Higher twist corrections to Bjorken sum rule
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
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
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
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
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
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
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
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
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
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.
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
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
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)
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.
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.