been performed on dipole sum enhancement and dispersion relation sum rules are considered. (BJ)
Spin Sum Rules and the Strong Coupling Constant at large distance.
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur
2009-07-01
We present recent results on the Bjorken and the generalized forward spin polarizability sum rules from Jefferson Lab Hall A and CLAS experiments, focusing on the low $Q^2$ part of the measurements. We then discuss the comparison of these results with Chiral Perturbation theory calculations. In the second part of this paper, we show how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.
The Orbital Angular Momentum Sum Rule
Aslan, Fatma; Burkardt, Matthias
2015-10-01
As an alternative to the Ji sum rule for the quark angular momentum, a sum rule for the quark orbital angular momentum, based on a twist-3 generalized parton distribution, has been suggested. We study the validity of this sum rule in the context of scalar Yukawa interactions as well as in QED for an electron.
QDC sum rules for heavy quark systems
International Nuclear Information System (INIS)
QCD sum rules for equal mass heavy quark meson states are presented and the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization are discussed. Using dispersion relations, sum rules are derived and applications made to the lowest lying states of the charmonium and upsilon systems. (U.K.)
Moments of Spin Structure Functions: Sum Rules and Polarizabilities
Energy Technology Data Exchange (ETDEWEB)
Jian-Ping Chen
2010-10-01
Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight for some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Bjorken, Burkhardt-Cottingham, Gerasimov-Drell-Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers.
Adler Function, DIS sum rules and the Crewther Relation in order αs4
International Nuclear Information System (INIS)
We report on the first analytical, valid for a generic gauge group, calculations of the O(αs4) corrections to the Adler function and to DIS sum rules, in particular to the the Gross-Llewellyn Smith and to the Bjorken ones. We discuss a decisive check of correctness of our previous calculations of R(s) in QCD and the quenched QED beta-function at five loops, which was carried out with the help of the newly computed contributions to the DIS sum rules and the Crewther relation. (author)
Systematics of strength function sum rules
Johnson, Calvin W.
2015-11-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
Symmetry energy from QCD sum rules
International Nuclear Information System (INIS)
We review the recent attempts to calculate the nuclear symmetry energy from QCD sum rules. Calculating the difference between the proton and neutron correlation function in an isospin asymmetric nuclear matter within the QCD sum rule approach, the potential part of the nuclear symmetry energy can be expressed in terms of local operators. We find that the scalar (vector) self-energy part gives negative (positive) contribution to the nuclear symmetry energy, consistent with the results from relativistic mean-field theories. Moreover, the magnitudes are consistent with phenomenological estimates. In terms of the operators, we find that an important contribution to self-energies contributing to the symmetry energy comes from the twist-4 matrix elements, whose leading density dependence can be extracted from deep inelastic scattering experiments. Our result also extends an early success of the QCD sum rule method in understanding the symmetric nuclear matter in terms of QCD variables to the asymmetric nuclear matter case. (orig.)
Integrals of Lagrange functions and sum rules
Energy Technology Data Exchange (ETDEWEB)
Baye, Daniel, E-mail: dbaye@ulb.ac.be [Physique Quantique, CP 165/82, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium); Physique Nucleaire Theorique et Physique Mathematique, CP 229, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium)
2011-09-30
Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x{sup 2} as well as for the kinetic energy. From these expressions, new sum rules involving Laguerre and shifted Jacobi zeros and weights are derived. (paper)
Vacuum corrections to QCD charmonium sum rules
International Nuclear Information System (INIS)
A detailed description is presented of a new method for computing higher gluonic power corrections to QCD charmonium sum rules. The method is equivalent to using the Schwinger gauge condition (xsup(μ) - zsub(Q)sup(μ))Asub(μ)(x) = 0 for vacuum gluons. As an application of the method O(G2) and O(G3) corrections are calculated
Sum rule approach to nuclear vibrations
International Nuclear Information System (INIS)
Velocity field of various collective states is explored by using sum rules for the nuclear current. It is shown that an irrotational and incompressible flow model is applicable to giant resonance states. Structure of the hydrodynamical states is discussed according to Tomonaga's microscopic theory for collective motions. (author)
Nuclear symmetry energy from QCD sum rules
International Nuclear Information System (INIS)
We calculated the nucleon self-energies in iso-spin asymmetric nuclear matter and obtained the nuclear symmetry energy by taking difference of these of neutron and proton. We find that the scalar (vector) self-energy part gives a negative (positive) contribution to the nuclear symmetry energy, consistent with the result from relativistic mean-field theories. Also, we found exact four-quark operator product expansion for nucleon sum rule. Among them, twist-4 matrix elements which can be extracted from deep inelastic scattering experiment constitute an essential part in the origin of the nuclear symmetry energy from QCD. Our result also extends early success of QCD sum rule in the symmetric nuclear matter to the asymmetric nuclear matter. (authors)
SVZ sum rules : 30 + 1 years later
Narison, Stephan
2010-01-01
For this exceptional 25th anniversary of the QCD-Montpellier series of conferences initiated in 85 with the name "Non-perturbative methods", we take the opportunuity to celebrate the 30 + 1 years of the discovery of the SVZ (also called ITEP, QCD or QCD spectral) sum rules by M.A. Shifman, A.I. Vainshtein and V.I. Zakahrov in 79 [1]. In this talk, I have the duty to present the status of the method. I shall (can) not enumerate the vast area of successful applications of sum rules in hadron physics but I shall focus on the historical evolution of field and its new developments. More detailed related discussions and more complete references can be found in the textbooks [2,3].
Double charm states in QCD sum rules
International Nuclear Information System (INIS)
In this note we revisit and improve the calculation of the Tcc mass using the double ratio of QCD sum rules (QCDSR), assuming that this state is described by a molecular current. In a previous work we used a tetraquark current. We conclude that with both currents we arrive at nearly the same results for the Tcc mass, which turns out to be close to the mass of the X(3872).
QCD sum rules with finite masses
Meyer-Hermann, M.; Schäfer, A.; Greiner, W.
1995-01-01
The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.
Beautiful mesons from QCD spectral sum rules
Energy Technology Data Exchange (ETDEWEB)
Narison, S. (OPM, Univ. Montpellier 2, 34 (France))
1991-08-01
We discuss the beautiful meson from the point of view of the QCD spectral sum rules (QSSR). The bottom quark mass and the mixed light quark-gluon condensates are determined quite accurately. The decay constant f{sub B} is estimated and we present some arguments supporting this result. The decay constants and the masses of the other members of the beautiful meson family are predicted. (orig.).
Hybrid quarkonia from QCD sum rules
International Nuclear Information System (INIS)
We present calculations of the vacuum polarization functions in QCD induced by heavy-quark anti qqG currents with the quantum numbers Jsup(PC)=1+-, 0++, 1-+ and 0--. In the framework of QCD sum rules we investigate the possible resonance structure in these channels. We obtain definite predictions for the masses of resonances in the channels 0--, 0++ and 1+-, but not in the exotic 1-+ channel. The resulting mass values are unexpectedly high. (orig.)
A cluster version of the GGT sum rule
Hencken, K.; Baur, G.; Trautmann, D.
2004-01-01
We discuss the derivation of a "cluster sum rule" from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed. (C) 2004 Elsevier B.V. All rights reserved.
A cluster version of the GGT sum rule
International Nuclear Information System (INIS)
We discuss the derivation of a 'cluster sum rule' from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed
A cluster version of the GGT sum rule
Hencken, Kai; Baur, Gerhard; Trautmann, Dirk
2004-03-01
We discuss the derivation of a "cluster sum rule" from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed.
A cluster version of the GGT sum rule
Hencken, K; Trautmann, D; Hencken, Kai; Baur, Gerhard; Trautmann, Dirk
2004-01-01
We discuss the derivation of a ``cluster sum rule'' from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed.
Compton Scattering and Photo-absorption Sum Rules on Nuclei
Gorchtein, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2011-01-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new "constituent quark model" sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition we extract the $\\alpha=0$ pole contribution for both proton...
Light four-quark states and QCD sum rule
Institute of Scientific and Technical Information of China (English)
ZHANG Ai-Lin
2009-01-01
The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.
International Nuclear Information System (INIS)
Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken , the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the U(1) and SU(Nc) models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical O(α4) and O(αs2) conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed
The Bjorken sum rule with Monte Carlo and Neural Network techniques
International Nuclear Information System (INIS)
Determinations of structure functions and parton distribution functions have been recently obtained using Monte Carlo methods and neural networks as universal, unbiased interpolants for the unknown functional dependence. In this work the same methods are applied to obtain a parametrization of polarized Deep Inelastic Scattering (DIS) structure functions. The Monte Carlo approach provides a bias-free determination of the probability measure in the space of structure functions, while retaining all the information on experimental errors and correlations. In particular the error on the data is propagated into an error on the structure functions that has a clear statistical meaning. We present the application of this method to the parametrization from polarized DIS data of the photon asymmetries A1p and A1d from which we determine the structure functions g1p(x,Q2) and g1d(x,Q2), and discuss the possibility to extract physical parameters from these parametrizations. This work can be used as a starting point for the determination of polarized parton distributions.
Experimental study of isovector spin sum rules
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur; Peter Bosted; Volker Burkert; Donald Crabb; Kahanawita Dharmawardane; Gail Dodge; Tony Forest; Keith Griffioen; Sebastian Kuhn; Ralph Minehart; Yelena Prok
2008-02-04
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which is large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also extracted the isovector part of the generalized forward spin polarizability $\\gamma_{0}$. Although this quantity provides a robust test of Chiral Perturbation Theory, our data disagree with the calculations.
Sum rules for the gross theory of beta-decay
International Nuclear Information System (INIS)
This paper presents a method for relating the β-decay strength function with the nuclear force. This relation is obtained as sum rules for the one-particle strength function which appears in the gross theory of β-decay. They sum rules were calculated for the Gamow-Teller transition with some central potentials and the Hamada-Johnston potential. The sum-rule values were found to depend strongly on the assumed nuclear force
Coulomb sum rules in the relativistic Fermi gas model
International Nuclear Information System (INIS)
Coulomb sum rules are studied in the framework of the Fermi gas model. A distinction is made between mathematical and observable sum rules. Differences between non-relativistic and relativistic Fermi gas predictions are stressed. A method to deduce a Coulomb response function from the longitudinal response is proposed and tested numerically. This method is applied to the 40Ca data to obtain the experimental Coulomb sum rule as a function of momentum transfer
Tuning sum rules with window functions for optical constant evaluation
Rodríguez-de Marcos, Luis V.; Méndez, José A.; Larruquert, Juan I.
2016-07-01
Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.
QCD sum rules and applications to nuclear physics
International Nuclear Information System (INIS)
Applications of QCD sum-rule methods to the physics of nuclei are reviewed, with an emphasis on calculations of baryon self-energies in infinite nuclear matter. The sum-rule approach relates spectral properties of hadrons propagating in the finite-density medium, such as optical potentials for quasinucleons, to matrix elements of QCD composite operators (condensates). The vacuum formalism for QCD sum rules is generalized to finite density, and the strategy and implementation of the approach is discussed. Predictions for baryon self-energies are compared to those suggested by relativistic nuclear physics phenomenology. Sum rules for vector mesons in dense nuclear matter are also considered. (author)
Octet magnetic Moments and their sum rules in statistical model
Batra, M
2013-01-01
The statistical model is implemented to find the magnetic moments of all octet baryons. The well-known sum rules like GMO and CG sum rules has been checked in order to check the consistency of our approach. The small discrepancy between the results suggests the importance of breaking in SU(3) symmetry.
Sum rules and cutoff effects in Wilson lattice QCD
International Nuclear Information System (INIS)
We use the transfer matrix formalism to derive non-perturbative sum rules in Wilson's lattice QCD with Nf flavours of quarks. The discretization errors on these identities are treated in detail. As an application, it is shown how the sum rules can be exploited to give improved estimates of the continuum spectrum and static potential. (orig.)
Radiative Corrections to the Sum Rule of Lepton Flavor Mixing
Zhang, Jue
2016-01-01
The simple correlation among three lepton flavor mixing angles $(\\theta^{}_{12}, \\theta^{}_{13}, \\theta^{}_{23})$ and the leptonic Dirac CP-violating phase $\\delta$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the sum rule $\\theta^{}_{12} \\approx \\theta^{\
Supersymmetric magnetic moments sum rules and spontaneous supersymmetry breaking
International Nuclear Information System (INIS)
In supersymmetry the anomalous magnetic moment of particles belonging to the same supermultiplet is related by simple sum rules. We study the modification of these sum rules in the case of the spontaneously broken N=1 global supersymmetry. (author). 9 refs, 3 figs
Y(2175) state in the QCD sum rule
International Nuclear Information System (INIS)
We study the mass of the state Y(2175) of JPC=1-- in the QCD sum rule. We construct both the diquark-antidiquark currents (ss)(ss) and the meson-meson currents (ss)(ss). We find that there are two independent currents for both cases and derive the relations between them. The operator product expansion convergence of these two currents is sufficiently fast, which enables us to perform good sum rule analysis. Both the SVZ (Shifman-Vainshtein-Zakharov) sum rule and the finite energy sum rule lead to a mass around 2.3±0.4 GeV, which is consistent with the observed mass within the uncertainties of the present QCD sum rule. The coupling of the four-quark currents to lower lying states such as φ(1020) turns out to be rather small. We also discuss possible decay properties of Y(2175) if it is a tetraquark state.
Application of the Maximum Entropy Method to QCD sum rules
International Nuclear Information System (INIS)
A new method of analyzing QCD sum rules employing the Maximum Entropy Method, is introduced and is applied successfully to the rho meson, the nucleon and the charmonium at finite temperature. This method enables us to directly obtain the spectral function from the sum rules, without having to introduce any model assumption about its functional form. In the nucleon sum rule, we show that the Gaussian sum rule successfully reproduces the ground state. Dependences on the interpolating field operator are discussed. Finite temperature effects for the charmonium sum rule are incorporated by changes of various gluonic condensates, extracted from lattice QCD. As a result, we find that both J/ψ and ηc dissolve into the continuum already at temperatures around 1.0 ∼ 1.2 Tc.
Adler-Weisberger sum rule for WLWL→WLWL scattering
International Nuclear Information System (INIS)
We analyse the Adler-Weisberger sum rule for WLWL→WLWL scattering. We find that at some energy, the WLWL total cross section must be large to saturate the sum rule. Measurements at future colliders would be needed to check the sum rule and to obtain the decay rates Γ(H→WLWL, ZLZL) which would be modified by the existence of a P-wave vector meson resonance in the standard model with strongly interacting Higgs sector or in technicolour models. (orig.)
Valid QCD sum rules for vector mesons in nuclear matter
International Nuclear Information System (INIS)
QCD sum rules for vector mesons (ρ, ω, φ) in nuclear matter are re-examined with an emphasis on the reliability of various sum rules. Monitoring the continuum contribution and the convergence of the operator product expansion plays crucial role in determining the validity of a sum rule. The uncertainties arising from less than precise knowledge of the condensate values and other input parameters are analyzed via a Monte Carlo error analysis. Our analysis leaves no doubt that vector-meson masses decrease with increasing density. This resolves the current debate over the behavior of the vector-meson masses and the sum rules to be used in extracting vector meson properties in nuclear matter. We find a ratio of ρ-meson masses of mρ*/mρ = 0.78 ± 0.08 at nuclear matter saturation density. (author). 37 refs., 6 figs
Spectral asymmetries in nucleon sum rules at finite density
Furnstahl, R. J.
1993-01-01
Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.
Charm and bottom hadronic form factors with QCD sum rules
International Nuclear Information System (INIS)
We present a brief review of some calculations of form factors and coupling constants in vertices with charm and bottom mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to charm and bottom decays processes. We first make a summarize of the QCD sum rules method. We give special attention to the uncertainties of the method introducing by the intrinsic variation of the parameters. Finally we conclude.
Dispersion relations and sum rules for natural optical activity
International Nuclear Information System (INIS)
Dispersion relations and sum rules are derived for the complex rotatory power of an arbitrary linear (nonmagnetic) isotropic medium showing natural optical activity. Both previously known dispersion relations and sum rules as well as new ones are obtained. It is shown that the Rosenfeld-Condon dispersion formula is inconsistent with the expected asymptotic behavior at high frequencies. A new dispersion formula based on quantum eletro-dynamics removes this inconsistency; however, it still requires modification in the low-frequency limit. (Author)
QCD sum rules with two-point correlation function
Kim, H; Oka, M; Kim, Hungchong; Lee, Su Houng; Oka, Makoto
2000-01-01
We construct three different sum rules from the two-point correlation function with pion, $i\\int d^4x e^{iq\\cdot x} $, beyond the soft-pion limit. The PS and PV coupling schemes in the construction of the phenomenological side are carefully considered in each sum rule. We discuss the dependence of the result on the specific Dirac structure and identify the source of the dependence by making specific models for higher resonances.
GDH sum rule measurement at low Q2
International Nuclear Information System (INIS)
The Gerasimov-Drell-Hearn (GDH) sum rule is based on a general dispersive relation for the forward Compton scattering. Multipole analysis suggested the possible violation of the sum rule. Some propositions have been made to modify the original GDH expression. An effort is now being made in several laboratories to shred some light on this topic. The purposes of the different planned experiments are briefly presented according to their Q2 range
A critique of the angular momentum sum rules and a new angular momentum sum rule
Bakker, B L G; Trueman, T L
2004-01-01
We show that the expressions in the literature for the tensorial structure of the hadronic matrix elements of the angular momentum operators J are incorrect. Given this disagreement with the published results, we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent, based upon the rotational properties of the state vectors. Surprisingly it turns out that the results are very sensitive to the type of relativistic spin state used to describe the motion of the particle i.e. whether a canonical (i.e. boost) state or a helicity state is utilized. We present results for the matrix elements of the angular momentum operators, valid in an arbitrary Lorentz frame, both for helicity states and canonical states. These results are relevant for the construction of angular momentum sum rules, relating the angular momentum of a nucleon to the spin and orbital angular momentum of its constituents. Moreover, we show that it i...
The black hole interior and a curious sum rule
International Nuclear Information System (INIS)
We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics
Polarizability sum rule across real and virtual Compton scattering processes
Pascalutsa, Vladimir
2014-01-01
We derive a sum rule relating various electromagnetic properties of a spin-1/2 particle and consider its empirical implications for the proton. Given the measured values of the proton anomalous magnetic moment, electric and magnetic charge radii, the slope of the first moment of the spin structure function $g_1$, and the recently determined proton spin polarizability $\\gamma_{E1M2}$, the sum rule yields a constraint on the low-momentum behavior of a generalized polarizability appearing in virtual Compton scattering. With the help of the presently ongoing measurements of different electromagnetic observables at the MAMI, Jefferson Lab, and HI$\\gamma$S facilities, the sum rule will provide a model-independent test of the low-energy spin structure of the nucleon.
On the Predictivity of Neutrino Mass Sum Rules
Gehrlein, Julia; Spinrath, Martin
2016-01-01
Correlations between light neutrino observables are arguably the strongest predictions of lepton flavour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a non-zero value of the lightest neutrino mass and to distinct predictions for the effective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modification of the predictions derived from neutrin...
The lowest hidden charmed tetraquark state from QCD sum rules
Wang, Zhi-Gang
2015-01-01
In this article, we study the $S\\bar{S}$ type scalar tetraquark state $cq\\bar{c}\\bar{q}$ in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the value $M_{Z_c}=\\left(3.82^{+0.08}_{-0.08}\\right)\\,\\rm{GeV}$, which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants $G_{Z_c\\eta_c\\pi}$ and $G_{Z_cDD}$ with the three-point QCD sum rules, then study the strong decays $ Z_c\\to \\eta_c\\pi\\, ,\\, DD$, and observe that the total width $\\Gamma_{Z_c}\\approx 21\\,\\rm{MeV}$. The present predictions can be confronted with the experimental data in the futures at the BESIII, LHCb and Belle-II.
QCD sum rules form factors and wave functions
Radyushkin, A V
1997-01-01
The shape of hadronic distribution amplitudes (DAs) is a critical issue for the perturbative QCD of hard exclusive processes. Recent CLEO data on gamma gamma* -> pi^0 form factor clearly favor a pion DA close to the asymptotic form. We argue that QCD sum rules for the moments of the pion DA \\varphi_\\pi(x) are unreliable, so that the humpy shape of \\varphi_\\pi (x) obtained by Chernyak and Zhitnitsky is a result of model assumptions rather than an unambigous consequence of QCD sum rules. This conclusion is also supported by a direct QCD sum rule calculation of the gamma gamma* -> pi^0 form factor which gives a result very close to the CLEO data.
QCD Sum Rules at Finite Temperature: a Review
Ayala, Alejandro; Loewe, M
2016-01-01
The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
JPC=1++ heavy hybrid masses from QCD sum-rules
International Nuclear Information System (INIS)
QCD Laplace sum-rules are used to calculate axial vector (JPC=1++) charmonium and bottomonium hybrid masses. Previous sum-rule studies of axial vector heavy quark hybrids did not include the dimension-six gluon condensate, which has been shown to be important in the 1−− and 0−+ channels. An updated analysis of axial vector heavy quark hybrids is performed, including the effects of the dimension-six gluon condensate, yielding mass predictions of 5.13 GeV for hybrid charmonium and 11.32 GeV for hybrid bottomonium. The charmonium hybrid mass prediction disfavours a hybrid interpretation of the X(3872), if it has JPC=1++, in agreement with the findings of other theoretical approaches. It is noted that QCD sum-rule results for the 1−−, 0−+ and 1++ channels are in qualitative agreement with the charmonium hybrid multiplet structure observed in recent lattice calculations
Broadening of dielectric response and sum rule conservation
International Nuclear Information System (INIS)
Different types of broadening of the dielectric response are studied with respect to the preservation of the Thomas–Reiche–Kuhn sum rule. It is found that only the broadening of the dielectric function and transition strength function conserve this sum rule, whereas the broadening of the transition probability function (joint density of states) increases or decreases the sum. The effect of different kinds of broadening is demonstrated for interband and intraband direct electronic transitions using simplified rectangular models. It is shown that the broadening of the dielectric function is more suitable for interband transitions while broadening of the transition strength function is more suitable for intraband transitions. - Highlights: • Preservation of the sum rule by different types of dielectric response broadening • Only broadening of dielectric function and transition strength function preserves it. • Broadening of joint density of states does not preserve the sum rule. • Broadening of dielectric function is better for direct interband transitions. • Broadening of transition strength is better for indirect interband transitions
Application of the maximum entropy method to QCD sum rules
International Nuclear Information System (INIS)
QCD sum rules have long been used to describe the physical properties of hadrons directly from QCD. While this approach was often quite successful, it also has its limitations, the most important one being the need to introduce some specific ansatz for parametrizing the spectral function. For allowing a more general analysis of the sum rules, a new analysis method based on the maximum entropy method has been introduced [1], and has in the meantime been applied to several channels in various environments. In these proceedings, we will discuss some recent results, which have been obtained with the help of this novel approach
Penta-quark baryon from the QCD Sum Rule
Sugiyama, J; Oka, M; Sugiyama, Jun; Doi, Takumi; Oka, Makoto
2004-01-01
Exotic penta-quark baryon with strangeness +1, \\Theta^+, is studied in the QCD sum rule approach. We derive sum rules for the positive and negative parity baryon states with J=1/2 and I=0. It is found that the standard values of the QCD condensates predict a negative parity \\Theta^+ of mass \\simeq 1.5 GeV, while no positive parity state is found. We stress the roles of chiral-odd condensates in determining the parity and mass of \\Theta^+.
QCD sum rules and properties of baryons in nuclei
International Nuclear Information System (INIS)
The use of medium-energy experiments to constrain in-medium four-quark condensates, whose uncertainty is currently the most important problem inhibiting the use of QCD sum rules to study hadrons in nuclear matter, is discussed. A value for a particular linear combination of these condensates is extracted using results of an Isobar-Doorway model analysis of pion-nucleus scattering data and a QCD sum rule analysis of the mass of the Δ(1232) in nuclei. Extending the analysis to include higher-lying baryon resonances is possible with data from modem facilities
Photodisintegration sum rule and electron distribution in metal clusters
International Nuclear Information System (INIS)
The inverse energy-weighted photodisintegration sum rule is investigated. This quantity can be reliably extracted from experimental measurements of the cluster photoabsorption cross section σ(ω), which is shown to reflect the strongly correlated character of the motion of valence electrons. A model-independent relation between σ-1 and the amplitude of the zero-point motion in the dipole mode is derived. Theoretical results for the sum rule are discussed and compared with experimental data. An expression for the mean distance between two electrons in a cluster is derived. (author) 12 refs.; 1 tab
Photodisintegration sum rule and electron distribution in metal clusters
International Nuclear Information System (INIS)
The inverse energy-weighted photodisintegration sum rule σ-1=∫[σ(ω)/ω]dω is investigated. This quantity can be reliably extracted from experimental measurements of the cluster photoabsorption cross section σ(ω), and is shown to reflect the strongly correlated character of the motion of valence electrons. A model-independent relation between σ-1 and the amplitude of the zero-point motion in the dipole mode is derived. Theoretical results for the sum rule are discussed and compared with experimental data. An expression for the mean distance between two electrons in a cluster is derived
Nucleon QCD sum rules in the instanton medium
International Nuclear Information System (INIS)
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is ws ≈ 2/3
Adler-Weisberger sum rule and hadronic models
International Nuclear Information System (INIS)
In order to understand the low value that several hadronic models predict for g/sub A/, we investigate the Δ contribution to the Adler-Weisberger sum rule in the MIT bag model and in the Skyrme model. It is shown that because of recoil corrections this value decreases 15% from (5/3) in the for- mer, and that it is very small in the latter because of the depressed prediction for g/sub π//sub N//sub Δ/. The meaning of the sum rule in the context of large-N/sub c/ models is also discussed
V-A sum rules with D=10 operators
Zyablyuk, K N
2004-01-01
The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of factorization hypothesis. It is compared to the result, obtained from operator fit of Borel sum rules in the complex q^2-plane, calculated from experimental data on hadronic tau-decays. This fit gives accurate values of the light quark condensate and quark-gluon mixed condensate. The size of the high-order operators and the convergence of operator series are discussed.
Temperature antipairing effect over the energy weighted sum rule
International Nuclear Information System (INIS)
We study the temperature dependence of the sum rules using the discontinuity of the first derivative of the Matsubara Green's functions of a bilinear particle-hole operator. Particularly we study the behavior of the dipole particle-hole operator. We applied the calculation to 114Sn, 138Ba, 154Gd and 170Yb. It is found that the energy weighted sum rule for the dipole operator changes as a function of the temperature depending on the square of the gap. This fact is related to the antipairing effect of the temperature over the nuclear system
QCD sum rule studies at finite density and temperature
Energy Technology Data Exchange (ETDEWEB)
Kwon, Youngshin
2010-01-21
In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)
Beauty vector meson decay constants from QCD sum rules
International Nuclear Information System (INIS)
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity
Renormalisation Group Corrections to Neutrino Mixing Sum Rules
Gehrlein, J; Spinrath, M; Titov, A V
2016-01-01
Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\\tilde{U}_{\
Unitary symmetry pattern of the QCD sum rules
International Nuclear Information System (INIS)
Relations between magnetic moments of Σ0 and Λ baryons are discussed. Physical meaning of the F- and D- couplings in SU(3) is established. The obtained results are generalized to the QCD sum rules which yield unitary pattern with the characteristic F and D structures.
QCD Sum Rule External Field Approach and Vacuum Susceptibilities
Institute of Scientific and Technical Information of China (English)
ZONG Hong-Shi; PING Jia-Lun; CHANG Chao-His; WANG Fan; ZHAO En-Guang
2002-01-01
Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuumsusceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shownthat the above two approaches of determination of the vector vacuum susceptibility may lead to different results. Thereason of this contradiction is discussed.
Decay Constants of Beauty Mesons from QCD Sum Rules
Lucha, Wolfgang; Simula, Silvano
2014-01-01
Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the $\\overline{\\rm MS}$ scheme $\\overline{m}_b(\\overline{m}_b)\\approx4.18\\;\\mbox{GeV},$ the sum-rule result $f_B\\approx210$-$220\\;\\mbox{MeV}$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\\approx190\\;\\mbox{MeV}.$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: $\\overline{m}_b(\\overline{m}_b)=4.247\\;\\mbox{GeV}.$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$ and $f_{D_s^*}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the specific scale s...
Beauty Vector Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Decay Constants of Beauty Mesons from QCD Sum Rules
Directory of Open Access Journals (Sweden)
Lucha Wolfgang
2014-01-01
Full Text Available Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b ≈ 4:18 GeV; the sum-rule result fB ≈ 210–220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b = 4:247 GeV: (ii Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty vector meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Beauty vector meson decay constants from QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Lucha, Wolfgang [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Melikhov, Dmitri [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991, Moscow (Russian Federation); Simula, Silvano [Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146, Roma (Italy)
2016-01-22
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Octet baryon magnetic moments in light cone QCD sum rules
Aliev, T M; Özpineci, A
2002-01-01
Octet baryon magnetic moments are calculated in framework of the light cone QCD sum rules. The analysis is carried for the general form of the interpolating currents for octet baryons. A comparison of our results on the magnetic moments of octet baryons with the predictions of other approaches and experimental data is presented.
QCD sum rule studies at finite density and temperature
International Nuclear Information System (INIS)
In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)
Helicity Amplitudes and Sum Rules for Real and Virtual Photons
Tiator, Lothar
2000-01-01
Results of the recently developed unitary isobar model (MAID) are presented for helicity amplitudes, spin asymmetries, structure functions and relevant sum rules for real and virtual photons in the resonance region. Our evaluation of the energy-weighted integrals is in good agreement for the proton but shows big discrepancies for the neutron.
Spectral sum rules for confining large- N theories
Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2016-06-01
We consider asymptotically-free four-dimensional large- N gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large- N confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ-1. Our results motivate us to conjecture some universal spectral sum rules for these large N gauge theories.
Spectral sum rules for confining large-N theories
Cherman, Aleksey; Yamazaki, Masahito
2015-01-01
We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale $\\Lambda^{-1}$. Our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.
Improved light quark masses from pseudoscalar sum rules
International Nuclear Information System (INIS)
Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300) and K(1460) decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI) quark masses (m^u+m^q):q≡d,s and the corresponding running masses (m¯u+m¯q) evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md) and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3) and K(1.46) hadronic widths and/or decay constants which are the dominant sources of errors in the analysis
Improved light quark masses from pseudoscalar sum rules
Directory of Open Access Journals (Sweden)
Stephan Narison
2014-11-01
Full Text Available Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300 and K(1460 decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI quark masses (mˆu+mˆq:q≡d,s and the corresponding running masses (m¯u+m¯q evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3 and K(1.46 hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.
Ds(0±) Meson Spectroscopy in Gaussian Sum Rules
Institute of Scientific and Technical Information of China (English)
WEN Shui-Guo; LIU Jue-Ping
2009-01-01
Masses of the Ds(0±) mesons are investigated from a view-point of ordinary light-heavy system in the framework of the Gaussian sum rules, which are worked out by means of the Laplacian transformation to the usual Borel sum rules. Using the standard input of QCD non-perturbative parameters, the corresponding mass spectra and couplings of the currents to the Ds(0±) mesons are obtained. Our results are mDs(O-) = 1.968±0.016±0.003 GeV and mDs(0+) = 2.320±0.014v0.003 GeV, which are in good accordance with the experimental data, 1.969 GeV and 2.317 GeV.
Bottom Mass from Nonrelativistic Sum Rules at NNLL
Stahlhofen, Maximilian
2013-01-01
We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) Upsilon sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M_b^{1S}=4.755 +- 0.057(pert) +- 0.009(alpha_s) +- 0.003(exp) GeV for the bottom 1S mass and m_b(m_b)= 4.235 +- 0.055(pert) +- 0.003(exp) GeV for the bottom MSbar mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.
Comparison between two strictly local QCD sum rules
International Nuclear Information System (INIS)
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex q2 plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic (g-2) factor of the muon. Their effectiveness is demonstrated in the calculation of the topological susceptibility where both methods lead to χt1/4=171±4 MeV
Improved sum rules for light mesons and thermal hadronic threshold
International Nuclear Information System (INIS)
The thermal properties of light vector and scalar mesons are investigated in the framework of QCD sum rules. The phenomenological side of the correlation function can be calculated using either the quark-hadron duality approach or in terms of two-pion continuum contributions. In the quark-hadron duality approach, a free parameter (hadronic threshold) arises in the phenomenological part and it is necessary to know the temperature dependence of the hadronic threshold. A comparison of above mentioned approaches gives us additional information about the temperature dependence of the hadronic threshold. Taking into account the thermal spectral density and additional operators appearing at finite temperature the thermal QCD sum rules are improved. The decay constants of ρ and σ mesons are calculated and our investigations show that the above mentioned methods give us the same results.
Gottfried sum rule and the ratio Fn2/Fp2
Arash, Firooz
1995-07-01
We describe the nucleon as a bound state of three constituent objects, called ``valons,'' which themselves have structure. At high enough Q2 it is the valon structure, governed by QCD, which is probed and, thus, the nucleon structure is described in terms of its partonic distributions, while at low Q2 the nucleon is described in terms of its valon distributions, independent of a probe and controlled by nonperturbative QCD. The implications of this phenomenological model, then, are applied to the New Muon Collaboration (NMC) data for Fn2/Fp2 and on the Gottfried sum rule. It is shown that the model successfully reproduces the experimental value of the Gottfried sum rule SG[0=4 GeV2]=0.243, consistent with the experimental results as well as the ratio Fn2/Fp2 down to the lowest x value.
SVZ sum rules: 30+1 years later
International Nuclear Information System (INIS)
For this exceptional 25th anniversary of the QCD-Montpellier series of conferences initiated in 85 with the name 'Non-perturbative methods', we take the opportunuity to celebrate the 30+1 years of the discovery of the SVZ (also called ITEP, QCD or QCD spectral) sum rules by M.A. Shifman, A.I. Vainshtein and V.I. Zakahrov in 79 [M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B 147 (1979) 385, 448]. In this talk, I have the duty to present the status of the method. I shall (can) not enumerate the vast area of successful applications of sum rules in hadron physics but I shall focus on the historical evolution of field and its new developments.
Parton model (Moessbauer) sum rules for b → c decays
International Nuclear Information System (INIS)
The parton model is a starting point or zero-order approximation in many treatments. The author follows an approach previously used for the Moessbauer effect and shows how parton model sum rules derived for certain moments of the lepton energy spectrum in b → c semileptonic decays remain valid even when binding effects are included. The parton model appears as a open-quote semiclassical close-quote model whose results for certain averages also hold (correspondence principle) in quantum mechanics. Algebraic techniques developed for the Moessbauer effect exploit simple features of the commutator between the weak current operator and the bound state Hamiltonian to find the appropriate sum rules and show the validity of the parton model in the classical limit, ℎ → 0, where all commutators vanish
A set of sum rules for anomalous gauge boson couplings
Papavassiliou, J; Papavassiliou, Joannis; Philippides, Kostas
1999-01-01
The dependence of the differential cross-section for on-shell W-pair production on the anomalous trilinear gauge couplings invariant under C and P is examined. It is shown that the contributions of the anomalous magnetic moments of the W boson due to the photon and the Z can be individually projected out by means of two appropriately constructed polynomials. The remaining four anomalous couplings are shown to satisfy a set of model-independent sum rules. Specific models which predict special relations among the anomalous couplings are then studied; in particular, the composite model of Brodsky and Hiller, and the linear and non-linear effective Lagrangian approaches. The relations predicted by these models, when combined with the aforementioned sum rules, give rise to definite predictions, particular to each model. These predictions can be used, at least in principle, in order to exclude or constrain such models.
Sum rule limitations of kinetic particle-production models
International Nuclear Information System (INIS)
Photoproduction and absorption sum rules generalized to systems at finite temperature provide a stringent check on the validity of kinetic models for the production of hard photons in intermediate energy nuclear collisions. We inspect such models for the case of nuclear matter at finite temperature employed in a kinetic regime which copes those encountered in energetic nuclear collisions, and find photon production rates which significantly exceed the limits imposed by the sum rule even under favourable concession. This suggests that coherence effects are quite important and the production of photons cannot be considered as an incoherent addition of individual NNγ production processes. The deficiencies of present kinetic models may also apply for the production of probes such as the pion which do not couple perturbatively to the nuclear currents. (orig.)
On the loop approximation in nucleon QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Drukarev, E. G., E-mail: drukarev@thd.pnpi.spb.ru; Ryskin, M. G.; Sadovnikova, V. A. [National Research Center “Kurchatov Institute”, B. P. Konstantinov Petersburg Nuclear Physics Institute (Russian Federation)
2015-10-15
There was a general belief that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d = 3 and d = 4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.
Model independent sum rules for B-> pi K decays
Matias, Joaquim
2001-01-01
We provide a set of sum rules relating CP-averaged branching ratios and CP-asymmetries of the $B \\to \\pi K$ modes. They prove to be useful as a mechanism to `test' experimental data given our expectations of the size of isospin breaking. A set of observables emerges providing a simpler interpretation of data in terms of isospin breaking. Moreover, the derivation is done in a completely model independent way, i.e., they can accommodate also New Physics contributions.
Applications of progenitor sum rules in nuclear theory
International Nuclear Information System (INIS)
The energy-weighted sum rules, obtained by taking matrix elements of double commutators with the nuclear Hamiltonian of appropriately defined densities, are didactically reviewed. Following a catalogue of applications such sum rules have found in theoretical nuclear physics, the progenitor sum rules (PSR's) are derived using standard commutator relations for second-quantized nucleon field operators. This leads to the extension of PSR's to coupled Fermi-Bose systems, and in particular, to a simple model of interacting mesons and nucleons. The effects of interactions are also discussed from the point of view of (static) exchange potentials. The relation of the dipole sum rule to nuclear photoabsorption is reviewed briefly. The application of PSR's to the calculation of longitudinal inelastic form factors, and the use of the 'doorway hypothesis' is discussed in detail, together with the semiclassical collective-oscillation interpretation of these results proposed by Bertsch. Suzuki's very interesting applications of PSR to the evaluation of collective mass parameters, coupling constants, and polarization functions of the Bohr-Mottelson self-consistent mean-field theory are also given a detailed treatment. Certain miscellaneous applications of PSR to calculation of Coulombic isospin mixing, to energy shifts in isospin multiplets, and to induced moments and effective charges are collected and discussed in a unified manner. The review concludes with a discussion of the qualitative character of the nuclear photoabsorption strength below the meson production threshold, especially with regard to the question of to what extent the (γ, NN) reaction is sensitive to pair correlations in the nuclear ground state. (Auth.)
Sum rules for the polarization correlations in photoionization and bremsstrahlung
Pratt, R. H.; Müller, R. A.; Surzhykov, A.
2016-05-01
The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters Ci j. We show that the squares of these parameters are connected by simple "sum rules." These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of K -, LI ,I I-, and MI ,I I-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into s1 /2 or p1 /2 states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all Ci j are available for experimental observation.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.
Cloët, Ian C; Bentz, Wolfgang; Thomas, Anthony W
2016-01-22
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei. PMID:26849589
Evaluating chiral symmetry restoration through the use of sum rules
Directory of Open Access Journals (Sweden)
Rapp Ralf
2012-11-01
Full Text Available We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector/axial-vector channel. We first present an update on obtaining quantitative results for pertinent vacuum spectral functions. These serve as a basis upon which the in-medium spectral functions can be constructed. A novel feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels.We also analyze the QCD sum rule for the finite temperature vector spectral function, based on a ρ spectral function tested in dilepton data which develops a shoulder at low energies.We find that the ρ′ peak flattens off which may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.
Energy Technology Data Exchange (ETDEWEB)
Kominis, Ioannis
2001-01-31
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized 3He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q2 = 0 and to the Bjorken sum rule at Q2 >> 1 GeV2. By studying the Q2 evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized 3He target with both longitudinal and transverse target orientations. The high density 3He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision 3He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV2< Q2 <1 GcV2 and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the 3He spin structure functions He and g1e Finally, we determine the extended GDH sum for the range 0.1 GeV2< Q2 <1 GeV2 for 3He and the neutron.
Proton Spin Sum Rule from Large Momentum Effective Field Theory
International Nuclear Information System (INIS)
In high energy scattering experiments, the proton spin is understood as the sum of the spin and orbital angular momentum of the quarks and gluons in Feynman’s parton picture. The Jaffe–Manohar form of the proton spin sum rule is justified as physical, and it is shown that the individual terms can be related to the proton matrix elements of certain quasi-observables through a large momentum effective field theory. The relation is expressed as a factorization formula where the leading contribution to the quasi-observable is factorized into the parton observables and perturbative matching coefficients, and we present the results for the latter at one-loop order in perturbation theory. This will provide us with the basis to extract the proton spin content from the lattice QCD calculations of the quasi-observables. (author)
Isoscalar quadratic energy weighted sum rules and quadrupole moment of giant quadrupole resonance
International Nuclear Information System (INIS)
Isoscalar sum rules homogeneous quadratic in energy weighting are derived for the electric multipole operators. Except for scaling factors the sum rule values for the pure quadrupole and monopole transitions are the same as that for the corresponding linear energy weighted sum rules. Through these sum rules the electric quadrupole moment of giant quadrupole resonance is found to be -2.7 Asup(1/3) efm2. (author)
Justifying the naive partonic sum rule for proton spin
International Nuclear Information System (INIS)
We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy
Justifying the naive partonic sum rule for proton spin
Directory of Open Access Journals (Sweden)
Xiangdong Ji
2015-04-01
Full Text Available We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy.
Justifying the naive partonic sum rule for proton spin
Energy Technology Data Exchange (ETDEWEB)
Ji, Xiangdong [INPAC, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China); Center for High-Energy Physics, Peking University, Beijing, 100080 (China); Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742 (United States); Zhang, Jian-Hui [INPAC, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China); Zhao, Yong, E-mail: yongzhao@umd.edu [Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742 (United States)
2015-04-09
We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy.
Light-cone sum rule approach for Baryon form factors
Offen, Nils
2016-01-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
$\\pi K$ sum rules and the SU(3) chiral expansion
Ananthanarayan, B.; Büttiker, P.; Moussallam, B.
2001-01-01
A recently proposed set of sum rules, based on the pion-Kaon scattering amplitudes and their crossing-symmetric conjugates are analysed in detail. A key role is played by the $l=0$ $\\pi\\pi\\to K\\overline K$ amplitude which requires an extrapolation to be performed. It is shown how this is tightly constrained from analyticity, chiral counting and the available experimental data, and its stability is tested. A re-evaluation of the $O(p^4)$ chiral couplings $L_1$, $L_2$, $L_3$ is obtained, as wel...
GKNΛ and gKNΣ from QCD sum rules
International Nuclear Information System (INIS)
GKNΛ and gKNΣ are calculated using a QCD sum rule motivated method used by Reinders, Rubinstein, and Yazaki to extract hadron couplings to Goldstone bosons. The SU(3) symmetry breaking effects are taken into account by including the contributions from the strange quark mass and assuming different values for the strange and the up-down quark condensates. We find gKNΛ/√4π=-1.96 and gKNΣ/√4π=0.33. copyright 1996 The American Physical Society
QCD sum rules for $\\Delta$ isobar in nuclear matter
Jin, Xuemin
1994-01-01
The self-energies of $\\Delta$ isobar propagating in nuclear matter are calculated using the finite-density QCD sum-rule methods. The calculations show that the Lorentz vector self-energy for the $\\Delta$ is significantly smaller than the nucleon vector self-energy. The magnitude of the $\\Delta$ scalar self-energy is larger than the corresponding value for the nucleon, which suggests a strong attractive net self-energy for the $\\Delta$; however, the prediction for the scalar self-energy is ver...
Kataev, A L
2013-01-01
Conformal symmetry based relations between the concrete perturbative QED and QCD approximations of the polarized Bjorken, the Ellis-Jaffe, the Gross-Llewellyn Smith sum rules and of the Adler functions of the axial vector and vector channels are derived. They are based on application of the operator product expansion to three triangle AVV Green functions, constructed from the non-singlet axial vector-vector-vector currents, the {\\it singlet} axial-vector and two {\\it non-singlet} vector currents and the {\\it non-singlet} axial-vector-vector and {\\it singlet} vector currents, in the limit when the conformal symmetry of gauge models with fermions is unbroken. We specify the conditions when the conformal symmetry is valid in the U(1) and $SU(N_c)$ models. The identity between perturbative approximations of the Bjorken, Ellis-Jaffe and the Gross-Llewellyn Smith sum rules, which follow from this theoretical limit, is proved. The expressions for the $O(\\alpha^4)$ and $O(\\alpha_s^3)$ conformal symmetry based contrib...
Bottom mass from nonrelativistic sum rules at NNLL
Energy Technology Data Exchange (ETDEWEB)
Stahlhofen, Maximilian
2013-01-15
We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) {Upsilon} sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI computed in the vNRQCD framework leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M{sub b}{sup 1S}=4.755{+-}0.057{sub pert}{+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.
Borel sum rules for octet baryons in nuclear medium
International Nuclear Information System (INIS)
Borel sum rules are examined for octet baryons in the nuclear medium. First, it is noticed that in the medium the dispersion relation is realized for the retarded correlation ΠR(ω, q2) in the energy ω. Then, ΠR(ω, q2) is split into even and odd parts of ω in order to apply the Borel transformation. The obtained Borel sum rules differ from those of previous works. The mass shifts of octet baryons are calculated in the leading order of the operator product expansion with linear density approximation for the condensates. It is found that both scalar and vector condensates of the quark field, and +q>, induce attraction to the octet baryons in the medium in contrast to the results of previous works. It is also found that |δMN| > |δMΛ| > |δMΣ| ∼ |δMΞ|. The absolute values, however, turn out to be one order of magnitude larger than those empirically known if a Borel mass of around 1 GeV is used in the present approximation. (author)
Evaluating chiral symmetry restoration through the use of sum rules
Hohler, Paul M
2012-01-01
We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector and axial-vector channels. We first present an update on constructing quantitative results for pertinent vacuum spectral functions. These spectral functions serve as a basis upon which the in-medium spectral functions can be constructed. A striking feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels. Preliminary results for the finite temperature vector spectral function are presented. Based on a rho spectral function tested in dilepton data which develops a shoulder at low energies, we find that the rho' peak flattens off. The flattening may be a sign of chiral restoration, though a study of the finite temperature axial-vector ...
Connections between chiral Lagrangians and QCD sum-rules
Fariborz, Amir H.; Pokraka, A.; Steele, T. G.
2016-01-01
In this paper, it is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g. quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet a0(980)-a0(1450) system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors lead to a remarkable agreement between the quark condensates in QCD and the mesonic vacuum expectation values that induce spontaneous chiral symmetry breaking in chiral Lagrangians. This concrete example shows a clear sensitivity to the underlying a0-system mixing angle, illustrating the value of this methodology in extensions to more complicated mesonic systems.
Connections between chiral Lagrangians and QCD sum-rules
Fariborz, Amir H; Steele, T G
2016-01-01
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet $a_0(980)$-$a_0(1450)$ system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors ...
Holographic RG flows, entanglement entropy and the sum rule
Casini, Horacio; Torroba, Gonzalo
2015-01-01
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and in d>2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.
Holographic RG flows, entanglement entropy and the sum rule
Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
2016-03-01
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.
On properties of the exotic hadrons from QCD sum rules
Lucha, Wolfgang
2016-01-01
We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order correlation functions provide the bulk of the hadron observable, e.g., of the form factor; inclusion of radiative corrections modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its width, we show that the disconnected leading-order diagrams are not related to the tetraquark properties. For a proper description of the tetraquark decay width, it is mandatory to calculate specific radiative corrections which generate the connected diagrams.
QCD Sum Rule Studies of Heavy Quarkonium-like States
Kleiv, Robin
2014-01-01
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the $Y(3940)$, $X(3872)$, $Z_c^\\pm\\left(3895\\right)$, $Y_b\\left(10890\\right)$, $Z_b^{\\pm}(10610)$ and $Z_b^{\\pm}(10650)$ particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.
QCD Sum Rules for the λb semileptonic decay
International Nuclear Information System (INIS)
We use the QCD Sum Rule approach to evaluate the form factors and decay rates of Λb → Λc+ + l + ν-barl decay. This decay is represented by a three point function of the weak transition current and the interpolating fields of Λb and Λc. We calculate the theoretical part by performing the Operator Product Expansion of this three point function. In the phenomenological side, we use the experimental information of the decay amplitude. As usual we perform a Borel transform in these two sides in order to obtain the form factors. With this information we can obtain the decay rates. After the calculation of these quantities we compare our results with the experimental ones. (author)
Optical sum rule anomalies in high-temperature superconductors
International Nuclear Information System (INIS)
Many unusual features recently observed in the optical spectroscopy experiments in the cuprates can be simply understood as arising from the vicinity to the Mott transition, without invoking more involved and exotic mechanisms. Specifically, we compare calculations based on the Dynamical Mean Field Theory (DMFT) of the Hubbard model with the optical spectral weight Wopt of different cuprates, explaining most of the anomalies found in the optical sum rules with respect to normal metals, including the existence of two different energy scales for the doping- and the T-dependence of Wopt. A further support to this result is provided by the analysis of the optical conductivity in a typical case of the Mott-Hubbard metal-insulator transition, namely the V2O3.
Calculation of the kaon B parameter using strictly local sum rules
International Nuclear Information System (INIS)
The kaon B-parameter is computed in the framework of strictly local QCD sum rules for a three-poin function involving pseudoscalar currents. As an application of these sum rules we derive a low energy formula for the B-parameter. We show that strictly local QCD sum rules yield more reliable results than other QCD sum rules, since they need less phenomenological information and do not suffer from stability problems. Our result for the B-parameter is B=0.74±0.17. (orig.)
Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
Adler, Stephen L
2007-01-01
We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell.
Relations between the QCD sum rules for BBV couplings and vector-dominance model
International Nuclear Information System (INIS)
Story of QCD sum rules is briefly reviewed. The dispersion superconvergence sum rule is shown to relate πN coupling constant with the 33-resonance width without unitary symmetry arguments. The QCD sum rules instead reveal the unitary symmetry pattern as all the correlation functions can be reduced to 2 ones repeating the F and D couplings for the octet baryons 1/2+. Strong relations between the correlators are established. Vector dominance hypothesis allows to put new restrictions to the QCD sum rules for VBB couplings
Analysis of the heavy tensor meson's strong decay with QCD sum rules
Li, Zhen-Yu; Yu, Guo-Liang
2015-01-01
In this article, the tensor-vector-pseudoscalar type of vertex is analyzed with the QCD sum rules and the local-QCD sum rules. Correspondingly, the hadronic coupling constants of D2*(2460), Ds2*(2573), B2*(5747) and Bs2*(5840), and their decay widths are calculated. The results indicate that the QCD sum rules and the local-QCD sum rules give the consistent descriptions. Finally, the full widths of these 4 tensor mesons are discussed in detail.
QCD sum rule study of hidden-charm pentaquarks
Chen, Hua-Xing; Chen, Wei; Steele, T G; Liu, Xiang; Zhu, Shi-Lin
2016-01-01
We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\\over2},{3\\over2},{5\\over2}$ and quark contents $uud c \\bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. We also find the lowest-lying hidden-charm $J^P = 1/2^-$ pentaquark state of mass $4.33^{+0.17}_{-0.13}$ GeV, while the $J^P = 1/2^+$ mass prediction of 4.7--4.9 GeV is significantly higher. Similarly, the lowest-lying hidden-charm $J^P = 3/2^-$ pentaquark state mass is $4.37^{+0.18}_{-0.13}$ GeV, consistent with the $J^P = 3/2^-$ $P_c(4380)$, while the $J^P = 3/2^+$ is also significantly higher with a mass above 4.6 GeV. The hidden-charm $J^P = 5/2^-$ pentaquark state mass is 4.5--4.6 GeV, slightly larger than the $J^P = 5/2^+$ $P_c(4450)$.
The energy-weighted sum rule and the nuclear radius
Schröder, Hans Peter
2015-09-01
The energy-weighted integrated cross-section for photon absorption --known as sum rule -- is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at . Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections and the uncorrelated function as a ratio it shows that tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)).
The energy-weighted sum rule and the nuclear radius
Energy Technology Data Exchange (ETDEWEB)
Schroeder, Hans Peter [Aleph-Consulting GmbH Verlag, Wiesbaden (Germany)
2015-09-15
The energy-weighted integrated cross-section for photon absorption -known as sum rule σ{sub -1} - is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at σ{sub -1}. Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated σ{sub -1} and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of σ{sub -1} differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections g(A) and the uncorrelated function f(A) as a ratio it shows that g(A)/f(A) tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)). (orig.)
Vacuum corrections to QCD sum rules for charmonium
International Nuclear Information System (INIS)
Results are presented of calculating power corrections to QCD sum rules for charmonium in channels from Jsup(PC)=0++, 0-+, 1--, 1++ up to O(G4) term including. Using available QCD-vacuum models for the estimation of higher vacuum averages (VA), series over 1/msub(c)sup(2) which have slow convergence in the range of n-values, where the contribution from the lower state dominates, are obtained for the ratios rsub(n)=Mn/Mnsub(-1) of Mn momenta in the vector and pseudoscalar channels. To obtain the plato of the rsub(n) function stable relative to the following power corrections it is evidently necessary to take into account the following contributions, at least O(G5) and O(G6). However, it is not excluded that the existing instanton models present a distorted picture of QCD-vacuum. It is quite possible that in reality the VA values are correlated in such a way that the account of every next power correction provides agreement between theory and experiment in a still wider range of n. In this case, the mechanism of a considerable suppression of higher VA must exist which is not embraced by instanton model This renders the prblm of model-free estimates of the higher VA value most urgent, in particular, the problem of calculating VA values of the G4-type in the framework QCD lattice approximations
On the Friedel sum rule in ab initio calculations of optical properties
Knyazev, D. V.; Levashov, P. R.
2013-01-01
We investigate the influence of technical parameters in dynamic electrical conductivity calculations by the Kubo-Greenwood formula on the value of the so-called sum rule. We propose a possible explanation of the slight overestimation of the sum rule in most of our results.
Two-point correlation function with pion in QCD sum rules
Kim, H; Oka, M; Kim, Hungchong; Lee, Su Houng; Oka, Makoto
1999-01-01
Within the framework of the conventional QCD sum rules, we study the pion two-point correlation function, $i\\int d^4x e^{iq\\cdot x} $, beyond the soft-pion limit. We construct sum rules from the three distinct Dirac structures, $i \\gamma_5\
The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths
DEFF Research Database (Denmark)
Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens; Sauer, Stephan P. A.
1999-01-01
Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase...
Sum rules for four-spinon exact dynamic structure function in antiferromagnetic XXX model
International Nuclear Information System (INIS)
In this work, we continue the description of the exact four-spinon dynamic structure factor S4in the antiferromagnetic Heisenberg spin chain started in a previous work. We compute for S4a number of sum rules the total dynamic structure factor S is known to satisfy exactly. The sum rules for S2 have been evaluated in the literature. We want to know by how much the sum rules for S2 + S4 correct that of S the total dynamic structure function. The sum rules we consider are those related to the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that for each sum rule, S4 corrects only by a small amount the contribution from the two-spinon dynamic structure factor S2. (author)
Exact vector channel sum rules at finite temperature and their applications to lattice QCD
Gubler, Philipp
2016-01-01
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: We propose an ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity $\\sigma$ and the second order transport coefficient $\\tau_J$.
B-decay form factors from QCD sum rules
International Nuclear Information System (INIS)
In the Standard Model of particle physics there is only one source of CP-violation. Namely, a single complex phase in the unitary 3 x 3 CKM-Matrix governing flavor transitions in the weak interaction. The unitarity is usually visualized by a triangle in the complex ρ - η-plane. Therefore testing this framework comes down to measuring weak decays, relating observables to sides and angles of this so called Unitarity Triangle(UT). Particular interest in this respect is payed to decays of mesons containing a heavy b-quark, giving the opportunity to alone determine all parameters of the UT. Doing this is far from easy. Besides tedious experimental measurements the theoretical calculations are plagued by hadronic quantities which cannot be determined by perturbation theory. In this work several of these quantities so called form factors are computed using the well known method of light cone sum rules(LCSR). Two different setups have been used. One, established in this work, utilizing a correlation function with an on-shell B-Meson and one following the traditional calculation by taking the light meson on-shell. Both using light cone expansion in the respective on-shell mesons distribution amplitudes. While the first approach allows to calculate a whole bunch of phenomenologically interesting quantities by just changing Dirac-structures of the relevant currents it has the drawback that it does not have access to the well developed twist expansion of the latter. To incorporate higher Fock-state contributions the first models for three-particle distribution amplitudes of the B-Meson have been derived. αs-corrections remain out of the scope of this work. Nevertheless does a comparison with more sophisticated methods show an encouraging numerical agreement. In the second setup all known corrections especially the never verified αs-corrections to Twist three terms have been recalculated and a competitive result for the CKM-matrixelement vertical stroke Vub vertical stroke
$\\Delta I = 1/2$ enhancement and the Glashow-Schnitzer-Weinberg sum rule
Nasrallah, N F
2000-01-01
In 1967 Glashow, Schnitzer and Weinberg derived a sum rule in the soft-pion and soft kaon limit relating the Delta I=1/2 non-leptonic K->2pi amplitude to integrals over strange and non-strange spectral functions. Using the recent ALEPH data from tau-decay, we show that the sum rule, slightly modified to reduce contributions near the cut, yields the correct magnitude decay amplitude corresponding to the Delta I=1/2 rule.
Matching lightcone- and anomaly-sum-rule predictions for the pion-photon transition form factor
Oganesian, A G; Stefanis, N G; Teryaev, O V
2015-01-01
The pion-photon transition form factor is studied by employing two types of Sum Rules: Light Cone Sum Rules (LCSR) and Anomaly Sum Rules (ASR). By comparing the predictions for the pion-photon transition form factor, obtained from these two approaches, the applicability limit of the LCSRs at low momenta is determined. Reciprocally, the ASR threshold dependence on the momentum was extracted using our LCSR-based method in combination with two different types of pion distribution amplitudes and found that at higher Q2 it approaches a constant.
Restrictions on exact current correlators and reliability of sum rules results
International Nuclear Information System (INIS)
Criteria of reliability for results obtained within sum rules approach in QCD and in some quantum field theory models is studied. The criterion of validity of the approximation for current correlators based on operator product expansion within Borel sum rules, Suggested previously in the literature, is critically reexamined. A new criterion of validity of perturbative approximation which makes use of Kallen-Lehmann representation and finite energy sum rules is proposed. The stability of criteria against the small variations of expansion coefficients is investigated in an exactly solvable model and in QCD
Sum rule for the response function third moment in electron scattering by nuclei
International Nuclear Information System (INIS)
The sum rule for the response function third moment taking into account the nucleon-nucleon potential exchange is obtained. The sum rule is shown to be specified by the radial internucleonic potential, correlation functions as well as by the average kinetic proton energy in the nucleus. The correction introduced into the sum rule for the third moment of the response function due to exchange force is twice as low as the corresponding values obtained for the first and the second moments. The obtained results are in satisfactory agreement with the experiment
Analytic structure of ϕ4 theory using light-by-light sum rules
International Nuclear Information System (INIS)
We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ4 quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain however, they appear as tachyon solutions, showing the inconsistency of the approximation in this region
A Variational Sum-Rule Approach to Collective Excitations of a Trapped Bose-Einstein Condensate
Kimura, Takashi; Saito, Hiroki; Ueda, Masahito
1998-01-01
It is found that combining an excitation-energy sum rule with Fetter's trial wave function gives almost exact low-lying collective-mode frequencies of a trapped Bose-Einstein condensate at zero temperature.
Exotic tetraquark udss of JP=0+ in the QCD sum rule
International Nuclear Information System (INIS)
We study a QCD sum rule analysis for an exotic tetraquark udss of JP=0+ and I=1. We construct qqqq currents in a local product form and find that there are five independent currents for this channel. Because of the high dimensional nature of the current, it is not easy to form a good sum rule when using a single current. This means that we do not find any sum rule window to extract reliable results, due to the insufficient convergence of the operator product expansion and to the exceptional important role of QCD continuum. Then we examine sum rules by using currents of linear combinations of two currents among the independent ones. We find two reasonable cases that predict a mass of the tetraquark around 1.5 GeV
General solution of superconvergent sum rules for scattering of I=1 reggeons on baryons
International Nuclear Information System (INIS)
Superconvergent sum rules for reggeon-particle scattering are applied to scattering of reggeons αi (i=π, ρ, A2) with isospin I=1 on baryons with strangeness S=-1. The saturation scheme of these sum rules is determined on the basis of experimental data. Two series of baryon resonances with arbitrary isospins I and spins J=I+1/2 and J=I-1/2 are predicted. A general solution for vertices of interaction of these resonances with αi is found. Predictions for coupling vertices BαiB'(B, B'=Λ, Σ, Σ*) agree well with the experiment. It is shown that the condition of sum rules saturation by minimal number of resonances brings to saturation schemes resulting from experimental data. A general solution of sum rules for scattering of αi reggeons on Ξ and Ω hyperons is analyzed
Calculation of baryon sum rules and SU(4) mass formulae for mesons and baryons
International Nuclear Information System (INIS)
Light cone coordinates and field-field anticommutators for the free quark model on the light cone are introduced and light cone charges and light cone currents for the free quark model as well as sum rules for the meson and quark states are derived. The derivation of sum rules for the baryons is attempted. It is seen that it is possible formally to derive the same sum rules for the baryons and for the quarks. The baryon sums were derived through the symmetry properties of the baryon fields. Explicit assumptions about the spatial distribution of the three quarks in the baryons were not utilized. The meson-baryon Σ-terms, Zweig's rules in the SU (4) and a number of properties of the M-matrix are discussed. (BJ)
Modified Kramers-Kronig relations and sum rules for meromorphic total refractive index
International Nuclear Information System (INIS)
Modified Kramers-Kronig relations and corresponding sum rules are shown to hold for the total refractive index that can be presented as a sum of complex linear and nonlinear refractive indices, respectively. It is suggested that a self-action process, involving the degenerate third-order nonlinear susceptibility, can yield a negative total refractive index at some spectral range
Couplings of heavy hadrons with soft pions from QCD sum rules
International Nuclear Information System (INIS)
The couplings in the Heavy Hadron Chiral theory Lagrangian from the QCD sum rules in an external axial field are estimated. Stability of the sum rules at moderate values of the Borel parameter is poor that probably signals slow convergence of the OPE series. At large values of the Borel parameter they stabilize, and yield the couplings much lower than the constituent quark model expectations. 18 refs.; 5 figs
What can we learn from sum rules for vertex functions in QCD
International Nuclear Information System (INIS)
We demonstrate that the light-cone sum rules for vertex functions based on the operator product expansion and QCD perturbation theory lead to interesting relationships between various non-perturbative parameters associated with hadronic bound states (e.g. vertex couplings and decay constants). We also show that such sum rules provide a valuable means of estimating the matrix elements of the higher spin operators in the meson wave functions. (orig.)
Fate of QCD sum rules or fate of vector meson dominance in a nuclear medium
Leupold, S
2006-01-01
A current-current correlator with the quantum numbers of the omega meson is studied in a nuclear medium. Using weighted finite energy sum rules and dispersion relations for the current-nucleon forward scattering amplitude it is shown that strict vector meson dominance and QCD sum rules are incompatible with each other. This implies that at least one of these concepts -- which are both very powerful in the vacuum -- has to fade in the nuclear environment.
Sum rule analysis of vector and axial-vector spectral functions with excited states in vacuum
Hohler, Paul M.; Rapp, Ralf
2012-01-01
We simultaneously analyze vector and axial-vector spectral functions in vacuum using hadronic models constrained by experimental data and the requirement that Weinberg-type sum rules are satisfied. Upon explicit inclusion of an excited vector state, viz. rho', and the requirement that the perturbative continua are degenerate in vector and axial-vector channels, we deduce the existence of an excited axial-vector resonance state, a1', in order that the Weinberg sum rules are satisfied. The resu...
Bulk spectral function sum rule in QCD-like theories with a holographic dual
Hohler, Paul M.; Stephanov, Mikhail A.
2011-01-01
We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between larg...
Generalization of the sum rule for double Gamow-Teller operators
International Nuclear Information System (INIS)
We show that for Pauli-blocked nuclei, in the closure approximation, the summed strength for the double Gamow-Teller 0+→0+ transitions is less than the value 6(N-Z)(N-Z+1) and that the difference can be related to sum rules for magnetic dipole transitions, which in turn can be related to the double Gamow-Teller matrix element for the transition from the 0+ initial state to its double isobaric analog state. A ''wrong isospin phase sum rule'' is found that is valid in limited cases
Sum rules for the spontaneous chiral symmetry breaking parameters of QCD
International Nuclear Information System (INIS)
We discuss in the spirit of the work of Shifman, Vainshtein and Zakharov (SVZ), sum rules involving current-current vacuum correlation functions, whose Wilson expansion starts off with the operators anti qq or (anti qq)2, and thus provide information about the chiral symmetry breaking parameters of QCD. We point out that under the type of crude approximations made by SVZ, a value of sub(vac) (250MeV)3 is obtained from one of these sum rules, in agreement with current expectations. Further we show that a Borel transformed version of the Weinberg sum rule, for VV - AA, current products seem only to make sense for an A1 mass close to 1.3GeV and it makes little sense with the current algebra mass Msub(A)=anti 2M. We also give an estimate for the chiral symmetry breaking parameters μ16=22(anti qsub(L) lambda sup(a)γsub(μ)qsub(L))(anti qsub(R) lambdasup(a) γsup(μ)qsub(R)) >sub(vac) entering in the Weinberg sum rules and μ26=g2sub(vac) entering in a new sum rule we propose involving antisymmetric tensor currents J=anti q σsub(μnu) q. (author)
Supersymmetric Flavor-Changing Sum Rules as a Tool for b -> s gamma
Dudley, Brian
2008-01-01
The search for supersymmetry (SUSY) and other classes of new physics will be tackled on two fronts, with high energy, direct detection machines, and in high precision experiments searching for indirect signatures. While each of these methods has its own strengths, even more can be gained by finding ways to combine their results. In this paper, we examine one way of bridging these two types of experiments by calculating sum rules which link physical squark masses to the flavor-violating squark mixings. These sum rules are calculated for minimally flavor-violating SUSY theories at both high and low tan(beta). We also explore how the sum rules could help to disentangle the relative strengths of different SUSY contributions to b -> s gamma, a favored channel for indirect searches of new physics. Along the way, we show that the gluino contributions to b -> s gamma can be very sizable at large tan(beta).
Charge form factor and sum rules of electromagnetic response functions in $^{12}$C
Energy Technology Data Exchange (ETDEWEB)
Lovato, Alessandro [ANL; Gandolfi, Stefano [LANL; Carlson, Joseph A. [LANL; Butler, Ralph [Middle Tennessee State University; Lusk, Ewing [ANL; Pieper, Steven C. [ANL; Schiavilla, Rocco [Old Dominion University, JLAB
2013-08-01
An {\\it ab initio} calculation of the $^{12}$C elastic form factor, and sum rules of longitudinal and transverse response functions measured in inclusive (e,e') scattering, is reported, based on realistic nuclear potentials and electromagnetic currents. The longitudinal elastic form factor and sum rule are found to be in satisfactory agreement with available experimental data. A direct comparison between theory and experiment is difficult for the transverse sum rule. However, it is shown that the calculated one has large contributions from two-body currents, indicating that these mechanisms lead to a significant enhancement of the quasi-elastic transverse response. This fact may have implications for the anomaly observed in recent neutrino quasi-elastic charge-changing scattering data off $^{12}$C.
Charmonium spectrum at finite temperature from a Bayesian analysis of QCD sum rules
Directory of Open Access Journals (Sweden)
Morita Kenji
2012-02-01
Full Text Available Making use of a recently developed method of analyzing QCD sum rules, we investigate charmonium spectral functions at finite temperature. This method employs the Maximum Entropy Method, which makes it possible to directly obtain the spectral function from the sum rules, without having to introduce any strong assumption about its functional form. Finite temperature effects are incorporated into the sum rules by the change of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which are extracted from lattice QCD. As a result, J/ψ and ηc dissolve into the continuum already at temperatures around 1.0 ~ 1.1 Tc.
Sum rules for four-spinon dynamic structure factor in XXX model
International Nuclear Information System (INIS)
In the context of the antiferromagnetic spin 12 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S2is between 70% and 75%. The calculations are numerical and Monte Carlo based. Good statistics are obtained
The calculation of the quark distribution amplitudes of decuplet baryons by means of QCD sum rules
International Nuclear Information System (INIS)
Using the QCD sum rule technique, we derive the quark distribution amplitudes of the decuplet memebers Δ(1232), Σ*(1385), Ξ*(1530) and Ω(1672). Generalizing the treatment of the Bethe-Salpeter amplitude, we can distinguish spin- and orbital- angular momentum parts of the quark distributions and establish separate sum rules for the contributions. Projecting out the angular momentum 1/2 contributions, we obtain sum rules which are saturated by the lowest resonance in the given iso spin channel, thus resolving deficiencies of the standard approach. We find that for helicity 1/2 the spin part of the quark distributions is asymmetric. Also the orbital angular momentum contributions are extremely asymmetric and tend to decrease the asymmetry of the spin part. As a result of SU(3) symmetry breaking, configuration mixing occurs and the decuplet baryons Σ* and Ξ* receive octet contributions. The antisymmetric part of these octet contributions is calculated. (orig.)
Factorization, resummation and sum rules for heavy-to-light form factors
Wang, Yu-Ming
2016-01-01
Precision calculations of heavy-to-light form factors are essential to sharpen our understanding towards the strong interaction dynamics of the heavy-quark system and to shed light on a coherent solution of flavor anomalies. We briefly review factorization properties of heavy-to-light form factors in the framework of QCD factorization in the heavy quark limit and discuss the recent progress on the QCD calculation of $B \\to \\pi$ form factors from the light-cone sum rules with the $B$-meson distribution amplitudes. Demonstration of QCD factorization for the vacuum-to-$B$-meson correlation function used in the sum-rule construction and resummation of large logarithms in the short-distance functions entering the factorization theorem are presented in detail. Phenomenological implications of the newly derived sum rules for $B \\to \\pi$ form factors are further addressed with a particular attention to the extraction of the CKM matrix element $|V_{ub}|$.
Light Cone Sum Rules for gamma*N ->Delta Transition Form Factors
Energy Technology Data Exchange (ETDEWEB)
V.M. Braun; A. Lenz; G. Peters; A. Radyushkin
2006-02-01
A theoretical framework is suggested for the calculation of {gamma}* N {yields} {Delta} transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ''soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ''minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum.
Thermal behaviors of light unflavored tensor mesons in the framework of QCD sum rule
International Nuclear Information System (INIS)
In this paper, we investigated the sensitivity of the masses and decay constants of f2(1270) and a2(1320) tensor mesons to the temperature using OCD sum rule approach. In our calculations, we take into account new additional operators appearing in operator product expansion (OPE). At the end of numerical analyses we show that at deconfinement temperature the decay constants and masses decreased by 6% and 96% of their vacuum values, respectively. Our results on the masses and decay constants at zero temperature of the tensor mesons are consistent with the experimental data as well as the vacuum sum rules predictions
Thermal behaviors of light unflavored tensor mesons in the framework of QCD sum rule
Azizi, K; Sundu, H; Veliev, E Veli; Yazici, E
2014-01-01
In this study, we investigate the sensitivity of the masses and decay constants of the light $f_{2}(1270)$ and $a_{2}(1320)$ tensor mesons to the temperature using QCD sum rule approach. In our calculations, we take into account the additional operators appearing in operator product expansion at finite temperature. It is obtained that at deconfinement temperature the decay constants and masses decrease with amount of $6\\%$ and $96\\%$ compared to their vacuum values, respectively. Our results on the masses at zero temperature are consistent with the vacuum sum rules predictions as well as the experimental data.
Sum rules for invariance of the fourth-rank hypermagnetisability in a gauge translation
Pagola, G. I.; Caputo, M. C.; Ferraro, M. B.; Lazzeretti, P.
2005-06-01
The conditions for invariance in a gauge translation of the fourth-rank molecular hypermagnetisability tensor, introduced to rationalize the cubic response of a molecule in the presence of an external magnetic field, are discussed in terms of quantum mechanical sum rules. Eight relationships, connecting electric dipole polarisability, polarisability of magnetisability, and other third- and fourth-rank tensors that can be regarded as intrinsic molecular properties tout court, have been obtained. Numerical tests have been carried out to determine the Hartree-Fock limit for the sum-rules in a set of small molecules.
The sigma meson from QCD sum rules for large-$N_c$ Regge spectra
Afonin, S S
2016-01-01
The QCD sum rules in the large-$N_c$ limit for the light non-strange vector, axial-vector and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose a improved method for a combined analysis of these channels that gives a reasonable description of the observed spectrum. Fixing the universal slope of radial trajectories and the quark condensate from the vector channels, we argue that, in contrast to a common belief, the prediction of a light quark-antiquark scalar state compatible with $f_0(500)$ can be quite natural within the planar QCD sum rules.
Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted to the experimental data in the future.
QCD Light-Cone Sum Rule Estimate of Charming Penguin Contributions in B -> pi pi
Khodjamirian, A.; Mannel, Th.; Melic, B.
2003-01-01
Employing the QCD light-cone sum rule approach we calculate the B -> pi pi hadronic matrix element of the current-current operator with c quarks in the penguin topology (``charming penguin''). The dominant contribution to the sum rule is due to the c-quark loop at short distances and is of O(alpha_s) with respect to the factorizable B -> pi pi amplitude. The effects of soft gluons are suppressed at least by O(alpha_s m_b^{-2}). Our result indicates that sizable nonperturbative effects generat...
QCD light-cone sum rule estimate of charming penguin contributions in B -> pi pi
Khodjamirian, A.; Mannel, Th.; Melić, Blaženka
2003-01-01
Employing the QCD light-cone sum rule approach we calculate the B --> pipi hadronic matrix element of the current-current operator with c quarks in the penguin topology ("charming penguin"). The dominant contribution to the sum rule is due to the c-quark loop at short distances and is of O(alpha(S)) with respect to the factorizable B --> pipi amplitude. The effects of soft gluons are suppressed at least by O (alpha(S) m(b)(-2)). Our result indicates that sizable nonperturbative effects genera...
Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
Broadhurst, D. J.; Kataev, A. L.; Maxwell, C. J.
2004-01-01
The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lepton scattering was based merely on a valence picture and is modified both by perturbative and non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/N_c^2, relative to those for higher moments, we propose that this suppression persists at higher orders ...
Compatibility of QCD sum-rules and Hadron field theory in a dense medium
Aguirre, R M
2005-01-01
The compatibility of the QCD sum rules and effective hadronic models predictions are examined. For this purpose we have considered the results for the nucleon self-energy in a dense hadronic environment provided by two independent QCD sum-rules calculations. They are immersed in a theory of hadronic fields giving rise to non-linear interactions, whose vertices are parameterized in different ways. Although all of them reproduce the self-energy used as input, very different descriptions of nuclear observables are obtained. Only under very definite circumstances we have found an acceptable agreement with the nuclear matter properties. To achieve this, phenomenological parameters are not required at all.
Strong coupling constant of negative parity nucleon with $\\pi$ meson in light cone QCD sum rules
Aliev, T M; Savcı, M
2016-01-01
We estimate strong coupling constant between the negative parity nucleons with $\\pi$ meson within the light cone QCD sum rules. A method for eliminating the unwanted contributions coming from the nucleon--nucleon and nucleon--negative parity nucleon transition is presented. It is observed that the value strong coupling constant of the negative parity nucleon $N^\\ast N^\\ast \\pi$ transition is considerably different from the one predicted by the 3--point QCD sum rules, but is quite close to the coupling constant of the positive parity $N N \\pi$ transition.
Mean value sum rules and test of scale breaking (in neutrino scattering)
Akama, K
1975-01-01
The author proposes sum rules which can be used for testing the scaling hypothesis and its powerlike breakdown in deep inelastic neutrino scattering. These sum rules are written in terms of the mean values of quantities determined solely by the outgoing leptons. By comparing with the latest CERN-Gargamelle data, they find that the Oth moment of structure function is still consistent with scaling. However, the 1st moment may have a scale breaking. In order to test such scale breaking more quantitatively, experimental determination of (E'/sup 2/), (v/sup 2/), (vE'), etc., is highly desirable in the near future. (15 refs).
Exact zero-momentum sum rules in d=3 gauge theory
International Nuclear Information System (INIS)
We derive, for non-abelian pure gauge theory, an infinite set of sum rules for connected zero-momentum matrix elements of the condensate operator Σ(Gaij)2(x) in d=3; these are equivalent to an effective action for this operator. These sum rules are analogous to similar ones derived, at the one-loop level, for d=4 gauge theory and predict a non-zero positive value of left angle G2ij right angle and a negative vacuum energy. Some applications to effective glueball couplings and approximations to the evaluation of left angle G2ij right angle are discussed. (orig.)
In-medium QCD sum rules for {omega} meson, nucleon and D meson
Energy Technology Data Exchange (ETDEWEB)
Thomas, Ronny
2008-07-01
The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the {omega} meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the {omega} meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. (orig.)
Fermion correction to the mass of the scalar glueball in QCD sum rule
Yuan, Xu-Hao(Center for High Energy Physics, Department of Engineering Physics, Tsinghua University, Beijing 100084, China); Tang, Liang
2009-01-01
Contributions of fermions to the mass of the scalar glueball $0^{++}$ are calculated at two-loop level in the framework of QCD sum rules. It obviously changes the coefficients in the operator product expansion (OPE) and shifts the mass of glueball.
Application of sum rule to the dispersion model of hydrogenated amorphous silicon
Czech Academy of Sciences Publication Activity Database
Franta, D.; Nečas, D.; Zajíčková, L.; Ohlídal, I.; Stuchlík, Jiří; Chvostová, Dagmar
2013-01-01
Roč. 539, JUL (2013), s. 233-244. ISSN 0040-6090 Institutional support: RVO:68378271 Keywords : optical constants * ellipsometry * spectrophotometry * a-Si:H * Urbach tail * localized states * sum rule Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.867, year: 2013
Extension of the sum rule for the transition rates between multiplets to the multiphoton case
Solovyev, D; Volotka, A; Plunien, G
2010-01-01
The sum rule for the transition rates between the components of two multiplets, known for the one-photon transitions, is extended to the multiphoton transitions in hydrogen and hydrogen-like ions. As an example the transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are compared with previous calculations.
Analysis of the Triply Heavy Baryon States with QCD Sum Rules
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang
2012-01-01
In this article, we study the (1/2)± and (3/2)± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2) and (3/2) triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.
Reanalyzing Pentaquark Θ+(1540) in Framework of QCD Sum Rules Approach with Direct Instantons
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, we study the pentaquark state Θ+(1540) with a (scalar) diquark-(pseudoscalar) diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.
In-medium QCD sum rules for ω meson, nucleon and D meson
International Nuclear Information System (INIS)
The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the ω meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the ω meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. (orig.)
J/ψD*D* form factor from QCD sum rules
International Nuclear Information System (INIS)
We calculate the J/ψD*D* form factor and coupling constant from QCD Sum Rules in the cases where J/ψ and D* mesons are off-shell. The results show that this method is consistent and allows to extract the same coupling constant for the vertex. (author)
Sum rules for e+e- → W+W- helicity amplitudes from BRS invariance
International Nuclear Information System (INIS)
BRS invariance of the electroweak gauge theory leads to relationships between amplitudes with external massive gauge bosons and amplitudes where some of these gauge bosons are replaced with their corresponding Nambu-Goldstone bosons. Unlike the equivalence theorem, these identities are exact at all energies. In this paper we discuss such identities which relate the process e+e- → W+W- to W±χ-+ and χ+χ- production. By using a general form factor decomposition for e+e- → W+W-, e+e- → W±χ-+ and e+e- → χ+χ-, amplitudes, these identities are expressed as sum rules among scalar form factors. Because these sum rules may be applied order by order in perturbation theory, they provide a powerful test of higher order calculations. By using additional Ward-Takahashi identities we find that the various contributions are divided into separately gauge-invariant subsets, the sum rules applying independently to each subset. After a general discussion of the application of the sum rules we consider the one-loop contributions of scalar-fermions in the Minimal Supersymmetric Standard Model as an illustration
Calculation of a weak nonleptonic matrix element using ``Weinberg'' sum rules
Donoghue, John F.
1994-01-01
There is a ``toy'' weak matrix element which can be expressed as an integral over the vector and axial vector spectral functions, $\\rho_V (s) - \\rho_A (s)$. I review our recent evaluation of these spectral functions, the study of four ``Weinberg'' sum rules and the calculation of this matrix element.
Analysis of $\\Omega_c^*(css)$ and $\\Omega_b^*(bss)$ with QCD sum rules
Wang, Zhi-Gang
2007-01-01
In this article, we calculate the masses and residues of the heavy baryons $\\Omega_c^*(css)$ and $\\Omega_b^*(bss)$ with spin-parity ${3/2}^+$ with the QCD sum rules. The numerical values are compatible with experimental data and other theoretical estimations.
The influence of gluonic operators on QCD sum rules for baryons
International Nuclear Information System (INIS)
In this thesis the operator product expansion (OPE) is extended up to operators of dimension d=10. The coefficient functions are calculated only up to order αsub(s). Thereby the performation of the OPE by means of the Schwinger operator formalism is extensively described. In the final section the sum rules for nucleon and delta are discussed. (orig./HSI)
Determination of the $\\Sigma$--$\\Lambda$ mixing angle from QCD sum rules
Aliev, T M; Savcı, M
2015-01-01
The $\\Sigma$--$\\Lambda$ mixing angle is calculated in framework of the QCD sum rules. We find that our prediction for the mixing angle is $(1.00\\pm 0.15)^0$ which is in good agreement with the quark model prediction, and approximately two times larger than the recent lattice QCD calculations.
Sum rules study and a scaling property of fragmentation mass yield curves
International Nuclear Information System (INIS)
Information obtained in mass yield distributions produced in protons and heavy ions induced reactions has been analyzed with two model independent sum rules. The average number of fragments of different sizes produced in one collision has been extracted. A scaling law for the mass yield has been deduced. (orig.)
Perturbative analysis of the energy-weighted sum rule of bilinear fermion operators
International Nuclear Information System (INIS)
It is shown that the value obtained for the energy-weighted sum rule for bilinear fermionic operators using dressed one-particle propagators plus two-body random-phase approximation corrections is preserved when any higher-order correction is introduced. This is proven through the evaluation of the corresponding perturbative diagrams
International Nuclear Information System (INIS)
This thesis presents an experimental study of the neutron (and 3He) spin structure with a particular emphasis in the resonance domain (experiment E94010 that took place in 1997 at Jefferson Lab (TJNAF or formerly CEBAF) in Virginia). A polarized 3He target was built in order to achieve this study since polarized 3He nuclei can be seen as polarized neutrons. This target allowed the measurement of the polarized absolute cross sections σ1/2(Q2, ν) and σ3/2(Q2, ν) from the inclusive reaction →3He(→e, e')X for incident beam energies ranging from 0.86 GeV to 5.07 GeV at a scattering angle of 15.5 deg. The Q2 evolution of the generalized Gerasimov-Drell-Hearn (GDH) integral on 3He and on neutron was measured from 0.1 GeV2 to 1.0 GeV2 in order to understand the transition between perturbative QCD and non-perturbative QCD. The integration domain in ν (the energy loss of the scattered electron) is from the pion threshold to about 2.5 GeV which covers both the resonance region and the Deep Inelastic Scattering. The high precision of our data constrains the models giving the Q2 evolution of the generalized GDH integral. The polarized quasi-elastic scattering was also measured. The cross section σTT(Q2, ν) on 3He and the spin structure functions g13He(Q2, ν) and g23He(Q2, ν) are presented. These data are an indication that the higher-twists are small in our kinematics domain and that the Bloom-Gilman duality seems to hold for the polarized spin structure functions. (author)
$J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
Zhao, Y M
2005-01-01
In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$ and $$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.
Pastore, A.; Davesne, D.; Lallouet, Y.; M. Martini; Bennaceur, K.; J. Meyer
2012-01-01
The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, $M_{-1}$, as a tool to detect instabilities in Skyrme functionals.
Light-cone sum rules for the nucleon form factors in NLO
International Nuclear Information System (INIS)
In this work the leading-twist next-to-leading order (NLO) correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon are calculated. Here the Ioffe nucleon interpolation current is used and it is worked in the MN=0 approximation, with MN being the mass of the nucleon. In this approximation, only the Pauli form factor F2 receives a correction and the calculated correction is quite sizable. The numerical results for the proton form factors show the improved agreement with the experimental data. Furthermore the problems encountered when going away from MN=0 approximation at NLO, as well as, gauge invariance of the perturbative results are discussed. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors. (orig.)
QCD sum rules for the neutron, $\\Sigma$ and $\\Lambda$ in neutron matter
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
The nuclear density dependencies of the neutron, $\\Sigma$ and $\\Lambda$ hyperon are important inputs in the determination of the neutron star mass as the appearance of hyperons coming from strong attractions significantly changes the stiffness of the equation of state (EOS) at iso-spin asymmetric dense nuclear matter. In-medium spectral sum rules have been analyzed for the nucleon, $\\Sigma$ and $\\Lambda$ hyperon to investigate their properties up to slightly above the normal nuclear matter density. Construction scheme of the interpolating fields without derivatives has been reviewed and used to construct a general interpolating field for each baryon with parameters specifying the strength of independent interpolating fields. Optimal choices for the interpolating fields were obtained by requiring the sum rules to be stable against variations of the parameters and the result to be consistent with known phenomenology. It is found that for the $\\Lambda$ hyperon interpolating field, the up and down quark combined ...
Coset construction and character sum rules for the doubly extended N = 4 superconformal algebras
Petersen, Jens Lyng; Taormina, Anne
1993-06-01
Character sum rules associated with the realization of the N = 4 superconformal algebra Ãγ on manifolds corresponding to the group cosets SU(3) k˜+ / U(1) are derived and developed as an important tool in obtaining the modular properties of Ãγ characters as well as information on certain extensions of that algebra. Their structure strongly suggests the existence of rational conformal field theories with central charges in the range 1 ⪕ c ⪕ 4. The corresponding characters appear in the massive sector of the sum rules and are completely specified in terms of the characters for the parafermionic theory SU(3)/(SU(2)×U(1)) and in terms of the branching functions of massless Ãγ characters into SU(2) k˜+× SU(2) 1 characters.
B→A transitions in the light-cone QCD sum rules with the chiral current
Institute of Scientific and Technical Information of China (English)
SUN Yan-Jun; WANG Zhi-Gang; HUANG Tao
2012-01-01
In this article,we calculate the form-factors of the transitions B → a1(1260),b1(1235) in the leading-order approximation using the light-cone QCD sum rules.In calculations,we choose the chiral current to interpolate the B-meson,which has the outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons make no contributions,and the resulting sum rules for the form-factors suffer from far fewer uncertainties.Then we study the semi-leptonic decays B → a1(1260)l(v1),b1(1235)l(v1) (l =e,μ,Τ),and make predictions for the differential decay widths and decay widths,which can be compared with the experimental data in the coming future.
Diagonal and transition magnetic moments of negative parity heavy baryons in QCD sum rules
Aliev, T M; Barakat, T; Savcı, M
2015-01-01
Diagonal and transition magnetic moments of the negative parity, spin-1/2 heavy baryons are studied in framework of the light cone QCD sum rules. By constructing the sum rules for different Lorentz structures, the unwanted contributions coming from negative (positive) to positive (negative) parity transitions are removed. It is obtained that the magnetic moments of all baryons, except $\\Lambda_b^0$, $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$, are quite large. It is also found that the transition magnetic moments between neutral negative parity heavy $\\Xi_Q^{\\prime 0}$ and $\\Xi_Q^0$ baryons are very small. Magnetic moments of the $\\Sigma_Q \\to \\Lambda_Q$ and $ \\Xi_Q^{\\prime \\pm} \\to \\Xi_Q^\\pm$ transitions are quite large and can be measured in further experiments.
Unitarity sum rules, three site moose model, and the ATLAS 2 TeV diboson anomalies
Abe, Tomohiro; Okawa, Shohei; Tanabashi, Masaharu
2015-01-01
We investigate $W'$ interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry relations are powerful enough to predict various nontrivial relations among $WWZ'$, $WZW'$, $WWh$, $WW'h$ and $ZZ'h$ coupling strengths in a model independent manner. We also perform surveys in the general parameter space of $W'$ models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a $W'$ particle of the three site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the non SM-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the $W'$ and $Z'$ bosons.
Coupling constant for the J/ψDsDs vertex from QCD sum rules
International Nuclear Information System (INIS)
The coupling constant of the meson vertex J/ψDsDs is calculated using the three point correlation function within the QCD sum rules formalism. We have considered alternately mesons J/ψ and Ds off-shell together with non-perturbative contributions up to the mixed quark–gluon condensates. When extrapolated, these two different form factors give the same coupling constant for the process gJ/ψDsDs=5.98−0.58+0.67
Supersymmetric Flavor-Changing Sum Rules as a Tool for b -> s gamma
Dudley, Brian; Kolda, Christopher
2008-01-01
The search for supersymmetry (SUSY) and other classes of new physics will be tackled on two fronts, with high energy, direct detection machines, and in high precision experiments searching for indirect signatures. While each of these methods has its own strengths, even more can be gained by finding ways to combine their results. In this paper, we examine one way of bridging these two types of experiments by calculating sum rules which link physical squark masses to the flavor-violating squark...
Effects of Nuclear Medium on the Sum Rules in Electron and Neutrino Scattering
Zaidi, F; Athar, M Sajjad; Singh, S K; Simo, I Ruiz
2016-01-01
In this work, we study the influence of nuclear medium effects on various parton model sum rules in nuclei and compare the results with the free nucleon case. We have used relativistic nucleon spectral function to take into account Fermi motion, binding and nucleon correlations. The pion and rho meson cloud contributions have been incorporated in a microscopic model. The effect of shadowing has also been considered.
Bs→f0(980) decays: Results from light-cone QCD Sum Rules
International Nuclear Information System (INIS)
We describe a light-cone QCD sum rule calculation of the Bs→f0(980) transition form factors useful to predict the branching ratios of the rare decays Bs→f0l+l-, Bs→f0νν-bar and of Bs→J/ψf0 decay assuming factorization. We compare this channel to Bs→J/ψφ as far as the possibility to determine the Bs mixing phase is concerned.
Sum rules for meson and baryon production in the quark recombination model
International Nuclear Information System (INIS)
A quark recombination model with quark distributions according to a generalized Kuti-Weisskopf model is used. Mesons are formed by v-s (valence-sea) and s-s recombination, baryons by vvv, vvs, vss and sss recombination. Sum rules for energy momentum concervation, baryon number, valence and sea quarks are shown to constrain the recombination parameters of the model significantly. The resulting model is consistent with experimental data. (author)
Adler-type sum rule, charge symmetry and neutral current in general multi-triplet model
International Nuclear Information System (INIS)
We derive Adler-type sum rule extended to general multi-triplet model. Paying attention to roles of the colour degree of freedom, we discuss the charge symmetry property of the weak charged current and the structure functions for ν(ν-)+N→l(l-)+X, and also the structure of the neutral current. A comment is given on implications in our theory of Koike and Konuma's result on the neutral hadronic current. (auth.)
Sum-rule analysis of radio-frequency spectroscopy of ultracold Fermi gas
Leggett, AJ; Zhang, S.
2008-01-01
We carried out an analysis based on sum rules and determined the radio-frequency spectroscopy shift observed in Chin 's experiment. It is shown that such a shift can be interpreted as spin correlations peculiar to a BCS-type state. An analytical form for the shift is obtained which enables us to make quantitative comparisons with the experiment throughout the crossover. We also calculated the width of the resonance. An interesting consequence is noticed, which can possibly be tested by future...
Nature of the X(5568) : a critical Laplace sum rule analysis at N2LO
Albuquerque, R; Rabemananjara, A; Rabetiarivony, D
2016-01-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)\\bar(bd) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (\\tau-sum rule variable, t_c continuum threshold and subtraction constant \\mu). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results + the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173- 5226) GeV, summarized in Table 7, for exotic hadrons built with four different flavours (buds), do not support some previous interpretations of the D0 candidate [1], X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could resul...
Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO
Albuquerque, R.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.
2016-06-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)(bd¯) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (τ-sum rule variable, tc continuum threshold and subtraction constant μ). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 ˜ 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,1 X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2𝜃 ≈ 0.15. One can also scan the region (2327 ˜ 2444) MeV (where the Ds0∗(2317) might be a good candidate) and the one (5173 ˜ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or π+hadrons decays.
Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
International Nuclear Information System (INIS)
The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lepton scattering was based merely on a valence picture and is modified both by perturbative and by non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/Nc2, relative to those for higher moments, we propose that this suppression persists at higher orders and also applies to higher-twist effects. Moreover, we propose that the differences between the corresponding radiative corrections to higher non-singlet moments in charged-lepton and neutrino deep inelastic scattering are suppressed by 1/Nc2, in all orders of perturbation theory. For the first moment, in the Gottfried sum rule, the substantial discrepancy between the measured value and the valence-model expectation may be attributed to an intrinsic isospin asymmetry in the nucleon sea, as is indeed the case in a chiral-soliton model, where the discrepancy persists in the limit Nc→∞
Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
Alastuey, Angel; Fantoni, Riccardo
2016-05-01
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.
J{sup PC}=1{sup ++} heavy hybrid masses from QCD sum-rules
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Kleiv, R.T. [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK, S7N 5E2 (Canada); Harnett, D. [Department of Physics, University of the Fraser Valley, Abbotsford, BC, V2S 7M8 (Canada); Steele, T.G. [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK, S7N 5E2 (Canada); Jin, Hong-ying [Zhejiang Institute of Modern Physics, Zhejiang University, Zhejiang Province (China)
2013-01-15
QCD Laplace sum-rules are used to calculate axial vector (J{sup PC}=1{sup ++}) charmonium and bottomonium hybrid masses. Previous sum-rule studies of axial vector heavy quark hybrids did not include the dimension-six gluon condensate, which has been shown to be important in the 1{sup −−} and 0{sup −+} channels. An updated analysis of axial vector heavy quark hybrids is performed, including the effects of the dimension-six gluon condensate, yielding mass predictions of 5.13 GeV for hybrid charmonium and 11.32 GeV for hybrid bottomonium. The charmonium hybrid mass prediction disfavours a hybrid interpretation of the X(3872), if it has J{sup PC}=1{sup ++}, in agreement with the findings of other theoretical approaches. It is noted that QCD sum-rule results for the 1{sup −−}, 0{sup −+} and 1{sup ++} channels are in qualitative agreement with the charmonium hybrid multiplet structure observed in recent lattice calculations.
Blümlein, Johannes; Falcioni, Giulio; De Freitas, Abilio
2016-09-01
We calculate analytically the flavor non-singlet O (αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep (x ,Q2) and g1,2ep (x ,Q2) and charged current non-singlet structure functions F1,2,3ν (ν bar) p (x ,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O (αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2 ≫mc,b2. We also study the target mass corrections to the above sum rules.
Re-analysis of the $D^* D\\pi$ coupling in the light-cone QCD sum rules
Kim, H
2003-01-01
The recent measurement from the CLEO experiment presents the $DD^*\\pi$ coupling, $17.9\\pm 0.3 \\pm 1.9$. This value is much larger than any of QCD sum rule predictions available in literature. We report that, with a relevant treatment of the continuum subtraction as well as with the asymptotic form of the twist-2 pion wave function, the light-cone QCD sum rule can provide the coupling comparable to the experimental value. The stability of the resulting sum rule becomes much better with these corrections.
Sum rules for the decays of the C-even charmonium states
International Nuclear Information System (INIS)
Sum rules for the decays of the C-even charmonium levels (1S0, 3P0, 3P2, 1D2) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers Jsup(PC)=Osup(-+), O++, 2++, 2-+. The contribution of the charmed continuum to some of the sum rules is small, and the latter are saturated by the contribution of the lowest charmonium levels. In this way the widths of the two-photon decays of the charmonium states are predicted. The total hadronic widths of these states are estimated by using the usual assumption that they are determined by widths of the two-gluon decays. Results are in qualitative agreement with the earlier calculations based on the nonrelativistic potential model with the confinement-like potentials
QCD corrections to B→π form factors from light-cone sum rules
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Yu-Ming Wang
2015-09-01
Full Text Available We compute perturbative corrections to B→π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+(q2 and fBπ0(q2 at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B→π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub|=(3.05−0.38+0.54|th.±0.09|exp.×10−3 with the inverse moment of the B-meson distribution amplitude ϕB+(ω determined by reproducing fBπ+(q2=0 obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B→πℓνℓ (ℓ=μ,τ in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B→π form factors fBπ+(q2 and fBπ0(q2 in brief.
Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules
Wang, Yu-Ming; Shen, Yue-Long
2016-02-01
We compute radiative corrections to Λ b → Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ b -baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ b -baryon correlation function is justified at leading power in Λ /m b , with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to- B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at {O}({α}_s) shift the Λ b → Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ b → Λ from factors we further investigate several decay observables in the electro-weak penguin Λ b → Λ ℓ + ℓ - transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the Λ b → Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
Berk, A.; Temkin, A.
1985-01-01
A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.
Analysis of the $e^{+}e^{-}\\rightarrow\\pi^{0}\\gamma$ process using anomaly sum rules approach
Khlebtsov, S; Teryaev, O
2016-01-01
The process $e^{+}e^{-}\\rightarrow\\gamma^{*}\\rightarrow \\pi^{0}\\gamma$ was considered using time-like pion transition form factor, obtained in the approach of the Anomaly Sum Rules(ASR). The total cross section and angular distribution of the process was calculated. As the result of the comparison with the data it was shown that ASR approach provides their good description in the regions far from the pole. Also there was proposed a method allowing to give reasonable description of data in the region of pole within the ASR approach. The strong restrictions for the parameters of the modified ASR approach were obtained.
Huitu, Katri; Pandita, P. N.; Tiitola, Paavo
2015-10-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.
Huitu, Katri; Tiitola, Paavo
2015-01-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which includes contributions from three mediation mechanisms, namely anomaly mediation, gravity mediation and gauge mediation, using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the soft supersymmetry breaking parameters in terms of the RGIs. We further discuss determining the supersymmetry breaking mechanism using a limited set of invariants, and derive sum rules valid for the DMMSB. In addition we examine some of the implications of the measured Higgs mass to the DMMSB spectrum.
The Study of Semileptonic Bc to Ds1 Transitions in QCD Sum Rules
International Nuclear Information System (INIS)
We consider the semileptonic Bc to Ds1 transitions in the frame work of three-point QCD sum rules. Here, we investigate the Ds1 meson as a conventional c s-bar meson in the pure state. The obtained results for the form factors are used to evaluate the decay rates and branching ratios. Any future experimental measurement on these form factors as well as decay rates and branching fractions and their comparison with the obtained results in the present work can give considerable information about the structure of this meson.
Analyzing Bs - anti Bs mixing. Non-perturbative contributions to bag parameters from sum rules
International Nuclear Information System (INIS)
We use QCD sum rules to compute matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the Bs mass eigenstates. Our analysis includes the leading-order operators Q and QS, as well as the subleading operators R2 and R3, which appear at next-to-leading order in the 1/mb expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
The relation between the photonuclear E1 sum rule and the effective orbital g-factor
Bentz, Wolfgang; Arima, Akito
2004-05-01
The connection between the enhancement factor (1+ κ) of the photonuclear E1 sum rule and the orbital angular momentum g-factor ( gℓ) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the κ- gℓ relation. By identifying the physical processes which are taken into account in κ and gℓ, the validity and limitations of this relation will be discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown.
The relation between the photonuclear E1 sum rule and the effective orbital g-factor
Bentz, W.; Arima, A
2003-01-01
The connection between the enhancement factor (1+kappa) of the photonuclear E1 sum rule and the orbital angular momentum g-factor (gl) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the kappa-gl relation. By identifying the physical processes which are taken into account in kappa and gl, the validity and limitations of this relation are discussed. The co...
The relation between the photonuclear E1 sum rule and the effective orbital g-factor
International Nuclear Information System (INIS)
The connection between the enhancement factor (1+κ) of the photonuclear E1 sum rule and the orbital angular momentum g-factor (gl) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the κ-gl relation. By identifying the physical processes which are taken into account in κ and gl, the validity and limitations of this relation will be discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown
Analysis of the Heavy Pseudoscalar Mesons with Thermal QCD Sum Rules
Wang, Zhi-Bin; Wang, Zhi-Gang
2016-07-01
In this article, we calculate the contributions of the condensates up to dimension-6, including the one-loop corrections to the quark condensates, in the operator product expansion in a consistent way, and study the masses and decay constants of the heavy pseudoscalar mesons with the thermal QCD sum rules. We reproduce the experimental values of the masses of the D, D s , B and B s and obtain the decay constants at zero temperature. Then we study the thermal behaviors of the masses and decay constants, which are useful in explaining the heavy-ion collision experiments.
Sum rule study of new vibrational modes of excitation in halo nuclei
International Nuclear Information System (INIS)
Sum rules are applied to studying soft multipole excitations in halo nuclei. The soft modes are considered as relative oscillations between the halo neutrons and the core part of a halo nucleus. It is shown by using the di-neutron cluster model that the excitation energies depend linearly on the separation energy of halo neutrons, while the transition strengths are inversely proportional to the separation energy. These relationships hold qualitatively in the independent particle model. An analytic formula for the transition density is obtained for the dipole mode and compared with the results of microscopic RPA calculations. (author) 27 refs., 2 figs
Normalization sum rule and spontaneous breaking of U(N) invariance in random matrix ensembles
International Nuclear Information System (INIS)
It is shown that the two-level correlation function R(s,s') in the invariant random matrix ensembles (RME) with soft confinement exhibits a ''ghost peak'' at s approx. -s'. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term var(n) = ηn that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, η playing the role of an order-parameter. (author). 16 refs, 1 fig
The F/D ratio and meson-baryon couplings from QCD sum rules, 2
Kim, H; Oka, M; Lee, S H; Kim, Hungchong; Doi, Takumi; Oka, Makoto; Lee, Su Houng
2000-01-01
Using QCD sum rules, we compute the diagonal meson-baryon couplings, $\\piNN$, $\\eta NN$, $\\pi \\Xi\\Xi$, $\\eta \\Xi\\Xi$, $\\pi \\Sigma \\Sigma$ and $\\eta\\Sigma \\Sigma$, from the baryon-baryon correlation function with a meson,$i\\int d^4x e^{iq\\cdot x} $. The calculationsare performed to leading order in $p_\\mu$ by considering the two separate Diracstructures, $i \\gamma_5 \\gamma_\\mu p^\\mu$ and $\\gamma_5 \\sigma_{\\mu \
Sum rules for meson and baryon production in the quark recombination model
International Nuclear Information System (INIS)
A quark-recombination model with quark distributions according to a generalized Kuti-Weisskopf model is used. Mesons are formed by v-s (valence-sea) and s-s recombination, baryons by vvv, vvs, vss and sss recombination. Sum rules for energy momentum conservation, baryon number, valence and sea quarks are shown to constrain the recombination parameters of the model significantly. The resulting model is consistent with experimental data. While the sss recombination into baryons is found to be quite normal we find a strong enhancement of ss recombination into mesons. This enhanced ss term represents in the model the central meson production via gluons. (author)
Analysis of 1/2+ baryon states containing fourth-family quarks from QCD sum rules
Institute of Scientific and Technical Information of China (English)
YOU Fu-Yi; WANG Zhi-Gang; WAN Shao-Long
2012-01-01
When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks,the hadrons made up from these quarks can be long-lived enough.We analyze the 1/2+ baryon statescontaining fourth-generation quarks and standard-model quarks,i.e.the charm or bottom quarks,in the QCD sum rules approach.Considering the perturbative and two gluon condensate contributions in the calculation,we give the numerical results of the masses and pole residues.
Subtracted Dispersion Relations for In-medium Meson Correlators in QCD Sum Rules
International Nuclear Information System (INIS)
We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out that importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of the vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels of the Fermi gas of nucleons. (author)
Bath-symmetries and hybridization sum-rules for CDMFT and DCA
International Nuclear Information System (INIS)
In the Hamiltonian formulation of CDMFT and DCA, the point symmetries of the cluster imply symmetries of the hybridization, which can substantially reduce the number of independent parameters to fit the bath Green function. We review these symmetries and derive general sum-rules for the hybridizations, which allow to check the quality of a fit using a finite set of bath sites and imply what hybridizations vanish. As examples we discuss calculations for the Hubbard model in one-dimension and for 2 x 2 clusters
The relation between the photonuclear E1 sum rule and the effective orbital g-factor
Bentz, W
2004-01-01
The connection between the enhancement factor (1+kappa) of the photonuclear E1 sum rule and the orbital angular momentum g-factor (gl) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the kappa-gl relation. By identifying the physical processes which are taken into account in kappa and gl, the validity and limitations of this relation are discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown.
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Aliev, T M
2015-01-01
The magnetic moment of the $\\Lambda \\to \\Sigma^0$ transition between negative parity, baryons is calculated in framework of the QCD sum rules approach, using the general form of the interpolating currents. The pollution arising from the positive--to--positive, and positive to negative parity baryons are eliminated by constructing the sum rules for different Lorentz structures. Nonzero value of the considered magnetic moment can be attributed to the violation of the $SU(3)$ symmetry.
Density of states and Friedel sum rule in one- and quasi-one-dimensional wires
International Nuclear Information System (INIS)
We analyze the relation between the density of states obtained from the energy derivative of the Friedel phase and that obtained from the Green's function of one- and quasi-one-dimensional wires with a double δ-potential. In the case of repulsive δ-potentials (in both one- and quasi-one-dimension), we show that the local Friedel sum rule is valid when a correction term is included. Various properties of the one-dimensional local density of states are also discussed. In the case of attractive δ-potentials in a quasi-one-dimensional wire, it is well known that the transmission probability may exhibit a Fano resonance (due to a zero-pole pair). In this case, we show that the local Friedel sum rule is valid provided that the tail of the quasibound state is taken into account by the integrated local density of states. In addition, we show that the density of states in a Fano resonance always has a Lorentz shape with peak position at the resonance energy regardless of the (Fano) asymmetry parameter.
Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the $C\\gamma_5\\otimes \\gamma_5C$ type and $C\\otimes C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $M_{C\\gamma_5\\otimes \\gamma_5C}=3.89\\pm 0.05\\,\\rm{GeV}$ and $M_{C\\otimes C}=5.48\\pm0.10\\,\\rm{GeV}$ support assigning the $X(3915)$ to be the ground state $C\\gamma_5\\otimes \\gamma_5C$ type tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the $X(4700)$ to be the ground state $C\\otimes C$ type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$ and $X(4500)$ to be the 1S and 2S $C\\gamma_5\\otimes \\gamma_5C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states respectively, and obtain the 1S mass $M_{\\rm 1S}=3.85^{+0.18}_{-0.17}\\,\\rm{GeV}$ and 2S mass $M_{\\rm 2S}=4.35^{+0.10}_{-0.11}\\,\\rm{GeV}$ from the QCD sum rules, which support assigning the $X(3915)$ to be the 1S $C\\gamma_5\\oti...
XYZ-like Spectra from Laplace Sum Rule at N2LO in the Chiral Limit
Albuquerque, R; Fanomezana, F; Rabemananjara, A; Rabetiarivony, D; Randriamanatrika, G
2016-01-01
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-like states at lowest order (LO) of perturbative (PT) QCD and up to $d=8$ condensates of the Operator Product Expansion (OPE). Then, we improve previous LO results from QCD spectral sum rules (QSSR), on the $XYZ$-like masses and decay constants (which suffer from the ill-defined heavy quark mass) by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria with respect to the variations of the $\\tau$-Laplace sum rule (LSR) variable, QCD continuum threshold $t_c $ and subtraction constant $\\mu$ are summarized in Tables 11 to 14. We conclude that the masses of the $XZ$ observed states are compatible with (almost) pure $J^{PC}=1^{...
Sum rules for interaction of $\\Upsilon$ resonances with $Z_b \\pi$
Voloshin, M B
2016-01-01
The strength of the amplitudes for the coupling between the bottomonium $\\Upsilon(nS)$ states, the bottomonium-like isovector resonances $Z_b$ and a pion, $\\Upsilon(nS) Z_b \\pi$, is considered. These amplitudes describe the decays $Z_b \\to \\Upsilon(nS) \\pi$ for $n=1,\\,2,\\,3$, and the processes $\\Upsilon(nS) \\to Z_b \\pi$ for $n=5,\\,6, \\ldots$ with either $Z_b(10610)$ or $Z_b(10650)$. It is pointed out that analyticity and unitarity impose a sum rule for these couplings to each of the $Z_b$ resonances. With the currently available data it appears to be difficult or impossible to simultaneously satisfy the sum rules for the $Z_b(10610)$ and $Z_b(10650)$ resonances. This difficulty can be resolved if there is a considerable dissimilarity in the yield of the states $Z_b(10610) \\pi$ and $Z_b(10650) \\pi$ in the $e^+e^-$ annihilation at energies above the $\\Upsilon(5S)$ resonance.
Study of the $D^*\\rho$ system using QCD sum rules
Torres, A Martinez; Nielsen, M; Navarra, F S; Oset, E
2013-01-01
In this talk I present a study of the $D^* \\rho$ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three $D^*$ mesons with isospin $I=1/2$, spin $S=0$, $1$, $2$ and with masses $2500\\pm 67$ MeV, $2523\\pm60$ MeV, and $2439\\pm119$ MeV, respectively. The last state can be related to $D^*_2(2460)$ (spin 2) listed by the Particle Data Group, while one of the first two might be associated with $D^*(2640)$, whose spin-parity is unknown. In the case of $I=3/2$ we also find evidences of three states with spin 0, 1 and 2, respectively, with masses $2467\\pm82$ MeV, $2420\\pm128$ MeV, and $2550\\pm56$ MeV.
Equivalence of post and prior sum rules for inclusive breakup reactions
International Nuclear Information System (INIS)
A critical examination of sum rules derived previously by Austern and Vincent (post form) and by Udagawa and Tamura (prior form) demonstrates that agreement between the two approaches is obtained if certain approximations implicit in the Udagawa-Tamura prior-form derivation are avoided. We examine the relation of the two approaches to singularities of the post-form distorted wave Born approximation matrix element and to the procedures for reduction of a many-body theory by use of effective operators in a model space. The two-step heuristic model is seen to be invalid for prior-form inelastic breakup; it is necessary to take account of nuclear excitations during projectile breakup. Careful treatment of the non-Hermiticity of kinetic energy operators with respect to continuum wave functions is required
Reanalysis of the (0+, 1+) states Bs1 with QCD sum rules
International Nuclear Information System (INIS)
We calculate the masses and decay constants of the P-wave strange-bottomed mesons Bs0 and Bs1 with the QCD sum rules, and observe that the central values of the masses Bs0 and Bs1 are smaller than the corresponding BK and B*K thresholds respectively, the strong decays Bs0→ BK and Bs1 → B*K are kinematically forbidden. They can decay through the isospin violation processes Bs0 → Bsη → BaΠ0 and Bs1 → Bs*η → Bs*π0. The bottomed mesons Bs0 and Bs1, just like their charmed cousins Ds0 (2317) and Ds1 (2460), may be very narrow. (author)
International Nuclear Information System (INIS)
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them
Understanding close-lying exotic charmonia states within QCD sum rules
Torres, A Martínez; Dias, J M; Navarra, F S; Nielsen, M
2016-01-01
Motivated by the experimental findings of some new exotic states decaying into channels like $J/\\psi$-phi, we investigate the formation of resonances/bound states in the $D^*_s\\bar D^*_s$ system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass varying in the range 3.8-4.2 GeV. Although the conditions of Borel stability, convergence of the OPE series and pole dominance are all well satisfied, we find the interpretation of the obtained results to be challenging.
D+→η(')l+νl semileptonic decays in light-cone sum rules
Institute of Scientific and Technical Information of China (English)
LI Jing-Wu; XUE Dan-Qing; XU Qing-Qiang; WU Xiang-Yao
2011-01-01
We calculate the D→η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D →η lν decays with the experimental data. By comparing the difference between the results of the branching ratios of D+ →ηlν from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η' mixing angle from the dependence of the branching ratios of D →ηlν decays on the η-η' mixing angle.
Searching for hidden-charm baryonium signals in QCD sum rules
Chen, Hua-Xing; Chen, Wei; Liu, Xiang; Zhu, Shi-Lin
2016-01-01
We give an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content $u\\bar u d\\bar d c\\bar c$, spin $J=0/1/2/3$, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, and find that these currents can couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion. The masses of the lowest-lying hidden-charm baryonium states with quantum numbers $J^P=2^-/3^-/0^+/1^+/2^+$ are evaluated to be around 5.0 GeV, so we suggest to search for hidden-charm baryonium states in the $D$-wave $J/\\psi \\pi \\pi$ and $S$-wave $J/\\psi \\rho$ and $J/\\psi \\omega$ channels in this energy region.
Parity-Violating Nuclear Force as derived from QCD Sum Rules
Hwang, W-Y P
2008-01-01
Parity-violating nuclear force, as may be accessed from parity violation studies in nuclear systems, represents an area of nonleptonic weak interactions which has been the subject of experimental investigations for several decades. In the simple meson-exchange picture, parity-violating nuclear force may be parameterized as arising from exchange of \\pi, \\rho, \\omega, or other meson(s) with strong meson-nucleon coupling at one vertex and weak parity-violating meson-nucleon coupling at the other vertex. The QCD sum rule method allows for a fairly complicated, but nevertheless straightforward, leading-order loop-contribution determination of the various parity-violating MNN couplings starting from QCD (with the nontrivial vacuum) and Glashow-Salam-Weinberg electroweak theory. We continue our earlier investigation of parity-violating \\pi NN coupling (by Henley, Hwang, and Kisslinger) to other parity-violating couplings. Our predictions are in reasonable overall agreement with the results estimated on phenomenologi...
QCD sum rule study of a charged bottom-strange scalar meson
Zanetti, C. M.; Nielsen, M.; Khemchandani, K. P.
2016-05-01
Using the QCD sum rule approach, we investigate the possible four-quark structure for the new observed Bs0π± narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of ms in full QCD, without relying on 1 /mQ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.
Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we take the $X(4140)$ as the diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass and pole residue with the QCD sum rules in details by constructing two types interpolating currents. The numerical results $M_{X_{L,+}}=3.95\\pm0.09\\,\\rm{GeV}$ and $M_{X_{H,+}}=5.00\\pm0.10\\,\\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type tetraquark state. Furthermore, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark states as a byproduct. The present predictions can be confronted to the experimental data in the future.
Exlusive radiative B-decays in the light-cone QCD sum rule approach
International Nuclear Information System (INIS)
We carry out a detailed study of exclusive radiative rare B-decays in the framework of the QCD sum rules on the light cone, which combines the traditional QCD sum rule technique with the description of final state vector mesons in terms of the light-cone wave functions of increasing twist. Our calculation is restricted to the leading twist-two operators. The decays considered are: Bu,d → K' + γ, Bu,d → ρ + γ, Bd → ω + γ and the corresponding decays of the Bs mesons, Bs → Φ + γ and Bs → K' + γ. Based on our estimate of the transition form factor F1B→K'(0) = 0.32 ± 0.05, we find for the branching ratio BR(B → K' + γ) = (4.8 ± 1.5) x 10-5, which is in agreement with the observed value of (4.5 ± 1.5 ± 0.9) x 10-5 measured by the CLEO collaboration. We present detailed estimates for the ratios of the radiative decay form factors, which are then used to predict the rates for the exclusive radiative B-decays listed above. This in principle allows the extraction of the CKM matrix element vertical stroke Vtdvertical stroke from the penguin-dominated CKM-suppressed radiative decays when they are measured. We give a detailed discussion of the dependence of the radiative transition form factors on the b-quark mass and on the momentum transfer, as well as their interrelation with the CKM-suppressed semileptonic decay form factors in B → ρ + l + νl, which we also calculate in our approach. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes; Falcioni, Giulio; Freitas, Abilio de
2016-05-15
We calculate analytically the flavor non-singlet O(α{sup 2}{sub s}) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F{sup ep}{sub 1,2,L}(x, Q{sup 2}) and g{sup ep}{sub 1,2}(x, Q{sup 2}) and charged current non-singlet structure functions F{sup ν(anti} {sup ν)p}{sub 1,2,3}(x, Q{sup 2}), at general virtualities Q{sup 2} in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q{sup 2} and the effects of the power corrections due to the heavy quark mass are of the size of the known O(α{sup 2}{sub s}) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q{sup 2} >> m{sup 2}{sub c,b}. We also study the target mass corrections to the above sum rules.
BcBcJ/ψ vertex form factor at finite temperature in the framework of QCD sum rules approach
International Nuclear Information System (INIS)
The strong form factor of the BcBcJ/ψ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T ≅ 100 MeV but slightly increases after this point. After T ≅ 160 MeV, the form factor suddenly decreases up to T ≅ 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q2 = -m2offshell at T = 0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments. (orig.)
Lower and upper bounds on the mass of light quark-antiquark scalar resonance in the SVZ sum rules
Afonin, S S
2016-01-01
The calculation of the mass of light scalar isosinglet meson within the Shifman--Vainshtein--Zakharov (SVZ) sum rules is revisited. We develop simple analytical methods for estimation of hadron masses in the SVZ approach and try to reveal the origin of their numerical values. The calculations of hadron parameters in the SVZ sum rules are known to be heavily based on a choice of the perturbative threshold. This choice requires some important ad hoc information. We show analytically that the scalar mass under consideration has a lower and upper bound which are independent of this choice. The lower limit lies around the $\\omega$-meson mass and the upper one does near the $f_1$-meson mass. Our analysis seems to finally exclude the interpretation of the $f_0(500)$ (called also $\\sigma$) meson as a quark-antiquark state in the SVZ sum rules.
Magnetic moment for the negative parity Λ→Σ0 transition in light cone QCD sum rules
Directory of Open Access Journals (Sweden)
T.M. Aliev
2016-07-01
Full Text Available The magnetic moment of the Λ→Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
gDsDK*0 and gBsDK*0 coupling constants in QCD sum rules
International Nuclear Information System (INIS)
In the present study, we calculate the strong coupling constants gDsDK*0(800) and gBsDK*0(800) within the three-point QCD sum rules approach. We evaluate the correlation function of the considered vertices taking into account both D[B] and K*0(800) mesons as off-shell states.
D^＋→η^（＇）l＋ν_l semileptonic decays in light-cone sum rules
Institute of Scientific and Technical Information of China (English)
李竞武; 薛丹青; 除庆强; 吴向尧
2011-01-01
We calculate the D → η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D＋ → η^（＇）l＋νl decays with the experimental data. By compa
Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang
2013-01-01
In this article,we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way,and make reasonable predictions for their masses in the vacuum and in the nuclear matter.
QCD sum rule analysis for light vector and axial-vector mesons in vacuum and nuclear matter
Leupold, Stefan
2001-01-01
Extending previous work we study the constraints of QCD sum rules on mass and width of light vector and axial-vector mesons in vacuum and in a medium with finite nuclear density. For the latter case especially the effect of nuclear pions leading to vector-axial-vector mixing is included in the analysis.
Renormalization group improved bottom mass from Υ sum rules at NNLL order
International Nuclear Information System (INIS)
We determine the bottom quark mass from non-relativistic large-n Υ sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of αs ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic αs ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling (αs(MZ)=0.1183±0.0010) we obtain Mb1S=4.755±0.057pert ±0.009αs±0.003exp GeV for the bottom 1S mass and anti mb(anti mb)=4.235±0.055pert±0.003exp GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.
Infrared Refractive Index of Silicon: Parity and Sum-Rule Tests
Karstens, William; Inokuti, Mitio; Smith, David Y.
2012-02-01
We have resolved conflicting reports for the IR refractive index of silicon using general considerations of linear response theory. We find that use of unphysical series expansions in the analysis of channel spectra has been a significant source of systematic error. Recognition that the index is an even function of photon energy is crucial for analysis of these measurements and clarifies data presentation. In the region of high IR transparency of elemental semiconductors, the index may be expanded in a rapidly convergent Taylor series. Coefficients of terms in the (2n)^th power of energy are proportional to the (2n+1)^th inverse moment of the electronic absorption spectrum. In the favorable case of intrinsic Si, the electronic absorption is sufficiently well known that independent values of the intercept, slope and curvature of plots of index vs. the square of photon energy may be calculated. Index data sets with parameters significantly different from these suffer from systematic errors or refer to impure samples. Using these parity and sum-rule tests we have prepared a composite index data set for intrinsic silicon that represents a best fit to reliable measurements from microwaves to the visible. Applications to germanium and diamond will be discussed.
Analysis of the semileptonic Bc → D10 transition in QCD sum rules and HQET
International Nuclear Information System (INIS)
We investigate the structure of the D10(2420 [2430])(JP = 1+) mesons via analyzing the semileptonic Bc → D10lν transition in the frame work of the three-point QCD sum rules and the heavy-quark effective theory. We consider the D10 meson in three ways: as a pure vertical stroke c anti u right angle state, as a mixture of the two vertical stroke 3P1 right angle and vertical stroke 1P1 right angle states with a mixing angle θ, and as a combination of the two mentioned states with mixing angle θ = 35.3 circle in the heavy-quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the three above conditions. These form factors are numerically calculated for vertical stroke c anti u right angle and the heavy-quark limit cases. The obtained results for the form factors are used to evaluate the decay rates and the branching ratios. Also for mixed states, all of the mentioned physical quantities are plotted with respect to the unknown mixing angle θ. (orig.)
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
Baru, V; Hoferichter, M; Kubis, B; Nogga, A; Phillips, D R
2011-01-01
We use chiral perturbation theory (ChPT) to calculate the $\\pi^- d$ scattering length with an accuracy of a few percent, including isospin-violating corrections both in the two- and three-body sector. In particular, we provide the technical details of a recent letter, where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths $a^+$ and $a^-$. We study isospin-breaking contributions to the three-body part of $a_{\\pi^-d}$ due to mass differences, isospin violation in the $\\pi N$ scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in $a_{\\pi^- d}$ due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the p...
Yaouanc, Alain Le
2014-01-01
We first discuss Uraltsev's and other sum rules constraining the $B \\to D^{**}(L=1)$ weak transitions in the infinite mass limit, and compare them with dynamical approaches in the same limit. After recalling these well established facts, we discuss how to apply infinite mass limit to the physical situation. We provide predictions concerning semi-leptonic decays and non-leptonic ones, based on quark models. We then present in more detail the dynamical approaches: the relativistic quark model \\`a la Bakamjian-Thomas and lattice QCD. We summarise lattice QCD results in the infinite mass limit and compare them to the quark model predictions. We then present preliminary lattice QCD results with finite $b$ and $c$ quark masses. A systematic comparison between theory and experiment is performed. We show that some large discrepancies exist between different experiments. Altogether the predictions at infinite mass are in fair agreement with experiment for non-leptonic decays contrary to what happens for semileptonic d...
Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA
Bohr, Jakob
2013-01-01
The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Molecules that are intrinsically chiral, such as double-stranded DNA, is one example. They exhibit a non-vanishing strain-twist coupling, which depends on the local geometry, i.e. on curvature and torsion, yet the paths of closed loops are restricted by White's theorem. We suggest that the reciprocation of these principles leads to a twist neutrality condition. I.e. to a zero sum rule for the incremental change in the rate of winding along the curve. This has direct implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. A first estimate of this minimum length is 120 base pairs. This is not far from the 80 base pairs which is about the smallest length observed in experimental studies. Slightly longer microDNAs are better described as an ellipse and a relationship between length and eccentricity for these ...
Charm-quark mass from weighted finite energy QCD sum rules
Bodenstein, S; Dominguez, C A; Peñarrocha, J; Schilcher, K
2010-01-01
The running charm-quark mass in the $\\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three diffe...
B→γeν transitions from QCD sum rules on the light-cone
International Nuclear Information System (INIS)
B→γeν transitions have recently been studied in the framework of QCD factorization. The attractiveness of this channel for such an analysis lies in the fact that, at least in the heavy quark limit, the only hadron involved is the B meson itself, so one expects a very simple description of the form factor in terms of a convolution of the B meson distribution amplitude with a perturbative kernel. This description, however, does not include contributions suppressed by powers of the b quark mass. In this letter, we calculate corrections to the factorized expression which are induced by the 'soft' hadronic component of the photon. We demonstrate that the power-suppression of these terms is numerically not effective for physical values of the b quark mass and that they increase the form factor by about 30% at zero momentum transfer. We also derive a sum rule for λB, the first negative moment of the B meson distribution amplitude, and find λB=0.6 GeV (to leading order in QCD). (author)
Parity-violating nuclear force as derived from QCD sum rules
Hwang, W.-Y. P.; Wen, Chih-Yi
2008-08-01
Parity-violating nuclear force, as may be accessed from parity-violation studies in nuclear systems, represents an area of nonleptonic weak interactions that has been the subject of experimental investigations for several decades. In the simple meson-exchange picture, a parity-violating nuclear force may be parametrized as arising from the exchange of π,ρ,ω, or other mesons with strong meson-nucleon coupling at one vertex and weak parity-violating meson-nucleon coupling at the other vertex. The QCD sum rule method allows for a fairly complicated, but nevertheless straightforward, leading-order loop-contribution determination of the various parity-violating MNN couplings starting from QCD (with the nontrivial vacuum) and Glashow-Salam-Weinberg electroweak theory. We continue our earlier investigation of the parity-violating πNN coupling (by Henley, Hwang, and Kisslinger) to other parity-violating couplings. Our predictions are in reasonable overall agreement with the results estimated on phenomenological grounds, such as in the now classic paper of Desplanques, Donoghue, and Holstein, in the global experimental fit of Adelberger and Haxton, or the effective field theory thinking of Ramsey-Musolf and Page.
Mass modification of /D-meson at finite density in QCD sum rule
Hayashigaki1, A.
2000-08-01
We evaluate the mass shift of isospin-averaged /D-meson in the nuclear medium. Borel-transformed QCD sum rules are used to describe an interaction between the /D-meson and a nucleon by taking into account all the lowest dimension-4 operators in the operator product expansion (OPE). We find at normal matter density the /D-meson mass shift is about /10 times (/~50 MeV) larger than that of /J/ψ. This originates from the fact that the dominant contribution in the OPE for the /D-meson is the nucleon matrix element of mcq¯q, where mc is the charm-quark mass and /q denotes light quarks. We also discuss that the mass shift of the /D-meson in nuclear matter may cause the level crossings of the charmonium states and the /DD¯ threshold. This suggests an additional mechanism of the /J/ψ suppression in high energy heavy-ion collisions.
Light quark masses from QCD sum rules with minimal hadronic bias
Domínguez, C A; Röntsch, R H; Schilcher, R
2009-01-01
The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are $m_u(Q= 2 {GeV}) = 2.9 \\pm 0.2 {MeV}$, $m_d(Q= 2 {GeV}) = 5.3 \\pm 0.4 {MeV}$, and $m_s(Q= 2 {GeV}) = 102 \\pm 8 {MeV}$, for $\\Lambda = 381 \\pm 16 {MeV}$, corresponding to $\\alpha_s(M_\\tau^2) = 0.344 \\pm0.009$. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in $\\Lambda$, the unknown six-loop PQ...
Light quark masses from QCD sum rules with minimal hadronic bias
Energy Technology Data Exchange (ETDEWEB)
Dominguez, C.A. [Centre for Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700 (South Africa); Department of Physics, Stellenbosch University, Stellenbosch 7600 (South Africa); Nasrallah, N.F. [Faculty of Science, Lebanese University, Tripoli (Lebanon); Roentsch, R.H. [Centre for Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700 (South Africa); Schilcher, K. [Institut fuer Physik, Johannes Gutenberg-Universitaet, Staudingerweg 7, D-55099 Mainz (Germany)
2009-01-15
The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are m{sub u}(Q=2 GeV)=2.9{+-}0.2 MeV, m{sub d}(Q=2 GeV)=5.3{+-}0.4 MeV, and m{sub s}(Q=2 GeV)=102{+-}8 MeV, for {lambda}=381{+-}16 MeV, corresponding to {alpha}{sub s}(M{sub {tau}}{sup 2})=0.344{+-}0.009. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in {lambda}, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement.
Renormalization group improved bottom mass from {Upsilon} sum rules at NNLL order
Energy Technology Data Exchange (ETDEWEB)
Hoang, Andre H.; Stahlhofen, Maximilian [Wien Univ. (Austria). Fakultaet fuer Physik; Ruiz-Femenia, Pedro [Wien Univ. (Austria). Fakultaet fuer Physik; Valencia Univ. - CSIC (Spain). IFIC
2012-09-15
We determine the bottom quark mass from non-relativistic large-n {Upsilon} sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of {alpha}{sub s} ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic {alpha}{sub s} ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling ({alpha}{sub s}(M{sub Z})=0.1183{+-}0.0010) we obtain M{sub b}{sup 1S}=4.755{+-}0.057{sub pert} {+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.
Precise f_{D*,B*} and f_{B_c} from QCD spectral sum rules
Narison, Stephan
2014-01-01
Anticipating future precise measurements of the B-like leptonic decays for alternative determinations of the CKM mixing angles or/and for predicting their semi-leptonic and hadronic decays, we pursue our program on the B-like mesons by improving the estimates of f_D* and f_B* [analogue to f_\\pi=130.4(2) MeV] using suitable ratios of the well-established (inverse) Laplace sum rules less affected by the systematics and known to N2LO pQCD and where the full d=6 non-perturbative condensate contributions are included. An estimate of the N3LO terms based on geometric growth of the pQCD series is included in the error calculations. Our optimal results based on stability criteria and on an (in)dependence on the choice of the QCD subtraction point read: f_D*/f_D=1.209(22),f_B*/f_B=1.031(8) which imply : f_D*=246(7) MeV and f_B*=212(8) MeV if we use our recent results in [1] for f_D and f_B. We complete the analysis by a direct estimate of f_Bc using the complete NLO + N2LO for massless m_c pQCD expression and complete...
Sum rules for B(M1,01+→1+) strength in IBM-3 and IBM-4
International Nuclear Information System (INIS)
Sum rules for B(M1,01+→1i+) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U(3) and U(6) contains SU(4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins. In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B(M1,01+→1i+) is given. (author)
Sum Rules for B(M1,0+ -> 1+) Strength in IBM-3 and IBM-4
Halse, P.; Van Isacker, P.; Barrett, B. R.
1995-01-01
Sum rules for $B(M1,0^+_1\\rightarrow1^+_i)$ strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin $U$(3) and $U(6)\\supset SU$(4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and $SU(4)$ representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of ...
Becirevic, D; Le Yaouanc, A; Oliver, L; Pène, O; Raynal, J C
2003-01-01
The introduction of an explicit negative radial excitation contribution in the hadronic side of the light cone QCD sum rule (LCSR) of Belyaev, Braun, Khodjamirian and Ruckl, can explain the large experimental value of g(D*Dpi), recently measured by CLEO. At the same time, it considerably improves the stability of the sum rule when varying the Borel parameter.
Energy Technology Data Exchange (ETDEWEB)
Peters, Gerhard
2008-05-15
In this work the leading-twist next-to-leading order (NLO) correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon are calculated. Here the Ioffe nucleon interpolation current is used and it is worked in the M{sub N}=0 approximation, with M{sub N} being the mass of the nucleon. In this approximation, only the Pauli form factor F{sub 2} receives a correction and the calculated correction is quite sizable. The numerical results for the proton form factors show the improved agreement with the experimental data. Furthermore the problems encountered when going away from M{sub N}=0 approximation at NLO, as well as, gauge invariance of the perturbative results are discussed. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors. (orig.)
International Nuclear Information System (INIS)
The distribution of the total transition strength, i.e. the right hand side of the integral form of Thomas–Reiche–Kuhn sum rule, into individual absorption processes is described for crystalline silicon containing interstitial oxygen. Utilization of the sum rule allows the construction of a dispersion model covering all elementary excitations from phonon absorption to core electron excitations. The dependence of transition strength of individual electronic and phonon contributions on temperature and oxygen content is described. - Highlights: • Distribution of transition strength for c-Si containing interstitial oxygen • Temperature dependence of transition strength of individual contributions • Dependence of transition strength on concentration of interstitial oxygen • Consideration of interband electronic transitions, free carriers, and phonons
How Precisely can we Determine the $\\piNN$ Coupling Constant from the Isovector GMO Sum Rule?
Loiseau, B; Thomas, A W
1999-01-01
The isovector GMO sum rule for zero energy forward pion-nucleon scattering iscritically studied to obtain the charged pion-nucleon coupling constant usingthe precise negatively charged pion-proton and pion-deuteron scattering lengthsdeduced recently from pionic atom experiments. This direct determination leadsto a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09(statistic) +- 0.17 (systematic). We obtain also accurate values for thepion-nucleon scattering lengths.
Decays D → Kev, D → K*ev, D → πev in QCD sum rules method
International Nuclear Information System (INIS)
The form factors of the semileptonic decays D → Kev, D → K*ev, D → πev are calculated by means of the QCD sum rules method for the three-point correlators. The decay widths are obtained. Our results agree with the experimental data within the theoretical and the experimental uncertainties involved. The restriction on the Kobayashi-Maskava matrix elements Vcs, Vcd are found. (author). 22 refs, 1 fig
The Q2-Dependence of the Gross-Llewellyn Smith Sum Rule and of the Parton Distributions
International Nuclear Information System (INIS)
We describe the results of our recent work on the determination of the value of the parameter Λ and of the Q2-dependence of the Gross-Llewellyn Smith (GLS) sum rule from the experimental data of the CCFR collaboration on neutrino-nucleon deep inelastic scattering, using the Jacobi polynomials QCD analysis. The new information on the Q2-dependence of the parton distributions is presented. 37 refs., 3 figs., 3 tabs
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.; Rittinger, J.
2012-01-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available...
General proof of the saturation of the Adler-Weisberger sum rule in a quark shell model
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The exact saturation of the Adler-Weisberger sum rule is demonstrated in a model of Dirac particles bound by a central potential. We use a method similar in spirit to the P→infinity approach, suitably modified to deal with a static potential. The pair contribution corresponding to exotic intermediate states is shown to be nonvanishing, but in a nonrelativistic expansion it vanishes order by order as found in low orders by the approach of the previous paper
Determination of αs from Gross-Llewellyn Smith sum rule by accounting for infrared renormalon
International Nuclear Information System (INIS)
We recapitulate the method which resums the truncated perturbation series of a physical observable in a way which takes into account the structure of the leading infrared renormalon. We apply the method to the Gross-Llewellyn Smith (GLS) sum rule. By confronting the obtained result with the experimentally extracted GLS value, we determine the value of the QCD coupling parameter, which turns out to agree with the present world average
Majewski, M
2003-01-01
Mass formulae for light meson multiplets derived by means of the exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the CMSR give the well known mass formulae for real masses (Gell-Mann-Okubo, Schwinger and ideal mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths - width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for the S nonet that the points (m,GAMMA) form a rectilinear stitch (RS) on the complex mass plane. For low-mass nonets the WSR are strongly violated due to ''kinematical'' suppression of the particle decays, but the violation decreases as the mass increases and disappears above propor to 1.5 GeV. The slope k sub s of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value -0.5. If k sub s is known for a nonet, w...
A QCD sum rule calculation of the X± (5568) → Bs0 π± decay width
Dias, J. M.; Khemchandani, K. P.; Martínez Torres, A.; Nielsen, M.; Zanetti, C. M.
2016-07-01
To understand the nature of the X (5568), recently observed in the mass spectrum of the Bs0 π± system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. We found that it is possible to obtain a stable value of the mass compatible with the D0 result, although a rigorous QCD sum rule constrained analysis led to a higher value of mass. As a continuation of our investigation, we calculate the width of the tetraquark state with same quark content as X (5568), to the channel Bs0 π±, using the three-point QCD sum rule. We obtain a value of (20.4 ± 8.7) MeV for the mass ∼ 5568 MeV, which is compatible with the experimental value of 21.9 ± 6.4 (sta)-2.5+5.0 (syst) MeV /c2. We find that the decay width to Bs0 π± does not alter much for a higher mass state.
Lattice QCD and QCD sum rule determination of the decay constants of ηc, J/ψ and hc states
Bečirević, Damir; Duplančić, Goran; Klajn, Bruno; Melić, Blaženka; Sanﬁlippo, Francesco
2014-01-01
We compute the decay constants of the lowest cc¯ -states with quantum numbers JPC=0−+ ( ηc ), 1−− ( J/ψ ), and 1+− ( hc ) by using lattice QCD and QCD sum rules. We consider the coupling of J/ψ to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched ( Nf=2 ) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate...
Sum rule measurements of the spin-dependent compton amplitude (nucleon spin structure at Q2 = 0)
International Nuclear Information System (INIS)
Energy weighted integrals of the difference in helicity-dependent photo-production cross sections (σ1/2 - σ3/2) provide information on the nucleon's Spin-dependent Polarizability (γ), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. (The latter forms the Q2=0 limit of recent spin-asymmetry experiments in deep-inelastic lepton-scattering.) There are no direct measurements of σ1/2 or σ3/2, for either the proton or the neutron. Estimates from current π-photo-production multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-l-loop Chiral calculations (χPT) for γ but predict large deviations from the DHG sum rule. Either (a) both the 2-loop corrections to the Spin-Polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon. The helicity-dependent photo-reaction amplitudes, for both the proton and the neutron, will be measured at LEGS from pion-threshold to 470 MeV. In these double-polarization experiments, circularly polarized photons from LEGS will be used with SPHICE, a new frozen-spin target consisting of rvec H · rvec D in the solid phase. Reaction channels will be identified in SASY, a large detector array covering about 80% of 4π. A high degree of symmetry in both target and detector will be used to minimize systematic uncertainties
Semiclassical interpretation of an M1 sum rule derived within the interacting boson model
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A summed M1 strength of the scissors mode derived within the proton-neutron interacting boson model under the assumption of F-spin symmetry is expressed in terms of classical quantities borrowed from the two-rotor model. In this classical form, the M1 strength shows explicitly a quadratic dependence on deformation in agreement with experiments. copyright 1996 The American Physical Society
Investigation of the D*s2(2573)+D+K0 vertex via QCD sum rules
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In this work the D*s2(2573)+D+K0 vertex is studied and the coupling constant corresponding to the D*s2(2573)+ → D+K0 transition is calculated. The calculation is performed using three point QCD sum rules method and the value of the coupling constant is obtained as gD*s2DK = (12.85 ± 3.85) GeV−1. The coupling constant is also used to calculate the decay width and the branching ratio of the considered transition
Calculation of the K^0-\\bar{K}^0 mixing parameter via the QCD sum rules at finite energies
Chetyrkin, K. G.; Kataev, A. L.; Krasulin, A. B.; Pivovarov, A. A.
2001-01-01
The QCD finite energy sum rules method is used to show that the parameter of the K^0-\\bar{K}_0 mixing \\hat{B} is mainly determined by the value of g m_s and the vacuum expectation values of four-quark operators. Assuming the hypothesis of vacuum dominance and/or unitarity symmetry to estimate latter, it is found that \\hat{B}=1.2\\pm 0.1. (The updated (March 2001) prediction reads \\hat{B} = 1.0 +- 0.1 (for more details, see Comments after the main text).
The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule
Garbali, A.; Nienhuis, B.
2014-01-01
This is the second part of our study of the ground state eigenvector of the transfer matrix of the dilute Temperley-Lieb loop model with the loop weight $n=1$ on a semi infinite strip of width $L$. We focus here on the computation of the normalization (otherwise called the sum rule) $Z_L$ of the ground state eigenvector, which is also the partition function of the critical site percolation model. The normalization $Z_L$ is a symmetric polynomial in the inhomogeneities of the lattice $z_1,..,z...
Strong coupling constant of hb vector to the pseudoscalar and vector Bc mesons in QCD sum rules
International Nuclear Information System (INIS)
The strong coupling constant ghbBcPSBcV is calculated using the three-point QCD sum-rule method. We use correlation functions to obtain these strong coupling constants with contributions of both BcPS and BcV mesons as off-shell states. The contributions of two gluon condensates as a radiative correction are considered. The results show that ghbBcPSBcV = 8.80 ± 2.84 GeV-1 and ghbBcPSBcV = 9.34 ± 3.12 GeV-1 in the BcPS and BcV off-shell state, respectively. (orig.)
International Nuclear Information System (INIS)
We analyze the behaviour that correlation functions ought to have on the lattice in order to reproduce QCD sum rules in the continuum limit. We formulate a set of relations between lattice correlation functions of meson operators at small time separation and the quark condensates responsible for spontaneous breakdown of chiral symmetry. We suggest that the degree to which such relations are satisfied will provide a set of consistency checks on the ability of lattice Monte Carlo simulations to reproduce the correct spontaneous chiral symmetry breaking of the continuum limit. (author)
Testing QCD sum rules on the light-cone in D->(π,K)l ν decays
International Nuclear Information System (INIS)
We compare the predictions for the form factors f+D→π,K(0) from QCD sum rules on the light-cone with recent experimental results. We find f+D→π(0)=0.63±0.11, f+D→K(0)=0.75±0.12 and f+D→π(0)/f+D→K(0)=0.84+/-0.04 in very good agreement with experiment. Although the uncertainties of the form factors themselves are larger than the current experimental errors and difficult to reduce, their ratio is determined much more accurately and with an accuracy that matches that of experiment
B→π and B→K transitions from QCD sum rules on the light-cone
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I calculate the form factors describing semileptonic and penguin-induced decays of $B$ mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist∼4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be $/sim/,$15/%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer. (author)
Koike, Y
1996-01-01
A new QCD sum rule analysis on the spin-isospin averaged $\\rho$, $\\omega$ and constraint relation on the the low energy limit of the vector-current nucleon forward scattering amplitude, we get $a_\\rho=-0.47\\pm 0.05$ fm, $a_\\omega=-0.41\\pm 0.05$ fm and $a_\\phi=-0.15\\pm 0.02$ fm, which suggests that these $V-N$ interactions are attractive. It is also proved that the previous studies on the mass shift of these vector mesons in the nuclear medium are essentially the ones obtained from these scattering lengths in the linear density approximation.
Wang, Zhi-Gang
2016-01-01
In this article, we take the $X(5568)$ as the diquark-antidiquark type tetraquark state with the spin-parity $J^P=0^+$, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value $M_X=\\left(5.57\\pm0.12 \\right) \\,\\rm{GeV}$, which is consistent with the experimental data. The present prediction favors assigning the $X(5568)$ to be the scalar tetraquark state.
Development of polarized targets for the measurement of the Gerasimov-Drell-Hearn sum rule at ELSA
International Nuclear Information System (INIS)
The Gerasimov-Drell-Hearn sum rule (GDH) relates the difference of the total absorption cross section of circularly polarized photons on parallelly and anti-parallelly polarized nucleons to their well known quantities mass and anomalous magnetic moment. For the experimental examination of the sum rule experiments were performed in two different configurations: From the pion threshold up to a photon energy of 800 MeV data have been taken at the Mainzer Microtron (MAMI). At the Electron Stretcher Accelerator (ELSA) the measurement covered a photon energy range up to 2.9 GeV. The polarized target is an essential part of the experiment. During the data taking the target was run in the frozen spin mode to minimize the absorption of the ejected particles. In order to match the required detector geometry for full acceptance a new horizontal dilution refrigerator with an internal holding magnet was developed and used. This allowed to measure the spin dependent total photo absorption cross section difference for the first time. (orig.)
Improved analysis of B→πeν from QCD sum rules on the light-cone
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We present a new calculation of the B→π form-factor f+, relevant for the measurement of vertical bar Vub vertical bar from semileptonic B→π transitions, from QCD sum rules on the light-cone. The new element is the calculation of radiative corrections to next-to-leading twist-3 accuracy. We find that these contributions are factorizable at O(αs), which lends additional support to the method of QCD sum rules on the light-cone. We obtain f+(0) 0.26±0.06±0.05, where the first error accounts for the uncertainty in the input-parameters and the second is a guesstimate of the systematic uncertainty induced by the approximations inherent in the method. We also obtain a simple parametrization of the form-factor which is valid in the entire kinematical range of semileptonic decays and consistent with vector-meson dominance at large momentum-transfer. (author)
Thermal Spectrum of Heavy Vector and Axial Vector Mesons in the Framework of QCD Sum Rules Method
Yazici, Enis
2016-01-01
The masses and the leptonic decay constants of vector and axial vector heavy-heavy mesons are calculated using the thermal QCD sum rules approach. While obtaining the QCD sum rules, additional operators in the Wilson expansion and also temperature dependency of the continuum threshold are taken into account. The masses and the decay constants remained unchanged up to $T\\simeq100~MeV$. After that point, they start to diminish. At the critical temperature, the masses decreased about $3\\%$, $5\\%$ and $14\\%$ for the vector mesons $\\Upsilon$, $B_{c}$ and $J/\\psi$; $6\\%$, $7\\%$ and $22\\%$ for the axial vector mesons $\\chi_{b1}$, $B_{c}$ and $\\chi_{c1}$, respectively. The decay constants reached about less than $20\\%$ of their vacuum values. The obtained results of the thermal mass and decay constant calculations at zero temperature are in a very good agreement with the other non-perturbative calculations at vacuum as well as with the experimental data.
Determination of Baryon wave functions of the ground-state octet by means of QCD sum rules
International Nuclear Information System (INIS)
In this work we investigate the wave functions of the baryons in the ground state octet by using the QCD sum rules technique, especially referring to the formalism of Chernyak and Zhitnitsky. The moments of the quark distibution amplitudes of the proton, Σ+ and Ξ- are determined by evaluating their sum rules graphically. For the necessary algebraic calculations we have developed a computer program package based on standard REDUCE, such that the Wilson coefficients could be calculated automatically. The contributions of the quark and gluon condensates up to energy dimension 6 have been taken into account. The corresponding quark distribution amplitudes of the cited baryons are plotted. Our results do not agree with those of a paper recently published by Chernyak, Ogloblin and Zhitnitsky and show, that the effects of the SU(3)F symmetry breaking by the mass of the strange quark are unexpectedly large. The electromagnetic form factors of the considered baryons are determined for an intermediate momentum transfer of several GeV. (orig.)
Perturbative Corrections to $\\Lambda_b \\to \\Lambda$ Form Factors from QCD Light-Cone Sum Rules
Wang, Yu-Ming
2015-01-01
We compute radiative corrections to $\\Lambda_b \\to \\Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\\Lambda_b$-baryon correlation function is justified at leading power in $\\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\\cal O}(\\alpha_s)$ shift the $\\Lambda_b \\to \\Lambda$ from factors at large recoil significantly and the dominant contribution originat...
Symmetry constraints on generalizations of Bjorken flow
Gubser, Steven S
2010-01-01
I explain a generalization of Bjorken flow where the medium has finite transverse size and expands both radially and along the beam axis. If one assumes that the equations of viscous hydrodynamics can be used, with p=epsilon/3 and zero bulk viscosity, then the flow I describe can be developed into an exact solution of the relativistic Navier-Stokes equations. The local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.
International Nuclear Information System (INIS)
Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non-forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1)nξ(n)(1) ≥ ((2n+1)!!/22n). Moreover, for the curvature we find ξ''(1) ≥ (1/5)[4ρ2 + 3(ρ2)2] where ρ2 = -ξ'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λ-barξ(w) and the sums n ΔEj(n)τj(n)(1)τj(n)(w) (j = (1/2), (3/2)), that involve leading quantities, Isgur-Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi · v', vf · v', vi · vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute ((1/2)+, (3/2)+). We also obtain new sum rules involving the elastic subleading form factors χi(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (jP, JP) = ((1/2)-, 1-),((3/2)-, 1-) that enter in the 1/mQ2 corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -δ1/m2(A1) in terms of the χi(w) and the shape of the elastic IW function ξ(w). An important theoretical implication is that χ1'(1), χ2(1) and χ3'(1) (χ1(1) = χ3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values ρ2 → (3/4), σ2 → (15/16). These constraints
Jugeau, F.; Le Yaouanc, A.; Oliver, L.; Raynal, J.-C.
2006-01-01
Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non-forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1)nξ(n)(1) ⩾ (2n+1)!!/22n. Moreover, for the curvature we find ξ″(1) ⩾ 1/5[4ρ2 + 3(ρ2)2] where ρ2 = -ξ'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λ¯ξ(w) and the sums ∑ n ΔEj(n)τj(n)(1)τj(n)(w) (j = 1/2, 3/2), that involve leading quantities, Isgur-Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi ṡ v', vf ṡ v', vi ṡ vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute (1/2+, 3/2+). We also obtain new sum rules involving the elastic subleading form factors χi(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (jP, JP) = (1/2-, 1-),(3/2-, 1-) that enter in the 1/mQ2 corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -δ1/m2(A1) in terms of the χi(w) and the shape of the elastic IW function ξ(w). An important theoretical implication is that χ1'(1), χ2(1) and χ3'(1)(χ1(1) = χ3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values ρ2 → 3/4, σ2 → 15/16. These constraints should be taken
Chiral sum rules for scrL(6)WZ parameters and its application to π0,η,η' decays
International Nuclear Information System (INIS)
The chiral expansion of the low-energy processes π0→γγ and η→γγ is reconsidered with particular emphasis on the question of the evaluation of the two low-energy parameters from scrL(6)WZ which are involved at chiral order six. It is shown how extensive use of sum rules and saturation with resonances as well as constraints from asymptotic QCD effectively determine their values. Predictions for the widths are presented for both standard and nonstandard values of the quark mass ratio ms/m. A precise relation is established between the usual phenomenological η-η' mixing parameters and those of the chiral expansion. The large size of the chiral correction to the η decay can be understood on the basis of a simple counting rule: O(1/Nc)∼O(mq). It is shown how this counting rule eventually allows one to include the η' into the effective Lagrangian in a consistent and systematic way
Analysis of the (1)/(2){sup ±} pentaquark states in the diquark model with QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China); Huang, Tao [Chinese Academy of Sciences, Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Beijing (China)
2016-01-15
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future. (orig.)
Estimating the mass of the hidden charm 1{sup +}(1{sup +}) tetraquark state via QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Qiao, Cong-Feng; Tang, Liang [University of Chinese Academy of Sciences, Department of Physics, Beijing (China)
2014-10-15
By using QCD sum rules, the mass of the hidden charm tetraquark [cu][ anti c anti d] state with I{sup G}(J{sup P}) = 1{sup +}(1{sup +}) (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance Z{sub c}{sup +} (3900). In the calculation, contributions up to dimension eight in the operator product expansion (OPE) are taken into account. We find m{sup c}{sub 1+} = (3912{sub -153}{sup +306}) MeV, which is consistent,within the errors, with the experimental observation of Z+ c (3900). Extending to the b-quark sector, m{sup b}{sub 1+} = (10561{sub -163}{sup +395})MeV is obtained. The calculational result strongly supports the tetraquark picture for the ''exotic'' states of Z{sub c}{sup +} (3900) and Z{sub b}{sup +} (10610). (orig.)
Adler function, sum rules and Crewther relation of order O(αs4): The singlet case
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.; Rittinger, J.
2012-07-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 [1]), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 [2], Baikov et al., 2010 [3]) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e- annihilation into hadrons in a general gauge theory.
Adler function, sum rules and Crewther relation of order O(αs4): The singlet case
International Nuclear Information System (INIS)
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 ), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 , Baikov et al., 2010 ) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e- annihilation into hadrons in a general gauge theory.
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
Baikov, by P A; Kühn, J H; Rittinger, J
2012-01-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\\cal O}(\\alpha_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\\cal O}(\\alpha_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions. PMID:16321073
Semileptonic $B(B_s, B_c)$ decays in the light-cone QCD sum rules
Huang, T; Wu, X-G; Zuo, F
2008-01-01
Semileptonic $B$($B_s, B_c$) decays are investigated systematically in the light-cone QCD sum rules. Special emphasis is put on the LCSR calculation on weak form factors with an adequate chiral current correlator, which turns out to be particularly effective to control the pollution by higher twist components of spectator mesons. The result for each channel depends on the distribution amplitude of the the producing meson. The leading twist distribution amplitudes of the related heavy mesons and charmonium are worked out by a model approach in the reasonable way. A practical scenario is suggested to understand the behavior of weak form factors in the whole kinematically accessible ranges. The decay widths and branching ratios are estimated for several $B$($B_c$) decay modes of current interest.
Analysis of the (1)/(2)± pentaquark states in the diquark-diquark-antiquark model with QCD sum rules
International Nuclear Information System (INIS)
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the JP = (1)/(2)± hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ = √(MP2-(2Mc)2) to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S = 0, -1, -2, -3, which can be confronted with the experimental data in the future. (orig.)
Shen, Yue-Long; Lü, Cai-Dian
2016-01-01
Within the framework of $B$-meson light-cone sum rules, we compute the one-loop level QCD corrections to $B\\to \\pi$ transition form factors at small $ q^{2}$ region, in implement of a complete renormalization group equation evolution. To solve the renormalization group equations, we work at the "dual" space where the anomalous dimensions of the jet function and the light-cone distribution amplitudes are diagonal. With the complete renormalization group equation evolution, the form factors are almost independent of the factorization scale, which is shown numerically. We also extrapolate the results of the form factors to the whole $q^2$ region, and compare their behavior with other studies.
D → a1, f1 transition form factors and semileptonic decays via 3-point QCD sum rules
Zuo, Yabing; Hu, Yue; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-07-01
By using the 3-point QCD sum rules, we calculate the transition form factors of D decays into the spin triplet axial vector mesons a1(1260), f1(1285), f1(1420). In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of a1(1260) is one, we calculate the D+ → a 10(1260) and D0 → a 1‑(1260) transition form factors separately. In the case of f1(1285), f1(1420), the mixing between light flavor SU(3) singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
$D \\rightarrow a_1, f_1$ transition form factors and semileptonic decays via 3-point QCD sum rules
Zuo, Yabing; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-01-01
By using the 3-point QCD sum rules, we calculate the transition form factors of $D$ decays into the spin triplet axial vector mesons $a_1(1260)$, $f_1(1285) $, $f_1(1420)$. In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of $a_1(1260)$ is one, we calculate the $D^+ \\rightarrow a_1^0 (1260)$ and $D^0 \\rightarrow a_1^- (1260)$ transition form factors separately. In the case of $ f_1(1285), f_1(1420)$, the mixing between light flavor $SU(3)$ singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
Analysis of the {1/2}^{± } pentaquark states in the diquark model with QCD sum rules
Wang, Zhi-Gang; Huang, Tao
2016-01-01
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the J^P={1/2}^± hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the J^P={3/2}^- and {5/2}+ hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future.
Wang, Zhi-Gang
2016-03-01
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the J^P={1/2}^± hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ =sqrt{M^2P-(2{{M}}_c)^2} to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S=0,-1,-2,-3, which can be confronted with the experimental data in the future.
Analysis of the ${\\frac{1}{2}}^{\\pm}$ pentaquark states in the diquark model with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the $J^P={\\frac{1}{2}}^\\pm$ hidden-charmed pentaquark states in details with the QCD sum rules by extending our previous work on the $J^P={\\frac{3}{2}}^+$ and ${\\frac{5}{2}}^{-}$ hidden-charmed pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future.
Relativistic chiral SU(3) symmetry, large Nc sum rules and meson-baryon scattering
International Nuclear Information System (INIS)
The relativistic chiral SU(3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel Bethe-Salpeter equation with the interaction kernel truncated at chiral order Q3 where we include only those terms which are leading in the large Nc limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large Nc baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking effects are well controlled by the combined chiral and large Nc expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of plab ≅ 500 MeV. (orig.)
Relation between (e,e') sum rules in 6,7Li and 4He nuclei.Experiment and cluster model
Efros, V D; Buki, A Yu
2016-01-01
The sums over (e,e') spectra of 6Li and 7Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the alpha-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm^{-1} the relations expressing the A=6 or 7 sum in terms of the A=4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm^{-1} the longitudinal correlation functions of 6Li and 7Li nuclei are found to be close to that of the alpha-particle. The experimental longitudinal sums in the range between 0.450 and 1.625 fm^{-1} are employed to perform comparison with those calculated in the framework of cluster models. Out of the mentioned experimental sums, those in the range between 0.750 and 1.000 fm^{-1} in the 6Li case ...
Energy Technology Data Exchange (ETDEWEB)
Yazici, E.; Sundu, H.; Veliev, E.V. [Kocaeli University, Department of Physics, Izmit (Turkey)
2016-02-15
The strong form factor of the B{sub c}B{sub c}J/ψ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T ≅ 100 MeV but slightly increases after this point. After T ≅ 160 MeV, the form factor suddenly decreases up to T ≅ 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q{sub 2} = -m{sup 2}{sub offshell} at T = 0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments. (orig.)
International Nuclear Information System (INIS)
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations
Aliev, T M; Savcı, M
2016-01-01
The light cone sum rules method is used in studying the radiative decays $\\Sigma_Q \\to \\Lambda_Q \\gamma$ and $\\Xi^\\prime_Q \\to \\Xi_Q \\gamma$. Firstly, the sum rules for the form factor $F_2(Q^2=0)$ responsible for these transitions is constructed. Using this result the decay widths of the above--mentioned decays are calculated and analyzed. A comparison of our predictions on the decay widths of considered transitions with the predictions of the other approaches is presented.
Energy Technology Data Exchange (ETDEWEB)
Deur, A
2000-10-01
This thesis presents an experimental study of the neutron (and {sup 3}He) spin structure with a particular emphasis in the resonance domain (experiment E94010 that took place in 1997 at Jefferson Lab (TJNAF or formerly CEBAF) in Virginia). A polarized {sup 3}He target was built in order to achieve this study since polarized {sup 3}He nuclei can be seen as polarized neutrons. This target allowed the measurement of the polarized absolute cross sections {sigma}{sub 1/2}(Q{sup 2}, {nu}) and {sigma}{sub 3/2}(Q{sup 2}, {nu}) from the inclusive reaction {sup {sup {yields}}{sup 3}He}({sup {yields}}e, e')X for incident beam energies ranging from 0.86 GeV to 5.07 GeV at a scattering angle of 15.5 deg. The Q{sup 2} evolution of the generalized Gerasimov-Drell-Hearn (GDH) integral on {sup 3}He and on neutron was measured from 0.1 GeV{sup 2} to 1.0 GeV{sup 2} in order to understand the transition between perturbative QCD and non-perturbative QCD. The integration domain in {nu} (the energy loss of the scattered electron) is from the pion threshold to about 2.5 GeV which covers both the resonance region and the Deep Inelastic Scattering. The high precision of our data constrains the models giving the Q{sup 2} evolution of the generalized GDH integral. The polarized quasi-elastic scattering was also measured. The cross section {sigma}{sup TT}(Q{sup 2}, {nu}) on {sup 3}He and the spin structure functions g{sub 1}{sup {sup 3}He}(Q{sup 2}, {nu}) and g{sub 2}{sup {sup 3}He}(Q{sup 2}, {nu}) are presented. These data are an indication that the higher-twists are small in our kinematics domain and that the Bloom-Gilman duality seems to hold for the polarized spin structure functions. (author)
Form factors in B¯0→π+π0ℓν¯ℓ from QCD light-cone sum rules
Directory of Open Access Journals (Sweden)
Christian Hambrock
2016-04-01
Full Text Available The form factors of the semileptonic B→ππℓν¯ decay are calculated from QCD light-cone sum rules with the distribution amplitudes of dipion states. This method is valid in the kinematical region, where the hadronic dipion state has a small invariant mass and simultaneously a large recoil. The derivation of the sum rules is complicated by the presence of an additional variable related to the angle between the two pions. In particular, we realize that not all invariant amplitudes in the underlying correlation function can be used, some of them generating kinematical singularities in the dispersion relation. The two sum rules that are free from these ambiguities are obtained in the leading twist-2 approximation, predicting the B¯0→π+π0 form factors F⊥ and F∥ of the vector and axial b→u current, respectively. We calculate these form factors at the momentum transfers 0
Polanco-Euán, E N; Sánchez-Colón, G; Bambah, B A
2016-01-01
The SU(3) octet states with baryon number B = 2, hexaquark dibaryons, are considered. Decay coupling constants sum rules for dibaryon octet into two ordinary baryon octets with ?$\\lambda_8$ first order SU(3) symmetry breaking are given. An SU(4) extension of the analysis is commented upon. Possibilities for the experimental observation of multibaryon and anti-multibaryon states are pointed out.
International Nuclear Information System (INIS)
We study the X-ray magnetic circular dichroism (XMCD) spectra at the U M4,5 and N4,5 edges of uranium monochalcogenides, UX where X=S, Se, and Te, examining the applicability of the XMCD sum rules to UX by the fully relativistic full-potential linear-combination-of-atomic-orbitals (LCAO) method based on the density functional theory. To extract the transitions relevant to the sum-rule analysis, we employ the Mulliken population analysis (MPA). Using the MPA, the orbital sum rule is found to be valid to 10-20% for the M4,5 edges and valid to 5-15% for the N4,5 edges. On the other hand, the spin sum rule is found to be valid to 10-20% for the M4,5 edges whereas valid to 30-35% for the N4,5 edges. Furthermore, it is found that the calculated XMCD spectra are consistent with a recent experimental observation that the intensity of the N4,5 XMCD signal is comparable to that of the M4,5 XMCD signal although contradicting a previous theoretical prediction that the XMCD intensity at the N4,5 edges is one order of magnitude smaller than that at the M4,5 edges. (author)
Hudspith, R J; Maltman, K; Wolfe, C E; Zanotti, J
2015-01-01
Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{us}$ using inclusive hadronic $\\tau$ decay data. Results for $V_{us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\\vert V_{us}\\vert$, but also $D>4$ effective condensates, fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging $D=2$ OPE series. The new sum rule implementation yields $\\vert V_{us}\\vert$ results free of unphysical $s_0$- and $w$-dependences and $\\sim 0.0020$ higher than that obtained using the conventional implementation. With preliminary new experimental results for the $K\\pi$ branching frac...
Energy Technology Data Exchange (ETDEWEB)
Baru, V. [Institut fuer Theoretische Physik II, Ruhr-Universitaet Bochum, D-44870 Bochum (Germany); Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Theoretical and Experimental Physics, B. Cheremushinskaya 25, 117218 Moscow (Russian Federation); Hanhart, C. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany); Hoferichter, M., E-mail: hoferichter@hiskp.uni-bonn.de [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, OH 45701 (United States); Kubis, B. [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Nogga, A. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany)
2011-12-15
We use chiral perturbation theory (ChPT) to calculate the {pi}{sup -}d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a{sup +} and a{sup -}. We study isospin-breaking contributions to the three-body part of a{sub {pi}}{sup -}{sub d} due to mass differences, isospin violation in the {pi}N scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a{sub {pi}}{sup -}{sub d} due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Analysis of the strong decays $D_{s3}^*(2860)\\to DK$, $D^{*}K$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we assign the $D_{s3}^*(2860)$ to be a D-wave $c\\bar{s}$ meson, study the vertices $D_{s3}^*(2860)DK$ and $D_{s3}^*(2860)D^*K$ in details to select the pertinent tensor structures, calculate the hadronic coupling constants $G_{D_{s3}^*(2860)DK}$ and $G_{D_{s3}^*(2860)D^*K}$ with the three-point QCD sum rules and obtain the decay widths $\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)$ and $\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)$. The predicted ratio $R=\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)/\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)=0.57\\pm0.38$ cannot reproduce the experimental data $R={\\rm Br}\\left(D_{sJ}^*(2860)\\to D^{*}K\\right)/{\\rm Br}\\left(D_{sJ}^*(2860)\\to DK\\right)=1.10 \\pm 0.15 \\pm 0.19$.
Interpretation of Z{sub c}(4025) as the hidden charm tetraquark states via QCD Sum Rules
Energy Technology Data Exchange (ETDEWEB)
Qiao, Cong-Feng [Graduate University of Chinese Academy of Sciences, School of Physics, Beijing (China); CAS Center for Excellence in Particle Physics, Beijing (China); Tang, Liang [Graduate University of Chinese Academy of Sciences, School of Physics, Beijing (China)
2014-03-15
By using QCD Sum Rules, we found that the charged hidden charm tetraquark [cu][ anti c anti d] states with J{sup P} = 1{sup -} and 2{sup +}, which are possible quantum numbers of the newly observed charmonium-like resonance Z{sub c}(4025), have masses of m{sup c}{sub 1-} = (4.54 ± 0.20) GeV and m{sup c}{sub 2+} = (4.04 ± 0.19) GeV. The contributions up to dimension eight in the operator product expansion were taken into account in the calculation. The tetraquark mass of J{sup P} = 2{sup +} state was consistent with the experimental data of Z{sub c}(4025), suggesting the Z{sub c}(4025) state to possess the quantum number of J{sup P} = 2{sup +}. Extending to the b-quark sector, the corresponding tetraquark masses m{sup b}{sub 1-} = (10.97 ± 0.25) GeV and m{sup b}{sub 2+} = (10.35 ± 0.25) GeV were obtained, which values are testable in future B-factories. (orig.)
International Nuclear Information System (INIS)
Pionic decays of hadrons are calculated using a PCAC (partial conservation of axial-vector current) prescription and a quark shell model with quarks bound by a central potential, described by the Dirac equation. The Dirac Hamiltonian and operators are expanded in v/c, the internal quark velocity. Then, one finds an exact saturation of the current-algebra sum rules as defined in the SU(2)xSU(2) symmetry of Gilman-Harari and Weinberg up to order v4/c4. The saturation is obtained without need of exotics, with the usual excitations of the ground state. The relation with the P = infinity approach is clarified. The corrections found with respect to previous quark models in L = 2 decays are discussed. They do not solve the problem of SU(6)/sub W/ coupling signs. Finally, the whole Weinberg scheme of linear SU(2)xSU(2) symmetry is completed by the expression of the chiral-breaking part of the mass operator m4/sup ts2/
Precision calculation of threshold π−d scattering, πN scattering lengths, and the GMO sum rule
International Nuclear Information System (INIS)
We use chiral perturbation theory (ChPT) to calculate the π−d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion–nucleon scattering lengths a+ and a−. We study isospin-breaking contributions to the three-body part of aπ−d due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in aπ−d due to virtual photons. Finally, we discuss the validity of the Goldberger–Miyazawa–Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion–nucleon coupling constant.
Duality in the Bjorken variable between small and large x
International Nuclear Information System (INIS)
By following the classical concept of duality in strong interactions, we show that the structure functions exhibit this property in the Bjorken variable x (partons' momentum fraction). Veneziano-like dual models for the structure functions are suggested
International Nuclear Information System (INIS)
A detailed NNLO QCD analysis of new CCFR data on xF3 structure function including the target mass, higher twist and nuclear corrections was performed and parametrizations of the perturbative and power terms of the structure function were constructed. The results of QCD analysis of the structure function were used to study the Q2-dependence of the Gross-Llewellyn Smith sum rule. The αS/π-expansion of SGLS(Q2) was studied and parameters of the expansion were found to be s1=2.74±0.01, s2=-2.22±0.23, s3=-7.86±1.74 which are in good agreement with the perturbative QCD predictions for the Gross-Llewellyn Smith sum rule in the next-to-leading and next-to-next-to-leading order
A QCD sum rule calculation of the $X^\\pm(5568) \\to B_{s}^0\\pi^\\pm$ decay width
Dias, J M; Torres, A Martínez; Nielsen, M; Zanetti, C M
2016-01-01
To understand the nature of the $X(5568)$, recently observed in the mass spectrum of the $B_{s}^0\\pi^\\pm$ system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. The result found for its mass agrees well with the experimental value. Encouraged by this finding we now extend our calculations to obtain the decay width of $X(5568)$ to $B_{s}^0\\pi^\\pm$ using the three-point QCD sum rule. We obtain a value of $(20.4\\pm8.7)\\MeV$, which, on comparing with the experimental value of $21.9\\pm6.4 (\\mbox{sta})^{+5.0}_{-2.5}(\\mbox{syst}) \\MeV/c^2$, reinforces the scalar four quark nature of $X(5568)$.
International Nuclear Information System (INIS)
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes Ds and D*0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
Energy Technology Data Exchange (ETDEWEB)
Hilger, Thomas Uwe
2012-04-11
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
International Nuclear Information System (INIS)
We present four kinds of sum rules for the exchange-correlation energy functional of the extended constrained-search theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.
International Nuclear Information System (INIS)
The computer program LIMES is based on an improved version of the extended sum-rule model for light and intermediate-mass fragment emission in heavy ion reactions. It includes a code for dynamical calculations of the critical angular momentum for fusion following the suggestions. The report briefly describes the use of this program, the necessary input for the calculations of the element distribution and partial cross sections and gives a Fortran listing. Using the fitting routine FITEX the program provides an option for fast parameter adjustments. The use is demonstrated by an application to a specific example. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research
2007-03-15
We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
Representations of the U$_{q}$(u$_{4,1}$) and a q-polynomial that determines baryon mass sum rules
Gavrilik, A M; Tertychnyj, A V; Gavrilik, A M; Kachurik, I I; Tertychnyj, A V
1995-01-01
With quantum groups U_q(su_n) taken as classifying symmetries for hadrons of n flavors, we calculate within irreducible representation D^+_{12}(p-1,p-3,p-4;p,p-2) (p \\in {\\bf Z}) of 'dynamical' quantum group U_q(u_{4,1}) the masses of baryons {1\\over 2}^+ that belong to {\\it 20}-plet of U_q(su_4). The obtained q-analog of mass relation (MR) for U_q(su_3)-octet contains unexpected mass-dependent term multiplied by the factor {A_q\\over B_q} where A_q, B_q are certain polynomials (resp. of 7-th and 6-th order) in the variable q+q^{-1}\\equiv [2]_q. Both values q=1 and q=e^{i\\pi \\over 6} turn the polynomial A_q into zero. But, while q=1 results in well-known Gell-Mann--Okubo (GMO) baryon MR, the second root of A_q reduces the q-MR to some novel mass sum rule which has irrational coefficients and which holds, for empirical masses, even with better accuracy than GMO mass sum rule.
Structure of the Ds0(2317) and the strong coupling constant gDs0DK with the light-cone QCD sum rules
International Nuclear Information System (INIS)
In this article, we take the point of view that the charmed scalar meson Ds0(2317) is the conventional cs meson and calculate the strong coupling constant gDs0DK within the framework of the light-cone QCD sum rules approach. The numerical values for the large scalar-DK coupling constant gDs0DK support the hadronic dressing mechanism. Just like the scalar mesons f0(980) and a0(980), the Ds0(2317) may have small scalar cs kernel of the typical cs meson size. The strong coupling to the hadronic channels (or the virtual mesons loops) may result in smaller mass than the conventional scalar cs meson in the constituent quark models, and enrich the pure cs state with other components. The Ds0(2317) may spend part (or most part) of its lifetime as virtual DK state
Analysis of the strong coupling form factors of $\\Sigma_bNB$ and $\\Sigma_c ND$ in QCD sum rules
Yu, Guo Liang; Li, Zhen Yu
2016-01-01
In this article, we study the strong interaction of the vertexes $\\Sigma_bNB$ and $\\Sigma_c ND$ using the three-point QCD sum rules under two different dirac structures. Considering the contributions of the vacuum condensates up to dimension $5$ in the operation product expansion, the form factors of these vertexes are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant. Our analysis indicates that the coupling constant for these two vertexes are $G_{\\Sigma_bNB}=0.43\\pm0.01GeV^{-1}$ and $G_{\\Sigma_cND}=3.76\\pm0.05GeV^{-1}$.
Energy Technology Data Exchange (ETDEWEB)
Jeffries, J R; Moore, K T; Butch, N P; Maple, M B
2010-05-19
We examine the degree of 5f electron localization in URu{sub 2}Si{sub 2} using spin-orbit sum rule analysis of the U N{sub 4,5} (4d {yields} 5f) edge. When compared to {alpha}-U metal, US, USe, and UTe, which have increasing localization of the 5f states, we find that the 5f states of URu{sub 2}Si{sub 2} are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for URu{sub 2}Si{sub 2} when the 5f electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of URu{sub 2}Si{sub 2}, where the degree of localization of the 5f electrons and their contribution to the Fermi surface are critical.
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-03-15
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ = √(M{sub P}{sup 2}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S = 0, -1, -2, -3, which can be confronted with the experimental data in the future. (orig.)
Agaev, S S; Sundu, H
2016-01-01
The full version of QCD light-cone sum rule method is applied to tetraquarks containing a single heavy $b$ or $c$ quark. To this end, investigations of the strong vertices $X_{b}X_{b}\\rho$ and $X_{c}X_{c}\\rho$ are performed, where $X_b=[su][\\bar b\\bar d]$ and $X_c=[su][\\bar c\\bar d]$ are the exotic states built of four quarks of different flavors. The strong coupling constants $G_{X_{b}X_{b}\\rho}$ and $G_{X_{c}X_{c}\\rho}$ corresponding to these vertices are found using the $\\rho$-meson leading and higher-twist distribution amplitudes. In the calculations $X_{b(c)}$ are treated as scalar bound states of a diquark and antidiquark.
Wang, Zhi-Gang
2015-01-01
In this article, we construct the diquark-diquark-antiquark type interpolating currents, and study the masses and pole residues of the $J^P={\\frac{3}{2}}^-$ and ${\\frac{5}{2}}^+$ hidden-charmed pentaquark states in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In calculations, we use the formula $\\mu=\\sqrt{M^2_{P_c}-(2{\\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. The present predictions favor assigning the $P_c(4380)$ and $P_c(4450)$ to be the ${\\frac{3}{2}}^-$ and ${\\frac{5}{2}}^+$ pentaquark states, respectively.
Wang, Zhi-Gang
2015-01-01
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^P={\\frac{1}{2}}^\\pm$ hidden-charmed pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula $\\mu=\\sqrt{M^2_{P}-(2{\\mathbb{M}}_c)^2}$ to determine the energy scales of the QCD spectral densities. We take into account the $SU(3)$ breaking effects of the light quarks, and obtain the masses of the hidden charmed pentaquark states with the strangeness $S=0,\\,-1,\\,-2,\\,-3$, which can be confronted with the experimental data in the future.
Analysis of P_c(4380) and P_c(4450) as pentaquark states in the diquark model with QCD sum rules
Wang, Zhi-Gang
2016-02-01
In this article, we construct the diquark-diquark-antiquark type interpolating currents, and we study the masses and pole residues of the J^P={3/2}^- and {5/2}^+ hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula μ =√{M^2_{P_c}-(2{{M}}_c)^2} to determine the energy scales of the QCD spectral densities. The present predictions favor assigning P_c(4380) and P_c(4450) to be the {3/2}^- and {5/2}^+ pentaquark states, respectively.
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-02-15
In this article,we construct the diquark-diquark- antiquark type interpolating currents, and we study the masses and pole residues of the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula μ = √(M{sup 2}{sub P{sub c}}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. The present predictions favor assigning P{sub c}(4380) and P{sub c}(4450) to be the (3)/(2){sup -} and (5)/(2){sup +} pentaquark states, respectively. (orig.)
Dynamical simulation of disoriented chiral condensate formation in Bjorken rods
International Nuclear Information System (INIS)
Using a semiclassical treatment of the linear σ model, we simulate the dynamical evolution of an initially hot cylindrical rod endowed with a longitudinal Bjorken scaling expansion (a ''Bjorken rod''). The field equation is propagated until full decoupling has occurred and the asymptotic many-body state of free pions is then obtained by a suitable Fourier decomposition of the field and a subsequent stochastic determination of the number of quanta in each elementary mode. The resulting transverse pion spectrum exhibits visible enhancements below 200 MeV due to the parametric amplification caused by the oscillatory relaxation of the chiral order parameter. Ensembles of such final states are subjected to various event-by-event analyses. The factorial moments of the multiplicity distribution suggest that the soft pions are nonstatistical. Furthermore, their emission patterns exhibit azimuthal correlations that have a bearing on the domain size in the source. Finally, the distribution of the neutral pion fraction shows a significant broadening for the soft pions which grows steadily as the number of azimuthal segments is increased. All of these features are indicative of disoriented chiral condensates and it may be interesting to apply similar analyses to actual data from high-energy nuclear collision experiments. (c) 2000 The American Physical Society
Wang, Zhi-Gang; Li, Jun-Fang
2010-01-01
In this article, we parameterize the vertexes $\\Omega^*_Q\\Omega_Q^*\\phi$, $\\Omega^*_Q\\Xi_Q^*K^*$, $\\Xi_Q^*\\Sigma^*_QK^*$ and $\\Sigma_Q^*\\Sigma^*_Q \\rho$ with four tensor structures due to Lorentz invariance, and study the corresponding four strong coupling constants with the light-cone QCD sum rules.
International Nuclear Information System (INIS)
Deep inelastic neutrino-deuteron scattering in the covariant approach in the light-cone variables is considered. The deuteron structure function F3D(x,Q2) is calculated in the relativistic impulse approximation on the basis of the relativistic wave function. The results are compared with available experimental data. The nuclear effect of relativistic Fermi motion described by the ratio RFD/N = F3D/F3N is estimated. The dependence of the ratio on x and Q2 is investigated. The dependence of the Gross-Llewellyn Smith integral SGLS(x,Q2) on x and Q2 is considered. On the basis of the QCD analysis of the xF3N structure function the correction for SGLS(x,Q2) due to the nuclear effect is estimated and it is shown that the nuclear effect should be taken into account to verify the Gross-Llewellyn Smith sum rule. 25 refs., 4 figs., 2 tabs
Mikhailov, S V; Stefanis, N G
2016-01-01
We consider the calculation of the pion-photon transition form factor $F^{\\gamma^*\\gamma\\pi^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale $M^2$, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for $F^{\\gamma^*\\gamma\\pi^0}(Q^2)$ are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the $Q^2$ range between 1 and 5 GeV$^2$, thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical p...
Analysis of the strong coupling constant GDs∗Dsϕ and the decay width of Ds∗→Dsγ with QCD sum rules
International Nuclear Information System (INIS)
In this article, we calculate the form factors and the coupling constant of the vertex Ds∗Dsϕ using the three-point QCD sum rules. We consider the contributions of the vacuum condensates up to dimension 7 in the operator product expansion. And all possible off-shell cases are considered, ϕ, Ds and Ds∗, resulting in three different form factors. Then we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant for the process. Our analysis indicates that the coupling constant for this vertex is GDs∗Dsϕ=4.12±0.70 GeV-1. The results of this work are very useful in the other phenomenological analysis. As an application, we calculate the coupling constant for the decay channel Ds∗→Dsγ and analyze the width of this decay with the assumption of the vector meson dominance of the intermediate ϕ(1020). Our final result about the decay width of this decay channel is Γ=0.59±0.15 keV
Energy Technology Data Exchange (ETDEWEB)
Mirez, Carlos; Trevisan, Luis A.; Tomio, Lauro [Universidade Estadual Paulista (IFT/UNESP), Sao Paulo, SP (Brazil). Inst. de Fisica Teorica
2010-07-01
In the present work the method used in ref. [1] is considered to obtain the function structure of pion F{sub 2}{sup {pi}}2 , In that model, it was needed an initial quark distribution and the observed distribution in the hadron. This method provides information about the sea quark distribution of mesons that are out of reach experimentally. The pion structure is determined fairly acc urated. The initial distribution for the anti-d quark may given by the thermal model ref. [2,3]. We compare our results with other models to describe the pion structure function ref. [4,5] and with the experimental data on pion structure. We also studied if there is a relation between the q{sup 2} and the measured violation of the Gottfried sum rule. Also, a comparison between the relations Gott x q{sup 2} and Gott x T, where the T is the temperature given by a statistical model ref.[1,2] is done. On this way, it is expected to understand if there is a relation q{sup 2} x T [3,4], that would mean that the scattering heats the hadron. (author)
New Constraints on the 18F(p,alpha) 15O Rate in Novae from (d,p) Reaction Sum Rules
Kozub, R L; Batchelder, J C; Blackmon, J C; Brune, C R; Champagne, A E; Cizewski, J A; Davinson, T; Greife, U; Gross, C J; Jewett, C C; Livesay, R J; Ma, Z; Moazen, B H; Nesaraja, C D; Sahin, L; Scott, J P; Shapira, D; Smith, M S; Thomas, J S; Woods, P J
2004-01-01
The degree to which the (p,gamma) and (p,alpha) reactions destroy 18F at temperatures 1-4x10^8 K is important for understanding the synthesis of nuclei in nova explosions and for using the long-lived radionuclide 18F, a target of gamma-ray astronomy, as a diagnostic of nova mechanisms. The reactions are dominated by low-lying proton resonances near the 18F+p threshold (E_x=6.411 MeV in 19Ne). To gain further information about these resonances, we have used a radioactive 18F beam from the Holifield Radioactive Ion Beam Facility to selectively populate corresponding mirror states in 19F via the inverse d(18F,p)19F neutron transfer reaction. Neutron spectroscopic factors were measured for states in 19F in the excitation energy range 0-9 MeV and appropriately scaled to conform to sum rule limits. The results would suggest significantly lower 18F(p,gamma)19Ne and 18F(p,alpha)15O reaction rates than reported previously, thereby increasing the prospect of observing the 511-keV annihilation radiation associated with ...
Bakulev, A P; Pimikov, A V; Stefanis, N G
2011-01-01
A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2016-06-01
We consider the calculation of the pion-photon transition form factor Fγ*γπ0(Q2) within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M2, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for Fγ*γπ0(Q2) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q2 range between 1 and 5 GeV2 , thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
Wang, Zhi-Gang
2015-01-01
In this article, we construct both the axialvector-diquark-scalar-diquark-antiquark type and the axialvector-diquark-axialvector-diquark-antiquark type currents to interpolate the $J^P={\\frac{3}{2}}^\\pm$ hidden-charm pentaquark states, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, study the masses and pole residues with the QCD sum rules in a systematic way, and obtain the masses of the hidden-charm pentaquark states with the strangeness $S=0,\\,-1,\\,-2,\\,-3$, which can be confronted to the experimental data in the future. The predicted masses of the pentaquark states $P_{uud}^{10\\frac{1}{2}}\\left({\\frac{3}{2}^-}\\right)$, $P_{uud}^{11\\frac{1}{2}}\\left({\\frac{3}{2}^-}\\right)$ and $P_{uud}^{11\\frac{3}{2}}\\left({\\frac{3}{2}^-}\\right)$ are compatible with the experimental value $M_{P_c(4380)}=4380\\pm 8\\pm 29\\,\\rm{MeV}$ from the LHCb collaboration, more experimental data are still needed to identify the $P_c(4380)$ unambiguously.
Burkardt, Matthias
2013-01-01
Definitions of orbital angular momentum based on Wigner distributions are used as a framework to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. We find that the difference between these two definitions can be interpreted as the change in the quark orbital angular momentum due to final state interactions as it leaves the target in a DIS experiment.
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2014-05-15
In this article, we distinguish the charge conjugations of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and we study the masses and pole residues of the J{sup PC} = 1{sup -±} hidden charmed tetraquark states with the QCD sum rules. We suggest a formula μ = √(M{sup 2}{sub X/Y/Z}-(2M{sub c}){sup 2}) with the effective mass M{sub c} = 1.8 GeV to estimate the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, which works very well. The numerical results disfavor assigning the Z{sub c}(4020), Z{sub c}(4025), and Y(4360) as the diquark-antidiquark (with the Dirac-spinor structure C - Cγ{sub μ}) type vector tetraquark states, and they favor assigning the Z{sub c}(4020), Z{sub c}(4025) as the diquark-antidiquark type 1{sup +-} tetraquark states. While the masses of the tetraquark states with symbolic quark structures c anti cs anti s and c anti c(u anti u + d anti d)/√(2) favor assigning the Y(4660) as the 1{sup --} diquark-antidiquark type tetraquark state, more experimental data are still needed to distinguish its quark constituents. There are no candidates for the positive charge conjugation vector tetraquark states; the predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II. (orig.)
Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics
Roy, Victor; Rezzolla, Luciano; Rischke, Dirk
2015-01-01
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $\\tau$ is the same as for the time-honored "Bjorken flow" without magnetic field. Furthermore, when the magnetic field is assumed to decay $\\sim \\tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the...
Two views on the Bjorken scenario for ultra-relativistic heavy-ion collisions
Maire, Antonin
2011-01-01
The sketch describes the Bjorken scenario foreseen for the collision of ultra-relativistic heavy-ions, leading to the creation of strongly-interacting hot and dense deconfined matter, the so-called Quark-Gluon Plasma (QGP).
International Nuclear Information System (INIS)
Using recent experimental results on Compton scattering by 208Pb at energies below pion threshold we explore the effects of enhancement due to mesonic currents and isovector vibrations on the giant resonances of nuclei. Quantitative information is given for the enhancements of the electric polarizability, the diamagnetic susceptibility and the energy-weighted quadrupole sum rule. It is shown that the average of results available from different laboratories on the ''nonretarded'' enhancement constant κGDR in the A = 197-209 mass range favours an effective nucleon mass of m*/m = 3/4. Some new results for the amplitude of Compton scattering by the giant resonances of nuclei are presented which allow a treatment of the retardation problem in a zero-order approximation. ((orig.))
A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
Akamatsu, Yukinao; Teaney, Derek
2016-01-01
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations. We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\\propto \\omega^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid. Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, evaluating the contribution of thermal noise from the earliest moments and at late times. In the Bjorken case, the solution to the kinetic equations determines the coefficient of the first fractional power of the gradient expansion ($\\propto 1/(\\tau T)^{3/2}$) for the expanding system. Numerically, we find that the contribution to the longitudinal pressure from hydrodynamic fluctuations is larger than second order hyd...
International Nuclear Information System (INIS)
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both
International Nuclear Information System (INIS)
The QCD sum rule approach of Chernyak and Zhitnitsky for calculating the quark distribution amplitudes is applied to the lowest lying nucleon resonance of spin 3/2 and positive parity, namely the Δ(1232). With the help of an especially developed REDUCE computer program package the sum rules for the first few moments of the wavefunction are calculated. It is found that no fiducial region exists, where the sum rules can be saturated such that the amount of the nonperturbative and continuum contributions are acceptable. A detailed analysis shows that the reasons for this defect are the spin-mixing on the light-cone and the canonical choice of the baryonic currents in connection with their correlation function. We show however that with the considered currents the sum rules can be saturated accurately by a dominating baryon resonance with a mass around 1600 MeV. The resulting quark distribution amplitude of this resonance, which is identified as the Δ(1600) with 1/2 and negative parity, is compatible with its asymptotic form and shows no asymmetry in the quark momenta. Its magnetic transition form factor at momentum transfer of several GeV is calculated refering to the perturbative QCD results of Carlson and Poor. (orig.)
International Nuclear Information System (INIS)
Making the assumption of explicit isospin violation arising from f0(980)-a0(980) mixing, we take the point of view that the scalar mesons f0(980) and a0(980) have both strange and non-strange quark-antiquark components and evaluate the strong coupling constants gf0K+K- and ga0K+K- within the framework of the light-cone QCD sum rules approach. The large strong scalar-KK couplings through both the n anti n and s anti s components g antinnf0K+K-, g antissf0K+K-, g antinna0K+K- and g antissa0K+K- will support the hadronic dressing mechanism; furthermore, in spite of the constituent structure differences between the f0(980) and a0(980) mesons, the strange components have larger strong coupling constants with the K+K- state than the corresponding non-strange ones, gf0K+K-antiss∼√(2)gf0K+K-antinn and ga0K+K-antiss∼√(2)ga0K+K-antinn. From the existing controversial values, we cannot reach a general consensus on the strong coupling constants gf0K+K-, ga0K+K- and the mixing angles. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2014-07-15
In this article, we calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and study the J{sup PC} = 0{sup ++}, 1{sup +-}, 2{sup ++} D{sup *} anti D{sup *}, D{sub s}{sup *} anti D{sub s}{sup *}, B{sup *} anti B{sup *}, B{sub s}{sup *} anti B{sub s}{sup *} molecular states with the QCD sum rules. In the calculations, we use the formula μ = √(M{sup 2}{sub X/Y/Z}-(2M{sub Q}){sup 2}) to determine the energy scales of the QCD spectral densities. The numerical results favor assigning the Z{sub c}(4020) and Z{sub c}(4025) to the J{sup PC} = 0{sup ++}, 1{sup +-} or 2{sup ++} D{sup *} anti D{sup *} molecular states, the Y(4140) to the J{sup PC} = 0{sup ++} D{sub s}{sup *} anti D{sub s}{sup *} molecular state, the Z{sub b}(10650) to the J{sup PC} = 1{sup +-} B{sup *} anti B{sup *} molecular state, and they disfavor assigning the Y(3940) to the (J{sup PC} = 0{sup ++}) molecular state. The present predictions can be confronted with the experimental data in the future. (orig.)
Sum Rule Approach to Nuclear Collective Vibration
Erbil, H.; Gerçeklioglu, M.; M. Ilhan; Kuliev, A.
1997-01-01
The NEWSR and the EWSR are studied microscopically within TDA and RPA methods. By exploiting the analytic properties of the electromagnetic and allowed β-transitions matrix elements the theory of residue and contour integrals is used IO show that exact calculation of the NEWSR and EWSR is possible. In TDA (non-degenerate limit) we deduce formula for the EWSR of Eλ transition strength We have given different way of the proof of Thouless theorem about exactly exhausting the EWSR of Eλ transitio...
Hermaphrodite mesons and QCD sum rules
International Nuclear Information System (INIS)
We present a new evaluation of the two-point function built from the colourless operators g anti psilambdasup(α)γν(γ5)psiFsup(μν)sub(α). Previous calculations for the dimension-six vacuum condensate contributions were incomplete. We give new predictions for the masses and decay amplitudes of 1-+ and 0-- hermaphrodite mesons. (orig.)
Weak probes and the Gottfried sum rule
International Nuclear Information System (INIS)
We investigate the possibility of probing the flavour asymmetric nucleon sea in the LLA using ν and ν-bar projectiles. We find that for the NC case it is difficult to disentangle the effects of this flavour asymmetry from other contributions in a clean way. However, it is possible to obtain a sizeable effect for the CC case which can easily be isolated. Our conclusions are valid up to first order in α. (author). 23 refs
Beautiful mesons from QCD spectral sum rules
Energy Technology Data Exchange (ETDEWEB)
Narison, S.
1988-08-18
We apply q/sup 2/ = 0 moments within n (number of derivatives) and t/sub c/ (continuum threshold) stability criteria to the beautiful-meson systems. The optimal predictions are reached for the same ranges of n and t/sub c/ values leading to the previous estimate of the decay constant f/sub B/. The QCD scales (b-quark 'physical' mass, mixed and four-quark condensates) are strongly constrained by the observed B and B/sup */ masses. The predictions for the S- and P-state splittings are much affected by the definition of the b-quark mass (pole or euclidian) entering into the Wilson coefficients of the non-perturbative condensates. The size of the SU(3)/sub F/ breaking on the mass splittings cannot be accurately predicted due to the imprecise value of the
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Bjorken flow from an anti-de Sitter space Schwarzschild black hole.
Alsup, James; Siopsis, George
2008-07-18
We consider a large black hole in asymptotically anti-de Sitter spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions. PMID:18764245
Experimental determination of the evolution of the Bjorken integral at low Q{sup 2}
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur; Peter Bosted; Volker Burkert; Gordon Cates; Jian-Ping Chen; Seonho Choi; Donald Crabb; Cornelis de Jager; Raffaella De Vita; Gail Dodge; Renee Fatemi; Tony Forest; Franco Garibaldi; Ronald Gilman; Emlyn Hughes; Xiaodong Jiang; Wolfgang Korsch; Sebastian Kuhn; Wolodymyr Melnitchouk; Zein-Eddine Meziani; Ralph Minehart; Alexander Skabelin; Karl Slifer; Mauro Taiuti; Junho Yun
2004-07-01
We extract the Bjorken integral {Gamma}{sub 1}{sup p-n} in the range 0.17 < Q{sup 2} < 1.10 GeV{sup 2} from inclusive scattering of polarized electrons by polarized protons, deuterons and {sup 3}He, for the region in which the integral is dominated by nucleon resonances. These data bridge the domains of the hadronic and partonic descriptions of the nucleon. In combination with earlier measurements at higher Q{sup 2}, we extract the non-singlet twist-4 matrix element f{sub 2}.
Fu, Hai-Bing; Wu, Xing-Gang; Ma, Yang; Cheng, Wei; Zhong, Tao
2016-08-01
We present a detailed calculation on the B\\to {K}* transition form factors (TFFs), {A}{0,1,2}, V and {T}{1,2,3}, within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude {φ }2;{K*}\\perp provides over 90% contribution, thus those TFFs provide good platforms for testing the property of {φ }2;{K*}\\perp . We suggest a model for {φ }2;{K*}\\perp , in which two parameters {B}2;{K*}\\perp and {C}2;{K*}\\perp dominantly control its longitudinal distribution. With a proper choice of {B}2;{K*}\\perp and {C}2;{K*}\\perp , our predictions on B\\to {K}* TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay B\\to {K}*{μ }+{μ }-. The predicted differential branching fraction {{d}}{B}/{{d}}{q}2(B\\to {K}*{μ }+{μ }-) is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q 2-region, we get the branching fraction, {B}(B\\to {K}*{μ }+{μ }-)=≤ft({1.088}-0.205+0.261\\right)× {10}-6, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of {φ }2;{K*}\\perp .
Measurement of neutral current cross-sections at high Bjorken- with the ZEUS detector at HERA
Indian Academy of Sciences (India)
Inderpal Singh; on behalf of the ZEUS Collaboration
2012-11-01
A new method is employed to measure the neutral current cross-section up to Bjorken values of 1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb-1 of electron–proton collisions and 142 pb-1 of positron–proton collisions, at a centre-of-mass energy of 318 GeV. Cross-sections have been extracted for 2 > 575 GeV2. A much improved precision with respect to the previous ZEUS publication, which used only 16.7 pb-1 of electron–proton collisions and 65.1 pb-1 of positron–proton collisions, is achieved, owing to the large data sample and improved kinematic reconstruction methods. The measurement is well-described by different theory predictions.
Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
Floerchinger, Stefan
2015-01-01
Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane and rapidity. We examine how the time evolution of linear perturbations depends on the equation of state as well as on shear viscosity, bulk viscosity and heat conductivity for modes with different azimuthal, radial and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.
Inclusive Dijet Production at Low Bjorken-x in Deep Inelastic Scattering
Aktas, A; Anthonis, T; Asmone, A; Babaev, A; Backovic, S; Bähr, J; Baranov, P; Barrelet, E; Bartel, Wulfrin; Baumgartner, S; Becker, J; Beckingham, M; Behnke, O; Behrendt, O; Belousov, A; Berger, C; Berndt, T; Bizot, J C; Böhme, J; Boenig, M O; Boudry, V; Bracinik, J; Braunschweig, W; Brisson, V; Broker, H B; Brown, D P; Bruncko, Dusan; Büsser, F W; Bunyatyan, A; Buschhorn, G; Bystritskaya, L; Campbell, A J; Caron, S; Cassol-Brunner, F; Chekelian, V; Clarke, D; Collard, Caroline; Contreras, J G; Coppens, Y R; Coughlan, J A; Cousinou, M C; Cox, B E; Cozzika, G; Cvach, J; Dainton, J B; Dau, W D; Daum, K; Delcourt, B; Delerue, N; Demirchyan, R; de Roeck, A; De Wolf, E A; Diaconu, C; Dingfelder, J; Dodonov, V; Dowell, John D; Dubak, A; Duprel, C; Eckerlin, G; Efremenko, V; Egli, S; Eichler, R; Eisele, F; Ellerbrock, M; Elsen, E; Erdmann, M; Erdmann, W; Faulkner, P J W; Favart, L; Fedotov, A; Felst, R; Ferencei, J; Fleischer, M; Fleischmann, P; Fleming, Y H; Flucke, G; Flügge, G; Fomenko, A; Foresti, I; Formánek, J; Franke, G; Frising, G; Gabathuler, Erwin; Gabathuler, K; Garvey, J; Gassner, J; Gayler, J; Gerhards, R; Gerlich, C; Ghazaryan, S; Görlich, L; Gogitidze, N; Gorbounov, S; Grab, C; Grabskii, V; Grässler, Herbert; Greenshaw, T; Gregori, M; Grindhammer, G; Haidt, Dieter; Hajduk, L; Haller, J; Heinzelmann, G; Henderson, R C W; Henschel, H; Henshaw, O; Heremans, R; Herrera-Corral, G; Herynek, I; Hildebrandt, M; Hiller, K H; Hladky, J; Hoting, P; Hoffmann, D; Horisberger, R P; Hovhannisyan, A; Ibbotson, M; Jacquet, M; Janauschek, L; Janssen, X; Jemanov, V; Jönsson, L B; Johnson, C; Johnson, D P; Jung, H; Kant, D; Kapichine, M; Karlsson, M; Katzy, J; Keil, F; Keller, N; Kennedy, J; Kenyon, I R; Kiesling, C; Klein, M; Kleinwort, C; Kluge, T; Knies, G; Koblitz, B; Kolya, S D; Korbel, V; Kostka, P; Koutouev, R; Kropivnitskaya, A; Kroseberg, J; Kueckens, J; Kuhr, T; Landon, M P J; Lange, W; Lastoviicka, T; Laycock, P; Lebedev, A; Leiner, B; Lemrani, R; Lendermann, V; Levonian, S; List, B; Lobodzinska, E; Loktionova, N A; López-Fernandez, R; Lubimov, V; Lüders, H; Lüders, S; Lüke, D; Lytkin, L; Makankine, A; Malden, N; Malinovskii, E I; Mangano, S; Marage, P; Marks, J; Marshall, R; Martyn, H U; Martyniak, J; Maxfield, S J; Meer, D; Mehta, A; Meier, K; Meyer, A B; Meyer, H; Meyer, J; Michine, S; Mikocki, S; Milstead, D; Moreau, F; Morozov, A; Morozov, I; Morris, J V; Müller, K; Murn, P; Nagovizin, V; Naroska, Beate; Naumann, J; Naumann, T; Newman, P R; Niebergall, F; Niebuhr, C B; Nikitin, D K; Nowak, G; Nozicka, M; Olivier, B; Olsson, J E; Ossoskov, G; Ozerov, D; Pascaud, C; Patel, G D; Peez, M; Pérez, E; Petrukhin, A; Pitzl, D; Pöschl, R; Povh, B; Raicevic, N; Rauschenberger, J; Reimer, P; Reisert, B; Risler, C; Rizvi, E; Robmann, P; Roosen, R; Rostovtsev, A A; Rusakov, S V; Rybicki, K; Sankey, D P C; Sauvan, E; Schatzel, S; Scheins, J; Schilling, F P; Schleper, P; Schmidt, S; Schmitt, S; Schneider, M; Schoeffel, L; Schöning, A; Schröder, V; Schultz-Coulon, H C; Schwanenberger, C; Sedlak, K; Sefkow, F; Shevyakov, I; Shtarkov, L N; Sirois, Y; Sloan, T; Smirnov, P; Soloviev, Yu; South, D; Spaskov, V; Specka, A; Spitzer, H; Stamen, R; Stella, B; Stiewe, J; Strauch, I; Straumann, U; Thompson, G; Thompson, P D; Tomasz, F; Traynor, D; Truöl, P; Tsipolitis, G; Tsurin, I; Turnau, J; Turney, J E; Tzamariudaki, E; Uraev, A; Urban, M; Usik, A; Valkár, S; Valkárová, A; Vallée, C; Van Mechelen, P; Vargas-Trevino, A; Vasilev, S; Vazdik, Ya A; Veelken, C; Vest, A; Vichnevski, A; Vinokurova, S; Volchinski, V; Wacker, K; Wagner, J; Waugh, B; Weber, G; Weber, R; Wegener, D; Werner, C; Werner, N; Wessels, M; Wessling, B; Winde, M; Winter, G G; Wissing, C; Woerling, E E; Wünsch, E; Zaicek, J; Zaleisak, J; Zhang, Z; Zhokin, A; Zomer, F; Zur Nedden, M
2003-01-01
Dijet production in deep inelastic ep scattering is investigated in the region of low values of the Bjorken-variable x (10^-4 < x < 10^-2) and low photon virtualities Q^2 (5 < Q^2 < 100 GeV^2). The measured dijet cross sections are compared with perturbative QCD calculations in next-to-leading order. For most dijet variables studied, these calculations can provide a reasonable description of the data over the full phase space region covered, including the region of very low x. However, large discrepancies are observed for events with small separation in azimuth between the two highest transverse momentum jets. This region of phase space is described better by predictions based on the CCFM evolution equation, which incorporates k_t factorized unintegrated parton distributions. A reasonable description is also obtained using the Color Dipole Model or models incorporating virtual photon structure.
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Vyawahare, Anant
2006-01-01
This paper deals with the sums of products of first n natural numbers, taken r at a time. Many interesting results about the summations are obtained. Ramasubramanian has already made some work in this direction. This paper is an extension of his work. In next part, the sums of odd and even natural numbers are discussed, and also of natural numbers, not necessarily beginning with one. After that, properties of sequences, arising out of these sums are obtained. Interest...
U.S. Geological Survey, Department of the Interior — The GIS layer "Census_sum_15" provides a standardized tool for examining spatial patterns in abundance and demographic trends of the southern sea otter (Enhydra...
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Jørgensen, Allan Grønlund
2008-01-01
In an array of n numbers each of the \\binomn2+nUnknown control sequence '\\binom' contiguous subarrays define a sum. In this paper we focus on algorithms for selecting and reporting maximal sums from an array of numbers. First, we consider the problem of reporting k subarrays inducing the k largest...... sums among all subarrays of length at least l and at most u. For this problem we design an optimal O(n + k) time algorithm. Secondly, we consider the problem of selecting a subarray storing the k’th largest sum. For this problem we prove a time bound of Θ(n · max {1,log(k/n)}) by describing an...... algorithm with this running time and by proving a matching lower bound. Finally, we combine the ideas and obtain an O(n· max {1,log(k/n)}) time algorithm that selects a subarray storing the k’th largest sum among all subarrays of length at least l and at most u....
Factorization of numbers with Gauss sums: I. Mathematical background
Wölk, S.; Merkel, W.; Schleich, W. P.; Averbukh, I.Sh.; Girard, B
2012-01-01
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.
Multiparty Symmetric Sum Types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes with the......This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...
The Hadronic Final State in Deep Inelastic ep Scattering at Low Bjorken-x at HERA
International Nuclear Information System (INIS)
The electron-proton collider HERA with centre of mass system energy of about 300 GeV has extended the available kinematic regime in deep inelastic scattering to low values of Bjorken-x (10-5-10-3) and made possible studies of the QCD dynamics in this region. The processes in which partons carry a very small fraction of the proton momentum may show deviations from the standard DGLAP dynamics and it is believed that their correct description is provided by the BFKL evolution formalism. Low x phenomena have been initially studied with the HERA data on F2 structure function and later with more exclusive measurements of the hadronic final state. In this report recent results of these studies and especially dedicated measurements of jets and π0 mesons, produced close to the proton remnant, are reviewed. The data are used to discriminate between QCD models with different parton evolution approximations. For completeness, measurements at e+e- and p-p colliders sensitive to the BFKL dynamics are also described. (author)
The extraction of the spin structure function, g2 (and g1) at low Bjorken x
International Nuclear Information System (INIS)
The Spin Asymmetries of the Nucleon Experiment (SANE) used the Continuous Electron Beam Accelerator Facility at Jefferson Laboratory in Newport News, VA to investigate the spin structure of the proton. The experiment measured inclusive double polarization electron asymmetries using a polarized electron beam, scattered off a solid polarized ammonia target with target polarization aligned longitudinal and near transverse to the electron beam, allowing the extraction of the spin asymmetries A1 and A2, and spin structure functions g1 and g2. Polarized electrons of energies of 4.7 and 5.9 GeV were used. The scattered electrons were detected by a novel, non-magnetic array of detectors observing a four-momentum transfer range of 2.5 to 6.5 GeV*V. This document addresses the extraction of the spin asymmetries and spin structure functions, with a focus on spin structure function, g2 (and g1) at low Bjorken x. The spin structure functions were measured as a function of x and W in four Q square bins. A full understanding of the low x region is necessary to get clean results for SANE and extend our understanding of the kinematic region at low x.
Multiparty Symmetric Sum Types
Directory of Open Access Journals (Sweden)
Lasse Nielsen
2010-11-01
Full Text Available This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs. Processes using the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient implementation of a prototypical tool for CPGs which automatically translates the original CPG specifications from a representation called the Process Matrix to symmetric sum types, type checks programs and executes them.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
Thin sums matroids and duality
Afzali, Hadi
2012-01-01
Thin sums matroids were introduced to extend the notion of representability to non-finitary matroids. We give a new criterion for testing when the thin sums construction gives a matroid. We show that thin sums matroids over thin families are precisely the duals of representable matroids (those arising from vector spaces). We also show that the class of tame thin sums matroids is closed under duality and under taking minors, by giving a new characterisation of the matroids in this class. Finally, we show that all the matroids naturally associated to an infinite graph are tame thin sums matroids.
Directory of Open Access Journals (Sweden)
Charles Swartz
2014-06-01
Full Text Available If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.
Aktay, Metin
2000-01-01
Goldbach`s Conjecture, "every even number greater than 2 can be expressed as the sum of two primes" is renamed Goldbach`s Rule for it can not be otherwise. The conjecture is proven by showing that the existence of prime pairs adding to any even number greater than 2 is a natural by-product of the existence of the prime sequence less than that even number. First it is shown that the remainder of cancellations process which identifies primes less than an even number also remainders prime pairs ...
Institute of Scientific and Technical Information of China (English)
贺丽; 余增强
2016-01-01
Sum rules for the dynamic structure factors are powerful tools to explore the collective behaviors in many-body systems at zero temperature as well as at finite temperatures. The recent remarkable realization of synthetic spin-orbit (SO) coupling in quantum gases is opening up new perspective to study the intriguing SO effects with ultracold atoms. So far, a specific type of SO coupling, which is generated by a pair of Raman laser beams, has been experimentally achieved in Bose-Einstein condensates of 87Rb and degenerate Fermi gases of 40K and 6Li. In the presence of SO coupling, the dynamic structure factors for the density fluctuation and spin fluctuation satisfy different sum rules. In particular, in the two-component quantum gases with inter-species Raman coupling, the f-sum rule for the spin fluctuation has an additional term proportional to the transverse spin polarization. Due to the coupling between the momentum and spin, the first moment of the dynamic structure factor does not necessarily possess the inversion symmetry, which is in strong contrast to the conventional system without SO coupling. Such an asymmetric behavior could be observed in both Fermi gases and Bose gases with Raman coupling. As a demonstration, we focus on the uniform case at zero temperature in this work. For the non-interacting Fermi gases, the asymmetric first moment appears only when the Raman detuning is finite. The asymmetric amplitude is quite limited, and it vanishes at both zero detuning and infinite detuning. For the weakly interacting Bose gases, the first moment is asymmetric in momentum space even at zero detuning, when the ground state spontaneously breaks the Z2 symmetry in the plane-wave condensation phase. Using the Bogoliubov method, the dynamic structure factor and its first moment are explicitly calculated for various interaction parameters. We find that the asymmetric behavior in the spin channel could be much more significant than in the density channel, and the
Social Security Administration — Staging Instance for all SUMs Counts related projects including: Redeterminations/Limited Issue, Continuing Disability Resolution, CDR Performance Measures, Initial...
On exponential sums of digital sums related to Gelfond's theorem
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
Recurrence Formulas for Fibonacci Sums
Brandao, Adilson J V
2008-01-01
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term differentiation theorem
Measurement of neutral current cross sections at high Bjorken-x with the ZEUS detector at HERA
International Nuclear Information System (INIS)
A new method is employed to measure the neutral current cross section up to Bjorken-x values of one with the ZEUS detector at HERA using an integrated luminosity of 65.1 pb-1 for e+p collisions and 16.7 pb-1 for e-p collisions at √(s)=318 GeV and 38.6 pb-1 for e+p collisions at √(s)=300 GeV. Cross sections have been extracted for Q2≥648 GeV2 and are compared to predictions using different parton density functions. For the highest x bins, the data have a tendency to lie above the expectations using recent parton density function parametrizations. (orig.)
Measurement of neutral current e{sup {+-}}p cross sections at high Bjorken x with the ZEUS detector
Energy Technology Data Exchange (ETDEWEB)
Abramowicz, H. [Tel Aviv Univ. (Israel). School of Physics; Max-Planck-Institute for Physics, Munich (Germany); Abt, I. [Max-Planck-Institute for Physics, Munich (Germany); Adamczyk, L. [AGH-Univ. of Science and Technology, Krakow (Poland). Faculty of Physics and Applied Computer Science; Collaboration: ZEUS Collaboration; and others
2013-12-15
The neutral current e{sup {+-}}p cross section has been measured up to values of Bjorken x{approx_equal}1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb{sup -1} of e{sup -}p and 142 pb{sup -1} of e{sup +}p collisions at {radical}(s)=318 GeV. Differential cross sections in x and Q{sup 2}, the exchanged boson virtuality, are presented for Q{sup 2}{>=}725 GeV{sup 2}. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.
Measurement of neutral current e±p cross sections at high Bjorken x with the ZEUS detector
International Nuclear Information System (INIS)
The neutral current e±p cross section has been measured up to values of Bjorken x≅1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb-1 of e-p and 142 pb-1 of e+p collisions at √(s)=318 GeV. Differential cross sections in x and Q2, the exchanged boson virtuality, are presented for Q2≥725 GeV2. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.
Dynamical Higher-Twist and High x-Bjorken Phenomena: A Window to Quark-Quark Correlations in QCD
International Nuclear Information System (INIS)
Measurements of the power-law corrections to Bjorken scaling and the behavior of structure functions in the highly stressed xbj --> 1 regime of electroproduction can lead to new information on the quark-quark correlations controlling the nucleon wavefunction at far-off-shell kinematics. Electroproduction on nuclei at A > xbj > 1 are sensitive to hidden-color components of the nuclear wavefunction. A distinctive dynamical higher-twist order of (1/Q2) correction, which is dynamically enhanced at high xbj, can arise from the interference of amplitudes where the lepton scatters from two different valence quarks of the target. Measurements of the parity-violating left-right asymmetry ALR in elastic and inelastic polarized electron scattering at large xbj can confirm the structure of the quark-quark correlations and other QCD physics at the amplitude level
Measurement of neutral current e+/-p cross sections at high Bjorken x with the ZEUS detector
Abramowicz, H; Adamczyk, L; Adamus, M; Aggarwal, R; Antonelli, S; Arslan, O; Aushev, V; Aushev, Y; Bachynska, O; Barakbaev, A N; Bartosik, N; Behnke, O; Behr, J; Behrens, U; Bertolin, A; Bhadra, S; Bloch, I; Bokhonov, V; Boos, E G; Borras, K; Brock, I; Brugnera, R; Bruni, A; Brzozowska, B; Bussey, P J; Caldwell, A; Capua, M; Catterall, C D; Chwastowski, J; Ciborowski, J; Cooper-Sarkar, A M; Corradi, M; Corriveau, F; Agostini, G D; Dementiev, R K; Devenish, R C E; Dolinska, G; Drugakov, V; Dusini, S; Ferrando, J; Figiel, J; Foster, B; Gach, G; Garfagnini, A; Geiser, A; Gizhko, A; Gladilin, L K; Gogota, O; Golubkov, Yu A; Grebenyuk, J; Gregor, I; Grzelak, G; Gueta, O; Guzik, M; Hain, W; Hartner, G; Hochman, D; Hori, R; Ibrahim, Z A; Iga, Y; Ishitsuka, M; Iudin, A; Januschek, F; Kadenko, I; Kananov, S; Kanno, T; Karshon, U; Kaur, M; Kaur, P; Khein, L A; Kisielewska, D; Klanner, R; Klein, U; Kondrashova, N; Kononenko, O; Korol, Ie; Korzhavina, I A; Kotanski, A; Koetz, U; Kovalchuk, N; Kowalski, H; Kuprash, O; Kuze, M; Levchenko, B B; Levy, A; Libov, V; Limentani, S; Lisovyi, M; Lobodzinska, E; Lohmann, W; Loehr, B; Lohrmann, E; Longhin, A; Lontkovskyi, D; Lukina, O Yu; Maeda, J; Makarenko, I; Malka, J; Martin, J F; Mergelmeyer, S; Idris, F Mohamad; Mujkic, K; Myronenko, V; Nagano, K; Nigro, A; Nobe, T; Notz, D; Nowak, R J; Olkiewicz, K; Onishchuk, Yu; Paul, E; Perlanski, W; Perrey, H; Pokrovskiy, N S; Proskuryakov, A S; Przybycien, M; Raval, A; Roloff, P; Rubinsky, I; Ruspa, M; Samojlov, V; Saxon, D H; Schioppa, M; Schmidke, W B; Schneekloth, U; Schoerner-Sadenius, T; Schwartz, J; Shcheglova, L M; Shevchenko, R; Shkola, O; Singh, I; Skillicorn, I O; Slominski, W; Sola, V; Solano, A; Spiridonov, A; Stanco, L; Stefaniuk, N; Stern, A; Stewart, T P; Stopa, P; Sztuk-Dambietz, J; Szuba, D; Szuba, J; Tassi, E; Temiraliev, T; Tokushuku, K; Tomaszewska, J; Trofymov, A; Trusov, V; Tsurugai, T; Turcato, M; Turkot, O; Tymieniecka, T; Verbytskyi, A; Viazlo, O; Walczak, R; Abdullah, W A T Wan; Wichmann, K; Wing, M; Wolf, G; Yamada, S; Yamazaki, Y; Zakharchuk, N; Zarnecki, A F; Zawiejski, L; Zenaiev, O; Zhautykov, B O; Zhmak, N; Zotkin, D S
2013-01-01
The neutral current e+/-p cross section has been measured up to values of Bjorken x of approximately 1 with the ZEUS detector at HERA using an integrated luminosity of 187 inv. pb of e-p and 142 inv. pb of e+p collisions at sqrt(s) = 318GeV. Differential cross sections in x and Q2, the exchanged boson virtuality, are presented for Q2 geq 725GeV2. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.
Generation of symmetric exponential sums
Sergeyev, Yaroslav D.
2011-01-01
In this paper, a new method for generation of infinite series of symmetric identities written for exponential sums in real numbers is proposed. Such systems have numerous applications in theory of numbers, chaos theory, algorithmic complexity, dynamic systems, etc. Properties of generated identities are studied. Relations of the introduced method for generation of symmetric exponential sums to the Morse-Hedlund sequence and to the theory of magic squares are established.
Comment concerning Leonardo's rule
Sotolongo-Costa, O; Oseguera-Manzanilla, T; Díaz-Guerrero, D S
2016-01-01
In this comment we propose a novel explanation for the Leonardo's rule concerning the tree branching. According to Leonardo's notebooks he observed that if one observes the branches of a tree, the squared radius of the principal branch is equal to the sum of the squared radius of the branch daughters.
Measurement sum theory and application - Application to low level measurements
International Nuclear Information System (INIS)
In laboratories, most of the Total Sum methods implemented today use substitution or censure methods for nonsignificant or negative values, and thus create biases which can sometimes be quite large. They are usually positive, and generate, for example, becquerel (Bq) counting or 'administrative' quantities of materials (= 'virtual'), thus artificially falsifying the records kept by the laboratories under regulatory requirements (environment release records, waste records, etc.). This document suggests a methodology which will enable the user to avoid such biases. It is based on the following two fundamental rules: - The Total Sum of measurement values must be established based on all the individual measurement values, even those considered non-significant including the negative values. Any modification of these values, under the pretext that they are not significant, will inevitably lead to biases in the accumulated result and falsify the evaluation of its uncertainty. - In Total Sum operations, the decision thresholds are arrived at in a similar way to the approach used for uncertainties. The document deals with four essential aspects of the notion of 'measurement Total Sums': - The expression of results and associated uncertainties close to Decision Thresholds, and Detection or Quantification Limits, - The Total Sum of these measurements: sum or mean, - The calculation of the uncertainties associated with the Total Sums, - Result presentation (particularly when preparing balance sheets or reports, etc.) Several case studies arising from different situations are used to illustrate the methodology: environmental monitoring reports, release reports, and chemical impurity Total Sums for the qualification of a finished product. The special case of material balances, in which the measurements are usually all significant and correlated (the covariance term cannot then be ignored) will be the subject of a future second document. This
Character Sums Over The Prime Numbers
Carella, N. A.
2012-01-01
A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.
Compressibility sum rule for the two-dimensional electron gas.
Das, M P; Golden, K I; Green, F
2001-07-01
The authors establish formulas for the isothermal compressibility and long-wavelength static density-density response function of a weakly correlated two-dimensional electron gas in the 1pressure calculation in the latter domain is based on the Totsuji classical cluster-expansion formula for the correlation energy [H. Totsuji, J. Phys. Soc. Jpn. 40, 857 (1976); Phys. Rev. A 19, 889 (1979)]. PMID:11461304
Balandraud, Eric; Girard, Benjamin; Griffiths, Simon; Hamidoune, Yahya Ould
2011-01-01
Denoting by Sigma(S) the set of subset sums of a subset S of a finite abelian group G, we prove that |Sigma(S)| >= |S|(|S|+2)/4-1 whenever S is symmetric, |G| is odd and Sigma(S) is aperiodic. Up to an additive constant of 2 this result is best possible, and we obtain the stronger (exact best possible) bound in almost all cases. We prove similar results in the case |G| is even. Our proof requires us to extend a theorem of Olson on the number of subset sums of anti-symmetric subsets S from the...
Euler Sums of Hyperharmonic Numbers
Dil, Ayhan; Khristo N. Boyadzhiev
2012-01-01
The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\\sigma}(r,m)=\\sum_{n=1}^{\\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of series of Hurwitz zeta function values. This is a generalization of a result of Mez\\H{o} and Dil. We also provide an explicit evaluation of {\\sigma}(r,m) in a closed form in terms of zeta values and Stirling numbers of the first kind. Furthermore, we evalu...
Modular equations and lattice sums
Rogers, Mathew; Yuttanan, Boonrod
2010-01-01
We highlight modular equations discovered by Somos and Ramanujan, and use them to prove new relations between lattice sums and hypergeometric functions. We also discuss progress towards solving Boyd's Mahler measure conjectures, and we conjecture a new formula for $L(E,2)$ of conductor 17 elliptic curves.
EXTENSIONS OF EULER HARMONIC SUMS
Directory of Open Access Journals (Sweden)
Djurdje Cvijović
2012-10-01
Full Text Available Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Euler’s famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.
Torque-Summing Brushless Motor
Vaidya, J. G.
1986-01-01
Torque channels function cooperatively but electrically independent for reliability. Brushless, electronically-commutated dc motor sums electromagnetic torques on four channels and applies them to single shaft. Motor operates with any combination of channels and continues if one or more of channels fail electrically. Motor employs single stator and rotor and mechanically simple; however, each of channels electrically isolated from other so that failure of one does not adversely affect others.
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
Minimality of Symplectic Fiber Sums along Spheres
Dorfmeister, Josef G
2010-01-01
In this note we complete the discussion of minimality of symplectic fiber sums. We find, that for fiber sums along spheres the minimality of the sum is determined by the cases discussed by M. Usher and one additional case: If the sum is the result of the rational blow-down of a symplectic -4-sphere in X, then it is non-minimal if X contains a certain configuration of exceptional spheres in relation to this -4-sphere.
Polarized Quarks, Gluons and Sea in Nucleon Structure Functions
Bourrely, C.; Buccella, F.; Pisanti, O.; Santorelli, P.; Soffer, J.
1998-01-01
We perform a NLO analysis of polarized deep inelastic scattering data to test two different solutions to the so called spin crisis: one of them based on the axial gluon anomaly and consistent with the Bjorken sum rule and another one, where the defects in the spin sum rules and in the Gottfried sum rule are related. In this case a defect is also expected for the Bjorken sum rule. The first solution is slightly favoured by the SLAC E154 results, but both options seem to be consistent with the ...
Polarized Quarks, Gluons and Sea in Nucleon Structure Functions
Bourrely, C; Pisanti, O; Santorelli, P; Soffer, J
1998-01-01
We perform a NLO analysis of polarized deep inelastic scattering data to test two different solutions to the so called spin crisis: one of them based on the axial gluon anomaly and consistent with the Bjorken sum rule and another one, where the defects in the spin sum rules and in the Gottfried sum rule are related. In this case a defect is also expected for the Bjorken sum rule. The first solution is slightly favoured by the SLAC E154 results, but both options seem to be consistent with the CERN SMC data.
Quarks and Gluons in Nucleon Polarized Structure Functions
Bourrely, C.; Buccella, F.; Pisanti, O.; Santorelli, P.; Soffer, J.
1996-01-01
We study the available data in polarized e-p deep inelastic scattering to test two different solutions to the so called spin crisis: one of them based on the axial gluon anomaly and consistent with the Bjorken sum rule and another one, where the defects in the spin sum rules and in the Gottfried sum rule are related. In this case a defect is also expected for the Bjorken sum rule. Experimental data, especially the very recent SLAC E154, favour the first solution and demand a gluon polarizatio...
Polarized Quarks, Gluons and Sea in Nucleon Structure Functions
Bourrely, C.; Buccella, F.; Pisanti, O.; Santorelli, P.; Soffer, J.
1998-06-01
We perform a NLO analysis of polarized deep inelastic scattering data to test two different solutions to the so-called spin crisis, one of them based on the axial gluon anomaly and consistent with the Bjorken sum rule, and another in which the defects in the spin sum rules and in the Gottfried sum rule are related. In this case a defect is also expected for the Bjorken sum rule. The first solution is slightly favoured by the SLAC E154 results, but both options seem to be consistent with the CERN SMC data.
Nonnegative Polynomials and Sums of Squares
Blekherman, Grigoriy
2010-01-01
In the smallest cases where there exist nonnegative polynomials that are not sums of squares we present a complete classification of the differences between these sets. We show that in these cases the fundamental reason that the set of sums of squares is smaller than the set of nonnegative polynomials is that polynomials of degree d satisfy certain linear relations known as the Cayley-Bacharach relations, which are not satisfied by polynomials of full degree 2d. For any nonnegative polynomial that is not a sum of squares we can write down a linear inequality coming from a Cayley-Bacharach relation that certifies that the polynomial is not a sum of squares. We also present structure results on the strictly positive sums of squares that lie on the boundary of the cone of sums of squares and results on extreme rays of the cone dual to the cone of sums of squares.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
International Nuclear Information System (INIS)
Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Ablinger, Jakob; Raab, Clemens G; Schneider, Carsten
2014-01-01
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-07-15
Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Determinant Sums for Undirected Hamiltonicity
Björklund, Andreas
2010-01-01
We present a Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in $O^*(1.657^{n})$ time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for TSP almost fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the first open problem in Woeginger's 2003 survey on exact algorithms for NP-hard problems. For bipartite graphs, we improve the bound to $O^*(1.414^{n})$ time. Both the bipartite and the general algorithm can be implemented to use space polynomial in $n$. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for $k$-Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle covers over a finite field of characteristic two. We reduce Hamiltonicity to Labeled ...
Decompounding random sums: A nonparametric approach
DEFF Research Database (Denmark)
Hansen, Martin Bøgsted; Pitts, Susan M.
Observations from sums of random variables with a random number of summands, known as random, compound or stopped sums arise within many areas of engineering and science. Quite often it is desirable to infer properties of the distribution of the terms in the random sum. In the present paper we...... review a number of applications and consider the nonlinear inverse problem of inferring the cumulative distribution function of the components in the random sum. We review the existing literature on non-parametric approaches to the problem. The models amenable to the analysis are generalized considerably...
New continuity estimates of geometric sums
Directory of Open Access Journals (Sweden)
Evgueni Gordienko
2002-01-01
Full Text Available The paper deals with sums of a random number of independent and identically distributed random variables. More specifically, we compare two such sums, which differ from each other in the distributions of their summands. New upper bounds (inequalities for the uniform distance between distributions of sums are established. The right-hand sides of these inequalities are expressed in terms of Zolotarev's and the uniform distances between the distributions of summands. Such a feature makes it possible to consider these inequalities as continuity estimates and to apply them to the study of the stability (continuity of various applied stochastic models involving geometric sums and their generalizations.
Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers
Directory of Open Access Journals (Sweden)
E. Kılıç
2011-01-01
Full Text Available By considering Melham's sums (Melham, 2004, we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−12+1 involving the generalized Fibonacci and Lucas numbers.
Where Does Latin "Sum" Come From?
Nyman, Martti A.
1977-01-01
The derivation of Latin "sum,""es(s),""est" from Indo-European "esmi,""est,""esti" involves methodological problems. It is claimed here that the development of "sum" from "esmi" is related to the origin of the variation "est-st" (less than"esti"). The study is primarily concerned with this process, but chronological suggestions are also made. (CHK)
Sharp coincidences for absolutely summing multilinear operators
Pellegrino, Daniel
2012-01-01
In this note we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators. We connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar results obtained via the complex interpolation method.
A hybrid mean value related to the Dedekind sums and Kloosterman sums
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The main purpose of this paper is using the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums,and give some interesting mean value formulae and identities for it.
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
Directory of Open Access Journals (Sweden)
Shaofeng Ru
2014-01-01
Full Text Available The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
Gersbach, Hans; Hahn, Volker; Imhof, Stephan
2010-01-01
We examine the provision of public projects under tax and subsidy rules. We find that tax rules separated from project cum subsidy decisions exhibit several advantages when incentive problems of the agenda-setter are taken into account. In particular, tax rules may prevent the proposal of inefficient projects that benefit only a small lobby group. We propose “redistribution efficiency” as a socially desirable property of proposals and find that tax rules always guarantee this kind of efficien...
International Nuclear Information System (INIS)
Let D be a t-(v, k, λ) design and let Ni(D), for 1 ≤ i ≤ t, be the higher incidence matrix of D, a (0, 1)-matrix of size (v/i) x b, where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N1(D). A zero-sum k-flow of D is a zero-sum flow with values in {±,...,±(k-1)}. In this paper we show that every non-symmetric design admits an integral zero-sum flow, and consequently we conjecture that every non-symmetric design admits a zero-sum 5-flow. Similarly, the definition of zero-sum flow can be extended to Ni(D), 1 ≤ i ≤ t. Let D = t-(v,k, (v-t/k-t)) be the complete design. We conjecture that Nt(D) admits a zero-sum 3-flow and prove this conjecture for t = 2. (author)
Sums-of-Products and Subproblem Independence
Stearns, Richard E.; Hunt, Harry B.
Sums-of-products provide a basis for describing certain computational problems, particularly problems related to constraint satisfaction including SAT, MAX SAT, and #SAT. They also can be used to describe many problems arising from graph theory. By modeling a problem as a sum-of-products problem, the concept of “subproblem independence” takes on a clear meaning. Subproblem independence has immediate computational implications since it can be used to create programs with reduced levels of nesting and programs which exploit memoization. The concept of subproblem independence also extends to quantified sums.
Parton Distributions in the Nucleon and the Pauli Principle
Buccella, Franco; Soffer, Jacques
The Pauli principle is used, together with some deep inelastic scattering data, to guide us in making reasonable assumptions for various polarized parton distributions in terms of unpolarized distributions. We relate the violation of the Gottfried and Ellis-Jaffe sum rules and we anticipate a substantial violation of the Bjorken sum rule.
What can we learn from polarized structure function data?
International Nuclear Information System (INIS)
We summarise the perturbative QCD analysis of the structure function data for g1 from longitudinally polarized deep inelastic scattering from proton, deuteron and neutron targets, with particular emphasis on testing sum rules, determining helicity fractions, and extracting the strong coupling from both scaling violations and the Bjorken sum rule
What can we learn from polarized structure function data?
Ball, R D; Altarelli, Guido; Forte, Stefano; Ball, Richard D.; Ridolfi, Giovanni; Altarelli, Guido; Forte, Stefano
1997-01-01
We summarise the perturbative QCD analysis of the structure function data for g_1 from longitudinally polarized deep inelastic scattering from proton, deuteron and neutron targets, with particular emphasis on testing sum rules, determining helicity fractions, and extracting the strong coupling from both scaling violations and the Bjorken sum rule.
Fiber sums of genus 2 Lefschetz fibrations
Auroux, Denis
2003-01-01
Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.
Sum formulas for reductive algebraic groups
DEFF Research Database (Denmark)
Andersen, Henning Haahr; Kulkarni, Upendra
2008-01-01
\\supset V^1 \\cdots \\supset V^r = 0$. The sum of the positive terms in this filtration satisfies a well known sum formula. If $T$ denotes a tilting module either for $G$ or $U_q$ then we can similarly filter the space $\\Hom_G(V,T)$, respectively $\\Hom_{U_q}(V,T)$ and there is a sum formula for the positive...... terms here as well. We give an easy and unified proof of these two (equivalent) sum formulas. Our approach is based on an Euler type identity which we show holds without any restrictions on $p$ or $l$. In particular, we get rid of previous such restrictions in the tilting module case....
On Learning Ring-Sum-Expansions
DEFF Research Database (Denmark)
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2...
Structural relations between nested harmonic sums
International Nuclear Information System (INIS)
We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)
Exponential sums over primes in short intervals
Institute of Scientific and Technical Information of China (English)
LIU; Jianya
2006-01-01
[1]Vinogradov,I.M.,Estimation of certain trigonometric sums with prime variables,Izv.Acad.Nauk.SSSR,1939,3:371-398.[2]Zhan,T.,On the representation of large odd integer as a sum of three almost equal primes,Acta Math.Sin.,1991,7:259-272.[3]Ren,X.M.,On exponential sums over primes and application in the Waring-Goldbach problem,Sci.China,Ser.A-Math.,2005,48(6):785-797.[4]Liu,J.Y.,Wooley,T.D.,Yu,G.,The quadratic Waring-Goldbach problem,J.Number Theory,2004,107:298-321.[5]Hua,L.K.,Some results in the additive prime number theory,Quart.J.Math.(Oxford),1938,9:68-80.[6]Liu,J.Y.,Zhan,T.,On sums of five almost equal prime squares,Acta Arith.,1996,77:369-383.[7]Bauer,C.,A note on sums of five almost equal prime squares,Arch.Math,1997,69:20-30.[8]Liu,J.Y.,Zhan,T.,Sums of five almost equal prime squares,Science in China,Ser.A,1998,41:710-722.[9]Liu,J.Y.,Zhan,T.,Hua's theorem on prime squares in short intervals,Acta Math.Sin.,2000,16:1-22.[10]Bauer,C.,Sums of five almost equal prime squares,Acta Math.Sin.,2005,21(4):833-840.[11]Lü,G.S.,Hua's Theorem with five almost equal prime variables,Chin.Ann.Math.,Ser.B,2005,26(2):291-304.[12]Vinogradov,I.M.,Elements of Number Theory,Dover Publications,1954.[13]Titchmarsh,E.C.,The Theory of the Riemann Zeta-function,2nd ed.,Oxford:Oxford University Press,1986.
Partial sum approaches to mathematical parameters of some growth models
Korkmaz, Mehmet
2016-04-01
Growth model is fitted by evaluating the mathematical parameters, a, b and c. In this study, the method of partial sums were used. For finding the mathematical parameters, firstly three partial sums were used, secondly four partial sums were used, thirdly five partial sums were used and finally N partial sums were used. The purpose of increasing the partial decomposition is to produce a better phase model which gives a better expected value by minimizing error sum of squares in the interval used.
SANE's Measurement of the Proton's Virtual Photon Spin Asymmetry, A^{p}_{1}, at Large Bjorken x
Energy Technology Data Exchange (ETDEWEB)
Mulholland, Jonathan [Univ. of Virginia, Charlottesville, VA (United States)
2012-05-01
The experiment SANE (Spin Asymmetries of the Nucleon Experiment) measured inclusive double polarization electron asymmetries on a proton target at the Continuous Electron Beam Accelerator Facility at the Thomas Jefferson National Laboratory in Newport News Virgina. Polarized electrons were scattered from a solid ^{14}NH_{3} polarized target provided by the University of Virginia target group. Measurements were taken with the target polarization oriented at 80 degrees and 180 degrees relative to the beam direction, and beam energies of 4.7 and 5.9 GeV were used. Scattered electrons were detected by a multi-component novel non-magnetic detector package constructed for this experiment. Asymmetries measured at the two target orientations allow for the extraction of the virtual Compton asymmetries A_{1}^{p} and A_{2}^{p} as well as the spin structure functions g_{1}^{p} and g_{2}^{p}. This work addresses the extraction of the virtual Compton asymmetry A_{1}^{p} in the deep inelastic regime. The analysis uses data in the kinematic range from Bjorken x of 0.30 to 0.55, separated into four Q^{2} bins from 1.9 to 4.7 GeV^{2}.
Dowker, J S
2015-01-01
The finite sums of powers of cosecs occur in numerous situations, both physical and mathematical, examples being the Casimir effect, Renyi entropy, Verlinde's formula and Dedekind sums. I here present some further discussion which consists mainly of a reprise of early work by H.M.Jeffery in 1862-64 which has fallen by the wayside and whose results are being reproduced up to the present day. The motivation is partly historical justice and partly that, because of the continuing appearance of the sums, his particular methods deserve re--exposure. For example, simple trigonometric generating functions are found and these have a field theoretic, Green function significance and I make a few comments in the topic of R\\'enyi entropies.
Subset sum phase transitions and data compression
Merhav, Neri
2011-01-01
We propose a rigorous analysis approach for the subset sum problem in the context of lossless data compression, where the phase transition of the subset sum problem is directly related to the passage between ambiguous and non-ambiguous decompression, for a compression scheme that is based on specifying the sequence composition. The proposed analysis lends itself to straightforward extensions in several directions of interest, including non-binary alphabets, incorporation of side information at the decoder (Slepian-Wolf coding), and coding schemes based on multiple subset sums. It is also demonstrated that the proposed technique can be used to analyze the critical behavior in a more involved situation where the sequence composition is not specified by the encoder.
Separating OR, SUM, and XOR Circuits
Find, Magnus; Göös, Mika; Järvisalo, Matti; Kaski, Petteri; Koivisto, Mikko; Korhonen, Janne H.
2013-01-01
Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on \\emph{separating} these models in terms of their circuit complexities. We give three results towards this goal: (1) We prove a direct sum type theorem on the monotone complexity of ...
Cyclotomy of Weil Sums of Binomials
Aubry, Yves; Katz, Daniel J.; Langevin, Philippe
2013-01-01
The Weil sum $W_{K,d}(a)=\\sum_{x \\in K} \\psi(x^d + a x)$ where $K$ is a finite field, $\\psi$ is an additive character of $K$, $d$ is coprime to $|K^\\times|$, and $a \\in K^\\times$ arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where $W_{K,d}(a)$ assumes three distinct values as $a$ runs through $K^\\times$. A Galois-theoretic approach, combined with...
Large- quantum chromodynamics and harmonic sums
Indian Academy of Sciences (India)
Eduardo De Rafael
2012-06-01
In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is discussed.
Zero-Sum Problems with Subgroup Weights
Indian Academy of Sciences (India)
S D Adhikari; A A Ambily; B Sury
2010-06-01
In this note, we generalize some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider $\\mathbb{Z}^d_p$ for a general and subgroups of $Z^∗_p$ as weights.
Summing threshold logs in a parton shower
Nagy, Zoltan
2016-01-01
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in $\\alpha_s$ that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
Demonstration of a Quantum Nondemolition Sum Gate
DEFF Research Database (Denmark)
Yoshikawa, J.; Miwa, Y.; Huck, Alexander;
2008-01-01
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature...
Fibonacci Identities via the Determinant Sum Property
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
RIORDAN MATRICES AND SUMS OF HARMONIC NUMBERS
Directory of Open Access Journals (Sweden)
Emanuele Munarini
2011-10-01
Full Text Available We obtain a general identity involving the row-sums of a Riordan matrixand the harmonic numbers. From this identity, we deduce several particular identities involving numbers of combinatorial interest, such as generalized Fibonacci and Lucas numbers, Catalan numbers, binomial and trinomial coefficients and Stirling numbers.
Coincidence summing in gamma-ray spectroscopy
International Nuclear Information System (INIS)
A new technique has been developed to calculate coincidence-summing corrections in γ-ray spectroscopy. In this technique the general coincidence-summing equations were derived in matrix notation, which allowed extracting either the first-order correction (combinations of only two coincident γ-rays) or a full correction (all possible combinations of emitted γ-rays). Subsequently, it is shown how the technique can be applied to the determination of the source disintegration rate, γ-ray emission rates or peak efficiencies in the presence of coincidence summing. In particular, the technique has been applied to the determination of peak efficiencies of a germanium detector. The peak efficiencies were iterated self-consistently using the coincidence-summing equations. The above calculation showed that, in general, the full correction is necessary for complicated decay schemes. In addition, a method has been developed to determine the peak-to-total ratio for a germanium detector in the presence of an interfering γ-ray. (orig.)
On Learning Ring-Sum-Expansions
DEFF Research Database (Denmark)
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2...... cannot be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only. Moreover, it is proved that 2-term-RSE is learnable by a...
Improved approach to the heavy-to-light form factors in the light-cone QCD sum
Huang, Tao; Li, Zuo-Hong; Wu, Xiang-Yao
2000-01-01
A systematic analysis shows that the main uncertainties in the form factors are due to the twist-3 wave functions of the light mesons in the light-cone QCD sum rules. We propose an improved approach, in which the twist-3 wave functions doesn't make any contribution and therefore the possible pollution by them can be avoided, to re-examine $B \\to \\pi$ semileptonic form factors. Also, a comparison between the previous and our results from the light-cone QCD sum rules is made. Our method will be...
A New Generalization of Hardy-Berndt Sums
Indian Academy of Sciences (India)
Muhammet Cihat Dağli; Mümün Can
2013-05-01
In this paper, we construct a new generalization of Hardy–Berndt sums which are explicit extensions of Hardy–Berndt sums. We express these sums in terms of Dedekind sums $s_r(h,k:x,y|)$ with ==0 and obtain corresponding reciprocity formulas.
26 CFR 1.1502-36 - Unified loss rule.
2010-04-01
... (including rules for transfers of S stock between members), definitions, and an anti-abuse rule, respectively... is the sum of S's net operating and capital loss carryovers, deferred deductions, money, and basis in assets other than money, reduced by the amount of S's liabilities. For this purpose, S's basis in...
Transition Mean Values of Shifted Convolution Sums
Petrow, Ian
2011-01-01
Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let \\lambda(n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues \\lambda(n) after averaging over many shifts h and obtain asymptotic estimates. The result is somewhat surprising: one encounters a transition region depending on the ratio of the square of the length of the average over h to the length of the shifted convolution sum. The phenomenon is similar to that encountered by Conrey, Farmer and Soundararajan in their 2000 paper Transition Mean Values of Real Characters, and the connection of both results to Eisenstein series and multiple Dirichlet series is discussed.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
Theorems of Forming and Summing of Natural Numbers and Their Application
Manaye Getu Tsige
2013-01-01
This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular...
Gao's Conjecture on Zero-Sum Sequences
Indian Academy of Sciences (India)
B Sury; R Thangadurai
2002-08-01
In this paper, we shall address three closely-related conjectures due to van Emde Boas, W D Gao and Kemnitz on zero-sum problems on $\\mathbf{Z}_p \\oplus \\mathbf{Z}_p$. We prove a number of results including a proof of the conjecture of Gao for the prime = 7 (Theorem 3.1). The conjecture of Kemnitz is also proved (Propositions 4.6, 4.9, 4.10) for many classes of sequences.
Disjoint sum forms in reliability theory
Directory of Open Access Journals (Sweden)
B. Anrig
2014-01-01
Full Text Available The structure function f of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of f, an improved Abraham algorithm is proposed for generating the disjoint sum form of f. This form is the base for subsequent numerical reliability calculations. The approach is generalized to multivalued systems. Examples are discussed.
Sequences, Bent Functions and Jacobsthal sums
Helleseth, Tor; Kholosha, Alexander
2010-01-01
The $p$-ary function $f(x)$ mapping $\\mathrm{GF}(p^{4k})$ to $\\mathrm{GF}(p)$ and given by $f(x)={\\rm Tr}_{4k}\\big(ax^d+bx^2\\big)$ with $a,b\\in\\mathrm{GF}(p^{4k})$ and $d=p^{3k}+p^{2k}-p^k+1$ is studied with the respect to its exponential sum. In the case when either $a^{p^k(p^k+1)}\
Strong sum distance in fuzzy graphs
Tom, Mini; Sunitha, Muraleedharan Shetty
2015-01-01
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccent...
Sum of Bernoulli Mixtures: Beyond Conditional Independence
Taehan Bae; Ian Iscoe
2014-01-01
We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk ...
Sum Product Networks for Activity Recognition.
Amer, Mohamed R; Todorovic, Sinisa
2016-04-01
This paper addresses detection and localization of human activities in videos. We focus on activities that may have variable spatiotemporal arrangements of parts, and numbers of actors. Such activities are represented by a sum-product network (SPN). A product node in SPN represents a particular arrangement of parts, and a sum node represents alternative arrangements. The sums and products are hierarchically organized, and grounded onto space-time windows covering the video. The windows provide evidence about the activity classes based on the Counting Grid (CG) model of visual words. This evidence is propagated bottom-up and top-down to parse the SPN graph for the explanation of the video. The node connectivity and model parameters of SPN and CG are jointly learned under two settings, weakly supervised, and supervised. For evaluation, we use our new Volleyball dataset, along with the benchmark datasets VIRAT, UT-Interactions, KTH, and TRECVID MED 2011. Our video classification and activity localization are superior to those of the state of the art on these datasets. PMID:26390445
A 2-categorical state sum model
Energy Technology Data Exchange (ETDEWEB)
Baratin, Aristide, E-mail: abaratin@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario N2L 3G1 (Canada); Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Str. N, Waterloo, Ontario N2L 2Y5 (Canada)
2015-01-15
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.
DEFF Research Database (Denmark)
Christensen, Jørgen Riber
2011-01-01
climax of the masque was “Rule, Britannia!” This song advocated a strong navy as a guard against the absolutist European powers with their lack of civil liberties. Furthermore, a strong navy made a standing army superfluous, and so an army could not be deployed as a repressive force of the state. Later a...
Weigert, Heribert
2000-01-01
This paper presents a solution to the nonlinear small x ``projectile side'' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Lange...
Weigert, H
2002-01-01
This paper presents a solution to the nonlinear small x ``projectile side'' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Langevin equations are given as a basis for numerical simulations opening the field for future studies of dynamical issues of the evolution not analytically accessible. The methods used may be extended to the ``target side'' equations of Jalilian-Marian, Kovner, Leonidov and Weigert.
International Nuclear Information System (INIS)
This paper presents a solution to the nonlinear small-x 'projectile side' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Langevin equations are given as a basis for numerical simulations opening the field for future studies of dynamical issues of the evolution not analytically accessible. The methods used may be extended to the 'target side' equations of Jalilian-Marian, Kovner, Leonidov and Weigert
Energy Technology Data Exchange (ETDEWEB)
Weigert, Heribert E-mail: heribert.weigert@physik.uni-regensburg.de
2002-06-03
This paper presents a solution to the nonlinear small-x 'projectile side' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Langevin equations are given as a basis for numerical simulations opening the field for future studies of dynamical issues of the evolution not analytically accessible. The methods used may be extended to the 'target side' equations of Jalilian-Marian, Kovner, Leonidov and Weigert.