Nuclear pions and the Gottfried and Bjorken sum rules
Energy Technology Data Exchange (ETDEWEB)
Epele, L.N. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Fanchiotti, H. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Garcia Canal, C.A. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Leader, E. (Birkbeck Coll., Univ. of London (United Kingdom)); Sassot, R. (Lab. de Fisica Teorica, Dept. de Fisica, Univ. Nacional de La Plata (Argentina))
1994-10-01
An extremely simple but instructive, ''toy'' model is presented which shows that a small excess of pions in the nucleus can produce a significant change in the values expected for the Gottfried sum rule. The general question of the convergence of the sum rule and of the convergence of the experimental integral is also discussed. It is demonstrated that conclusions about the sum rule, based on deuterium data, are surprisingly model dependent. In contrast, it is stressed, that the Bjorken sum rule can be tested significantly using deuterium data. (orig.)
The nucleon axial isoscalar coupling constant and the Bjorken sum rule
International Nuclear Information System (INIS)
The nucleon coupling constant with the axial isoscalar current entering the Bjorken sum rule for the deep inelastic scattering of polarized electrons on a polarized target is calculated in nonperturbative QCD. The result, gsub(A)sup(s) approximately 0.5, is about a factor of two smaller as compared to that of the SU(6) symmetric quark model
Bjorken unpolarized and polarized sum rules comparative analysis of large-N_F expansions
Broadhurst, D J
2002-01-01
Analytical all-orders results are presented for the one-renormalon-chain contributions to the Bjorken unpolarized sum rule for the F_1 structure function of nu N deep-inelastic scattering in the large-N_F limit. The feasibility of estimating higher order perturbative QCD corrections, by the process of naive nonabelianization (NNA), is studied, in anticipation of measurement of this sum rule at a Neutrino Factory. A comparison is made with similar estimates obtained for the Bjorken polarized sum rule. Application of the NNA procedure to correlators of quark vector and scalar currents, in the euclidean region, is compared with recent analytical results for the O(alpha_s^4 N_F^2) terms.
Measurement of the neutron spin structure function---Test of the Bjorken sum rule
International Nuclear Information System (INIS)
As experiment to measure the neutron spin-dependent structure function g1n (x) over a range in x from 0.04 to 0.7 and with Q2 > 1 (GeV/c)2 is presented. The experiment consists of scattering a longitudinally polarized electron beam from the Stanford Linear Accelerator off a polarized 3He target and detecting scattered electrons in two magnetic spectrometers. The experiment will provide a critical test of the Bjorken sum rule and valuable information in understanding the nucleon spin structure and the violation of the Ellis-Jaffe sum rule. 3 figs., 1 tab
QCD effects to Bjorken unpolarized sum rule for νN deep-inelastic scattering
International Nuclear Information System (INIS)
The possibility of the first measurement of Bjorken unpolarized sum rule for F1 structure function of νN deep-inelastic scattering at neutrino factories is commented. The brief summary of various theoretical contributions to this sum rule is given. Using the next-to-leading set of parton distributions functions, we simulate the expected Q2-behaviour and emphasize that its measurement can allow us to determine the value of the QCD strong coupling constant αs with reasonable theoretical uncertainty, dominated by the ambiguity in the existing estimates of the twist-4 non-perturbative 1/Q2-effect
Yaouanc, A Le; Raynal, J -C
2015-01-01
We underline that the Bakamjian-Thomas relativistic quark model is the only known theoretical scheme, describing hadrons with a fixed number of constituents, that yields covariant Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules of the heavy quark limit of QCD (Bjorken-Uraltsev sum rules). In the heavy quark limit, it has been demonstrated that a formalism, based on Lorentz group representations in a Hilbert space, implies this class of sum rules. On the other hand, it has been recently shown that a Lorentz group representation in a Hilbert space underlies the Bakamjian-Thomas class of relativistic quark models in the heavy quark limit. Therefore, due to completeness in this space, the model satisfies the whole tower of Bjorken-Uraltsev sum rules. To illustrate in practice this feature we provide some examples. In particular, we demonstrate explicitly Bjorken and Uraltsev sum rules within the Bakamjian-Thomas framework, and also an interesting sum rule that involves only heavy mes...
Low-x contribution to the Bjorken sum rule within double logarithmic $ln^2x$ approximation
Kotlorz, D; Kotlorz, Dorota; Kotlorz, Andrzej
2004-01-01
The small-$x$ contributions to the Bjorken sum rule within double logarithmic $ln^2x$ approximation for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Analytical solutions of the evolution equations for full and truncated moments of the unintegrated structure function $f^{NS}(x,Q^2)$ are used. Theoretical predictions for $\\int_{0}^{0.003} g_1^{NS}(x,Q^2=10) dx$ are compared with the SMC small-$x$ data. Rough estimation of the slope $\\lambda$, controlling the small-$x$ behaviour of $g_1^{NS}\\sim x^{-\\lambda}$ from the SMC data is performed. Double logarithmic terms $\\sim (\\alpha_s ln^2x)^n$ become leading when $x\\to 0$ and imply the singular behaviour of $g_1^{NS}\\sim x^{-0.4}$. This seems to be confirmed by recent experimental SMC and HERMES data. Advantages of the unified $ln^2x$+LO DGLAP approach and the crucial role of the running coupling $\\alpha_s=\\alpha_s(Q^2/z)$ at low-$x$ are also discussed.
Cvetic, G
2001-01-01
A renormalization-scale-invariant generalization of the diagonal Pade approximants (dPA), developed previously, is extended so that it becomes renormalization-scheme-invariant as well. We do this explicitly when two terms beyond the leading order (NNLO,$\\sim {\\alpha}_s^3$) are known in the truncated perturbation series (TPS). Invariance under the change of the leading scheme parameter c_2 is achieved via a variant of the principle of minimal sensitivity. The subleading parameter c_3 is fixed so that a scale- and scheme-invariant Borel transform of the resummation approximant gives the correct location of the leading infrared renormalon pole. The leading higher-twist contribution, or a part of it, is thus believed to be contained implicitly in the resummation. We applied the approximant to the Bjorken polarized sum rule (BjPSR) at $Q^2 = 3 GeV^2$ and obtained in {bar MS} scheme ${\\alpha}_s(M_Z)=0.111^{+0.005}_{-0.012}$ or $0.113^{+0.004}_{-0.019}$, for two frameworks of extraction of the BjPSR-integral values ...
Baikov, P A; Chetyrkin, K G; Kühn, J H
2010-04-01
We compute, for the first time, the order alpha(s)(4) contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta(3) in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha(s)(4). PMID:20481875
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order αs4 in a General Gauge Theory
International Nuclear Information System (INIS)
We compute, for the first time, the order αs4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop β function in quenched QED. In particular, the appearance of an irrational contribution proportional to ζ3 in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order αs4.
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
2010-01-01
We compute, for the first time, the order alpha_s^4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (non-singlet) Adler function for the case of a generic colour gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta-function in quenched QED. In particular, the appearance of an irrational contribution ...
Low-x contribution to the Bjorken sum rule within unified $ln^2x+$LO DGLAP approximation
Kotlorz, D
2004-01-01
The small-$x$ contributions to the Bjorken sum rule within unified picture $ln^2x+$LO DGLAP for different input parametrisations $g_1^{NS}(x,Q_0^2)$ are presented. Theoretical predictions for $\\int_{0}^{0.003} g_1^{NS}(x,Q^2=10) dx$ are compared with the SMC small-$x$ data. Rough estimation of the slope $\\lambda$, controlling the small-$x$ behaviour of $g_1^{NS}\\sim x^{-\\lambda}$ from the obtained results and SMC data is performed. The crucial role of the running coupling $\\alpha_s=\\alpha_s(Q^2/z)$ at low-$x$ is taken into account.
The spin structure function g1p of the proton and a test of the Bjorken sum rule
Directory of Open Access Journals (Sweden)
C. Adolph
2016-02-01
Full Text Available New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p(x by about a factor of two in the region x≲0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS(x,Q2 yields as ratio of the axial and vector coupling constants |gA/gV|=1.22±0.05 (stat.±0.10 (syst., which validates the sum rule to an accuracy of about 9%.
The Spin Structure Function $g_1^{\\rm p}$ of the Proton and a Test of the Bjorken Sum Rule
Adolph, C.; Alexeev, M.G.; Alexeev, G.D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badelek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E.R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Buchele, M.; Burtin, E.; Capozza, L.; Chang, W.C.; Chiosso, M.; Choi, I.; Chung, S.U.; Cicuttin, A.; Crespo, M.L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S.S.; Dasgupta, S.; Denisov, O.Yu.; Dhara, L.; Donskov, S.V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Ferrero, A.; Finger, M.; M. Finger jr; Fischer, H.; Franco, C.; von Hohenesche, N. du Fresne; Friedrich, J.M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmuller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F.H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.Yu; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jorg, P.; Joosten, R.; Kabuss, E.; Ketzer, B.; Khaustov, G.V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J.H.; Kolosov, V.N.; Kondo, K.; Konigsmann, K.; Konorov, I.; Konstantinov, V.F.; Kotzinian, A.M.; Kouznetsov, O.; Kramer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z.V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R.P.; Lednev, A.A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V.I.; Novy, J.; Nowak, W.D.; Nunes, A.S.; Olshevsky, A.G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.C.; Pereira, F.; Pesek, M.; Peshekhonov, D.V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V.A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N.S.; Ryabchikov, D.I.; Rychter, A.; Samoylenko, V.D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I.A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schonning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O.Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Wolbeek, J. ter; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-01-01
New results for the double spin asymmetry $A_1^{\\rm p}$ and the proton longitudinal spin structure function $g_1^{\\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\\rm p}(x)$ by about a factor of two in the region $x\\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\\Delta \\Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\\rm p}$. The uncertainty of $\\Delta \\Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\\rm...
Cvetič, Gorazd; Kataev, A. L.
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the non-singlet part of the $e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering $C_{ns}^{Bjp}$, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is a two-fold series in terms of powers of the conformal anomaly and of $SU(N_c)$ coupling $\\alpha_s$. Explicit expressions are obtaine...
Cvetič, Gorazd
2016-01-01
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the $e^+e^-$-annihilation to hadrons Adler function, and the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering, and demonstrate its validity at the $O(\\alpha_s^4)$-level at least. It is expressed through a two-fold series in terms of powers of the conformal anomaly and the coupling constant $\\alpha_s$ of the $SU(N_c)$ gauge model. Subsequently, explicit expressions are obtained for the $\\{\\beta\\}$-expanded perturbation coefficients at $O(\\alpha_s^4)$ level in $\\overline{\\rm MS}$ scheme, for the nonsinglet contribution to the Adler function and the Bjorken polarized sum rule. Comparisons of the obtained terms in the $\\{\\beta\\}$-expanded perturbation coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\\delta}$-scheme motivated expansion in the Principle of Maximal Conformality. Relations are pres...
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
Energy Technology Data Exchange (ETDEWEB)
Djawotho, Pibero [College of William and Mary, Williamsburg, VA (United States)
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
Anomalous commutator corrections to sum rules
International Nuclear Information System (INIS)
In this paper we consider the contributions of anomalous commutators to various QCD sum rules. Using a combination of the Bjorken-Johnson-Low limit with the operator product expansion the results are presented in terms of the vacuum condensates of gauge-invariant operators. It is demonstrated that the anomalous contributions are non-negligible and reconcile various apparently contradictory calculations
DEFF Research Database (Denmark)
T. Frandsen, Mads; Masina, Isabella; Sannino, Francesco
2011-01-01
We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models.......We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models....
Adler Function, DIS sum rules and Crewther Relations
International Nuclear Information System (INIS)
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(αs4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(αs4) contribution to the singlet part of the Adler function.
Adler Function, DIS sum rules and Crewther Relations
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
2010-01-01
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) con...
Spinrath, Martin
2016-01-01
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. While the effect of the renormalisation group running can be visible, the qualitative features do not change. This changes somewhat for model dependent corrections which might alter even the qualitative predictions but only for large corrections and a high neutrino mass scale close to the edge of the current limits. This finding backs up the solidity of the predictions derived in the literature apart from some exceptions, and it thus marks a very important step in deriving testable and robust predictions from neutrino flavour models.
International Nuclear Information System (INIS)
An approach to gluonium based on QCD sum rules is given. The basic idea underlying the sum rules is that asymptotic freedom is violated first by interaction of quarks and gluons with vacuum fields. Formation of resonances is a phenomenological manifestation of this interaction. The emphasis is given to a new mass scale implied by the sum rules
Fluctuations in classical sum rules.
Elton, John R; Lakshminarayan, Arul; Tomsovic, Steven
2010-10-01
Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum-rule convergence may well be exponentially rapid for chaotic systems in a global phase-space sense with time, individual contributions to the sums may fluctuate with a width which diverges in time. Our interest is in the global convergence of sum rules as well as their local fluctuations. It turns out that a simple version of a lazy baker map gives an ideal system in which classical sum rules, their corrections, and their fluctuations can be worked out analytically. This is worked out in detail for the Hannay-Ozorio sum rule. In this particular case the rate of convergence of the sum rule is found to be governed by the Pollicott-Ruelle resonances, and both local and global boundaries for which the sum rule may converge are given. In addition, the width of the fluctuations is considered and worked out analytically, and it is shown to have an interesting dependence on the location of the region over which the sum rule is applied. It is also found that as the region of application is decreased in size the fluctuations grow. This suggests a way of controlling the length scale of the fluctuations by considering a time dependent phase-space volume, which for the lazy baker map decreases exponentially rapidly with time.
Uraltsev Sum Rule in Bakamjian-Thomas Quark Models addendum
Le Yaouanc, A; Oliver, L; Pène, O; Raynal, J C
2001-01-01
In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function $\\xi_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|\\tau_{1/2}(1)| \\ll |\\tau_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\\it production} rates of $P$-states $\\Gamma(\\bar{B}_d \\to D ({1 \\over 2}) \\ell \
Spin Sum Rules and the Strong Coupling Constant at large distance.
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur
2009-07-01
We present recent results on the Bjorken and the generalized forward spin polarizability sum rules from Jefferson Lab Hall A and CLAS experiments, focusing on the low $Q^2$ part of the measurements. We then discuss the comparison of these results with Chiral Perturbation theory calculations. In the second part of this paper, we show how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.
Dominguez, C. A.
2013-08-01
A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this issue. Collectively, these papers constitute the proceedings of the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013.
Sum rules in the response function method
Energy Technology Data Exchange (ETDEWEB)
Takayanagi, Kazuo (Regensburg Univ. (Germany, F.R.). Inst. fuer Physik 1 - Theoretische Physik)
1990-04-02
Sum rules in the response function method are studied in detail. A sum rule can be obtained theoretically by integrating the imaginary part of the response function over the excitation energy with a corresponding energy weight. Generally, the response function is calculated perturbatively in terms of the residual interaction, and the expansion can be described by diagrammatic methods. In this paper, we present a classification of the diagrams so as to clarify which diagram has what contribution to which sum rule. This will allow us to get insight into the contributions to the sum rules of all the processes expressed by Goldstone diagrams. (orig.).
Magnetic Dipole Sum Rules for Odd Nuclei
Ginocchio, J N
1997-01-01
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but not with the latter.
Remarks on sum rules in the heavy quark limit of QCD
Le Yaouanc, A; Pène, O; Raynal, J C; Morénas, V
2001-01-01
We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \\over 2}$ (wide states) or $j = {3 \\over 2}$ (narrow states). The leading order sum rules of Bjorken and Uraltsev suggest $\\Gamma [ \\bar{B} \\to D_{0,1} ({1 \\over 2}) \\ell \
Adler Function, DIS sum rules and the Crewther Relation in order αs4
International Nuclear Information System (INIS)
We report on the first analytical, valid for a generic gauge group, calculations of the O(αs4) corrections to the Adler function and to DIS sum rules, in particular to the the Gross-Llewellyn Smith and to the Bjorken ones. We discuss a decisive check of correctness of our previous calculations of R(s) in QCD and the quenched QED beta-function at five loops, which was carried out with the help of the newly computed contributions to the DIS sum rules and the Crewther relation. (author)
Weinberg sum rules at finite temperature
Ayala, A; Loewe, M; Zhang, Y
2014-01-01
The saturation of the two Weinberg sum rules is studied at finite temperature, using recent independent QCD sum rule results for the thermal behaviour of hadronic parameters in the vector and axial-vector channels. Both sum rules are very well satisfied from $T=0$ up to $T/T_c \\simeq 0.7-0.8$. At higher temperatures close to $T_c$ a hadronic, pion-loop contribution in the space-like region proportional to $T^2$, present at leading order in the vector but not in the axial-vector channel, induces an asymmetry leading to a small deviation. In this region, though, QCD sum rules for the hadronic parameters begin to have no solutions, as the hadronic widths of the $\\rho$ and the $a_1$ mesons diverge signalling deconfinement. Close to, and at $T=T_c$ there are no pions left in the medium and chiral symmetry is restored, so that the sum rules are trivially satisfied.
Sum rule of the correlation function
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.
Sum rule approach to nuclear vibrations
International Nuclear Information System (INIS)
Velocity field of various collective states is explored by using sum rules for the nuclear current. It is shown that an irrotational and incompressible flow model is applicable to giant resonance states. Structure of the hydrodynamical states is discussed according to Tomonaga's microscopic theory for collective motions. (author)
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].
Beautiful mesons from QCD spectral sum rules
Energy Technology Data Exchange (ETDEWEB)
Narison, S. (OPM, Univ. Montpellier 2, 34 (France))
1991-08-01
We discuss the beautiful meson from the point of view of the QCD spectral sum rules (QSSR). The bottom quark mass and the mixed light quark-gluon condensates are determined quite accurately. The decay constant f{sub B} is estimated and we present some arguments supporting this result. The decay constants and the masses of the other members of the beautiful meson family are predicted. (orig.).
Light four-quark states and QCD sum rule
Institute of Scientific and Technical Information of China (English)
ZHANG Ai-Lin
2009-01-01
The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.
International Nuclear Information System (INIS)
Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken , the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the U(1) and SU(Nc) models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical O(α4) and O(αs2) conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed
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.
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^{\
Adler-Weisberger sum rule for WLWL→WLWL scattering
International Nuclear Information System (INIS)
We analyse the Adler-Weisberger sum rule for WLWL→WLWL scattering. We find that at some energy, the WLWL total cross section must be large to saturate the sum rule. Measurements at future colliders would be needed to check the sum rule and to obtain the decay rates Γ(H→WLWL, ZLZL) which would be modified by the existence of a P-wave vector meson resonance in the standard model with strongly interacting Higgs sector or in technicolour models. (orig.)
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.
Sum Rules for the Dirac Spectrum of the Schwinger Model
Shifrin, L
2005-01-01
The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of arbitrary topological charge. We show that the sum rules can be obtained from the clustering property of the scalar correlation functions. This argument also holds for other theories with a mass gap and broken chiral symmetry such as QCD with one flavor. For QCD with several flavors a modified clustering property is derived from the low energy chiral Lagrangian. We also obtain sum rules for a fixed external gauge field and show their relation with the bosonized version of the Schwinger model. In the sector of topological charge $\
Dispersion relations and sum rules for natural optical activity
International Nuclear Information System (INIS)
Dispersion relations and sum rules are derived for the complex rotatory power of an arbitrary linear (nonmagnetic) isotropic medium showing natural optical activity. Both previously known dispersion relations and sum rules as well as new ones are obtained. It is shown that the Rosenfeld-Condon dispersion formula is inconsistent with the expected asymptotic behavior at high frequencies. A new dispersion formula based on quantum eletro-dynamics removes this inconsistency; however, it still requires modification in the low-frequency limit. (Author)
QCD Sum Rules and Models for Generalized Parton Distributions
Energy Technology Data Exchange (ETDEWEB)
Anatoly Radyushkin
2004-10-01
I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ansaetze are briefly discussed.
Nuclear effects in deuteron and the Gottfried sum rule
Energy Technology Data Exchange (ETDEWEB)
Epele, L.N.; Sassot, R. (Lab. de Fisica Teorica, Univ. Nacional de La Plata (Argentina)); Fanchiotti, H. (Theory Div., CERN, Geneva (Switzerland)); Carcia Canal, C.A. (Lab. de Fisica Teorica, Univ. Nacional de La Plata (Argentina) Theory Div., CERN, Geneva (Switzerland))
1992-01-23
Recent NMC data on the ratio of the deep inelastic structure functions F{sub 2} per nucleon for deuterium relative to hydrogen are analysed in the context of the Gottfried sum rule. It is shown that the discrepancy between the Gottfried sum rule prediction and NMC data analysis may be interpreted as a nuclear effect in deuterium as it is suggested by several models. This fact, applied to nuclear-deuterium measured ratios, modifies the standard picture of nuclear effects. (orig.).
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...
Sum Rules, Classical and Quantum - A Pedagogical Approach
Karstens, William; Smith, David Y.
2014-03-01
Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.
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.
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.
Heavy hybrid mesons in the QCD sum rule
Huang, Peng-Zhi
2011-01-01
We study the spectra of the hybrid mesons containing one heavy quark ($q\\bar{Q}g$) within the framework of QCD sum rules in the heavy quark limit. The derived sum rules are stable with the variation of the Borel parameter within their corresponding working ranges. The extracted binding energy for the heavy hybrid doublets $H(S)$ and $M(T)$ is almost degenerate. We also calculate the pionic couplings between these heavy hybrid and the conventional heavy meson doublets using the light-cone QCD sum rule method. The extracted coupling constants are rather small as a whole. With these couplings we make a rough estimate of the partial widths of these pionic decay channels.
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.
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...
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.
A new neutrino mass sum rule from inverse seesaw
Dorame, L; Peinado, E; Rojas, Alma D; Valle, J W F
2012-01-01
A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum-rules (MSR). One of these implies in a lower bound on the effective neutrinoless double beta mass parameter, even for normal hierarchy neutrinos. Here we propose a new model based on the S4 flavor symmetry that leads to the new neutrino mass sum-rule and discuss how to generate a nonzero value for the reactor mixing angle indicated by recent experiments, and the resulting correlation with the solar mixing angle.
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.
Adler-Weisberger sum rule and hadronic models
International Nuclear Information System (INIS)
In order to understand the low value that several hadronic models predict for g/sub A/, we investigate the Δ contribution to the Adler-Weisberger sum rule in the MIT bag model and in the Skyrme model. It is shown that because of recoil corrections this value decreases 15% from (5/3) in the for- mer, and that it is very small in the latter because of the depressed prediction for g/sub π//sub N//sub Δ/. The meaning of the sum rule in the context of large-N/sub c/ models is also discussed
Nucleon QCD sum rules in the instanton medium
International Nuclear Information System (INIS)
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is ws ≈ 2/3
Impact of Duality Violations on Spectral Sum Rule Analyses
Cata, O
2007-01-01
Recent sum rule analyses on the two-point correlator have led to significant discrepancies in the values found for the OPE condensates, most dramatically in the dimension eight condensate and to a lesser extent in the dimension six one. Precise knowledge of these condensates is of relevance in kaon decays and therefore it seems mandatory to assess the actual impact of what is commonly neglected in spectral sum rules, most prominently the issue of duality violations. We will explicitly compute them in a toy model and show that they are a priori non-negligible.
QCD sum rule studies at finite density and temperature
Energy Technology Data Exchange (ETDEWEB)
Kwon, Youngshin
2010-01-21
In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)
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
Energy Technology Data Exchange (ETDEWEB)
Lucha, Wolfgang [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Melikhov, Dmitri [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991, Moscow (Russian Federation); Simula, Silvano [Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146, Roma (Italy)
2016-01-22
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Decay Constants of Beauty Mesons from QCD Sum Rules
Directory of Open Access Journals (Sweden)
Lucha Wolfgang
2014-01-01
Full Text Available Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b ≈ 4:18 GeV; the sum-rule result fB ≈ 210–220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b = 4:247 GeV: (ii Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty Vector Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; 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.
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}_{\
Beauty vector meson decay constants from QCD sum rules
International Nuclear Information System (INIS)
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity
QCD Sum Rule External Field Approach and Vacuum Susceptibilities
Institute of Scientific and Technical Information of China (English)
ZONG Hong-Shi; PING Jia-Lun; CHANG Chao-His; WANG Fan; ZHAO En-Guang
2002-01-01
Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuumsusceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shownthat the above two approaches of determination of the vector vacuum susceptibility may lead to different results. Thereason of this contradiction is discussed.
QCD sum rule studies at finite density and temperature
International Nuclear Information System (INIS)
In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)
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.
Proof of Kochen-Specker Theorem: Conversion of Product Rule to Sum Rule
Institute of Scientific and Technical Information of China (English)
S.P.Toh; Hishamuddin Zainuddin
2009-01-01
Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen-Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≥ 3, these constraints contradict individually with the assumption of value definiteness.The two rules are not irrelated and Peres [Found. Phys. 26 (1996)807] has conceived a method of converting the product rule into a sum rule for the case of two qubits. Here we apply this method to a proof provided by Mermin based on the product rule for a three-qubit system involving nine operators. We provide the conversion of this proof to one based on sum rule involving ten operators.
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
Directory of Open Access Journals (Sweden)
Stephan Narison
2014-11-01
Full Text Available Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300 and K(1460 decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI quark masses (mˆu+mˆq:q≡d,s and the corresponding running masses (m¯u+m¯q evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3 and K(1.46 hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.
Direct instantons, topological charge screening and QCD glueball sum rules
Forkel, H
2003-01-01
Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0^{-+} glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological shor...
Sum rule limitations of kinetic particle-production models
International Nuclear Information System (INIS)
Photoproduction and absorption sum rules generalized to systems at finite temperature provide a stringent check on the validity of kinetic models for the production of hard photons in intermediate energy nuclear collisions. We inspect such models for the case of nuclear matter at finite temperature employed in a kinetic regime which copes those encountered in energetic nuclear collisions, and find photon production rates which significantly exceed the limits imposed by the sum rule even under favourable concession. This suggests that coherence effects are quite important and the production of photons cannot be considered as an incoherent addition of individual NNγ production processes. The deficiencies of present kinetic models may also apply for the production of probes such as the pion which do not couple perturbatively to the nuclear currents. (orig.)
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.
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.
Comparison between two strictly local QCD sum rules
International Nuclear Information System (INIS)
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex q2 plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic (g-2) factor of the muon. Their effectiveness is demonstrated in the calculation of the topological susceptibility where both methods lead to χt1/4=171±4 MeV
Ds(0±) Meson Spectroscopy in Gaussian Sum Rules
Institute of Scientific and Technical Information of China (English)
WEN Shui-Guo; LIU Jue-Ping
2009-01-01
Masses of the Ds(0±) mesons are investigated from a view-point of ordinary light-heavy system in the framework of the Gaussian sum rules, which are worked out by means of the Laplacian transformation to the usual Borel sum rules. Using the standard input of QCD non-perturbative parameters, the corresponding mass spectra and couplings of the currents to the Ds(0±) mesons are obtained. Our results are mDs(O-) = 1.968±0.016±0.003 GeV and mDs(0+) = 2.320±0.014v0.003 GeV, which are in good accordance with the experimental data, 1.969 GeV and 2.317 GeV.
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.
Energy Technology Data Exchange (ETDEWEB)
Kominis, Ioannis
2001-01-31
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized 3He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q2 = 0 and to the Bjorken sum rule at Q2 >> 1 GeV2. By studying the Q2 evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized 3He target with both longitudinal and transverse target orientations. The high density 3He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision 3He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV2< Q2 <1 GcV2 and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the 3He spin structure functions He and g1e Finally, we determine the extended GDH sum for the range 0.1 GeV2< Q2 <1 GeV2 for 3He and the neutron.
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
Proton Spin Sum Rule from Large Momentum Effective Field Theory
International Nuclear Information System (INIS)
In high energy scattering experiments, the proton spin is understood as the sum of the spin and orbital angular momentum of the quarks and gluons in Feynman’s parton picture. The Jaffe–Manohar form of the proton spin sum rule is justified as physical, and it is shown that the individual terms can be related to the proton matrix elements of certain quasi-observables through a large momentum effective field theory. The relation is expressed as a factorization formula where the leading contribution to the quasi-observable is factorized into the parton observables and perturbative matching coefficients, and we present the results for the latter at one-loop order in perturbation theory. This will provide us with the basis to extract the proton spin content from the lattice QCD calculations of the quasi-observables. (author)
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...
$\\pi K$ 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...
Justifying the naive partonic sum rule for proton spin
International Nuclear Information System (INIS)
We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy
Light-Cone Sum Rule Approach for Baryon Form Factors
Offen, Nils
2016-10-01
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.
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.
Isoscalar quadratic energy weighted sum rules and quadrupole moment of giant quadrupole resonance
International Nuclear Information System (INIS)
Isoscalar sum rules homogeneous quadratic in energy weighting are derived for the electric multipole operators. Except for scaling factors the sum rule values for the pure quadrupole and monopole transitions are the same as that for the corresponding linear energy weighted sum rules. Through these sum rules the electric quadrupole moment of giant quadrupole resonance is found to be -2.7 Asup(1/3) efm2. (author)
QCD Sum Rules: Intercrossed Relations for Sigma^0 and Lambda Magnetic Moments
Özpineci, A; Zamiralov, V S
2003-01-01
New relations between QCD Borel sum rules for magnetic moments of Sigma^0 and Lambda hyperons are constructed. It is shown that starting from the sum rule for the Sigma^0 hyperon magnetic moment it is straightforward to obtain the corresponding sum rule for the Lambda hyperon magnetic moment et vice versa.
QCD Sum Rules: Intercrossed Relations for the Sigma^0-Lambda Mass Splitting
Zamiralov, V S
2003-01-01
New relations between QCD Borel sum rules for masses of Sigma^0 and Lambda hyperons are constructed. It is shown that starting from the sum rule for the Sigma^0 hyperon mass it is straightforward to obtain the corresponding sum rule for the Lambda hyperon mass and vice versa.
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 ...
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.
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.
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.
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.
Optical sum rule anomalies in high-temperature superconductors
International Nuclear Information System (INIS)
Many unusual features recently observed in the optical spectroscopy experiments in the cuprates can be simply understood as arising from the vicinity to the Mott transition, without invoking more involved and exotic mechanisms. Specifically, we compare calculations based on the Dynamical Mean Field Theory (DMFT) of the Hubbard model with the optical spectral weight Wopt of different cuprates, explaining most of the anomalies found in the optical sum rules with respect to normal metals, including the existence of two different energy scales for the doping- and the T-dependence of Wopt. A further support to this result is provided by the analysis of the optical conductivity in a typical case of the Mott-Hubbard metal-insulator transition, namely the V2O3.
The DHG sum rule measured with medium energy photons
Energy Technology Data Exchange (ETDEWEB)
Hicks, K.; Ardashev, K. [Ohio Univ., Athens, OH (United States); Babusci, D. [INFN-Lab. Nazionali di Frascati (Italy)] [and others
1997-12-31
The structure of the nucleon has many important features that are yet to be uncovered. Of current interest is the nucleon spin-structure which can be measured by doing double-polarization experiments with photon beams of medium energies (0.1 to 2 GeV). One such experiment uses dispersion relations, applied to the Compton scattering amplitude, to relate measurement of the total reaction cross section integrated over the incident photon energy to the nucleon anomalous magnetic moment. At present, no single facility spans the entire range of photon energies necessary to test this sum rule. The Laser-Electron Gamma Source (LEGS) facility will measure the double-polarization observables at photon energies between 0.15--0.47 MeV. Either the SPring8 facility, the GRAAL facility (France), or Jefferson Laboratory could make similar measurements at higher photon energies. A high-precision measurement of the spin-polarizability and the Drell-Hearn-Gerasimov sum rule is now possible with the advent of high-polarization solid HD targets at medium energy polarized photon facilities such as LEGS, GRAAL and SPring8. Other facilities with lower polarization in either the photon beam or target (or both) are also pursuing these measurements because of the high priority associated with this physics. The Spin-asymmetry (SASY) detector that will be used at LEGS has been briefly outlined in this paper. The detector efficiencies have been explored with simulations studies using the GEANT software, with the result that both charged and uncharged pions can be detected with a reasonable efficiency (> 30%) over a large solid angle. Tracking with a TPC, which will be built at LEGS over the next few years, will improve the capabilities of these measurements.
Spin-1 charmonium-like states in QCD sum rule
Chen, Wei
2012-01-01
We study the possible spin-1 charmonium-like states by using QCD sum rule approach. We calculate the two-point correlation functions for all the local form tetraquark interpolating currents with $J^{PC}=1^{--}, 1^{-+}, 1^{++}$ and $1^{+-}$ and extract the masses of the tetraquark charmonium-like states. The mass of the $1^{--}$ $qc\\bar q\\bar c$ state is $4.6\\sim4.7$ GeV, which implies a possible tetraquark interpretation for Y(4660) meson. The masses for both the $1^{++}$ $qc\\bar q\\bar c$ and $sc\\bar s\\bar c$ states are $4.0\\sim 4.2$ GeV, which is slightly above the mass of X(3872). For the $1^{-+}$ and $1^{+-}$ $qc\\bar q\\bar c$ states, the extracted masses are $4.5\\sim4.7$ GeV and $4.0\\sim 4.2$ GeV respectively.
The energy-weighted sum rule and the nuclear radius
Energy Technology Data Exchange (ETDEWEB)
Schroeder, Hans Peter [Aleph-Consulting GmbH Verlag, Wiesbaden (Germany)
2015-09-15
The energy-weighted integrated cross-section for photon absorption -known as sum rule σ{sub -1} - is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at σ{sub -1}. Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated σ{sub -1} and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of σ{sub -1} differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections g(A) and the uncorrelated function f(A) as a ratio it shows that g(A)/f(A) tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)). (orig.)
The leptonic Dirac CP-violating phase from sum rules
Girardi, I.; Petcov, S. T.; Titov, A. V.
2016-05-01
In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv , where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.
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 $J^P = 5/2^+$ $P_c(4450)$.
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.
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.
Calculation of the kaon B parameter using strictly local sum rules
International Nuclear Information System (INIS)
The kaon B-parameter is computed in the framework of strictly local QCD sum rules for a three-poin function involving pseudoscalar currents. As an application of these sum rules we derive a low energy formula for the B-parameter. We show that strictly local QCD sum rules yield more reliable results than other QCD sum rules, since they need less phenomenological information and do not suffer from stability problems. Our result for the B-parameter is B=0.74±0.17. (orig.)
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M
2010-01-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form $S_{p}(n) = \\sum_{k \
Kuzyk, Mark G
2014-01-01
The Thomas Kuhn Reich sum rules and the sum-over-states (SOS) expression for the hyperpolarizabilities are truncated when calculating the fundamental limits of nonlinear susceptibilities. Truncation of the SOS expression can lead to an accurate approximation of the first and second hyperpolarizabilities due to energy denominators, which can make the truncated series converge to within 10% of the full series after only a few excited states are included in the sum. The terms in the sum rule series, however, are weighted by the state energies, so convergence of the series requires that the position matrix elements scale at most in inverse proportion to the square root of the energy. Even if the convergence condition is met, serious pathologies arise, including self inconsistent sum rules and equations that contradict reality. As a result, using the truncated sum rules alone leads to pathologies that make any rigorous calculations impossible, let alone yielding even good approximations. This paper discusses condi...
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.
Sum rules and moments for lepton-pair production. [Cross sections, Drell--Yan formula
Energy Technology Data Exchange (ETDEWEB)
Hwa, R.C.
1978-01-01
Sum rules on lepton-pair production cross sections are derived on the bases of the Drell--Yan formula and the known sum rules in leptoproduction. Also exact relations are obtained between the average transverse momenta squared of the valence quarks and moments of the dilepton cross sections. 12 references.
B-decay form factors from QCD sum rules
International Nuclear Information System (INIS)
In the Standard Model of particle physics there is only one source of CP-violation. Namely, a single complex phase in the unitary 3 x 3 CKM-Matrix governing flavor transitions in the weak interaction. The unitarity is usually visualized by a triangle in the complex ρ - η-plane. Therefore testing this framework comes down to measuring weak decays, relating observables to sides and angles of this so called Unitarity Triangle(UT). Particular interest in this respect is payed to decays of mesons containing a heavy b-quark, giving the opportunity to alone determine all parameters of the UT. Doing this is far from easy. Besides tedious experimental measurements the theoretical calculations are plagued by hadronic quantities which cannot be determined by perturbation theory. In this work several of these quantities so called form factors are computed using the well known method of light cone sum rules(LCSR). Two different setups have been used. One, established in this work, utilizing a correlation function with an on-shell B-Meson and one following the traditional calculation by taking the light meson on-shell. Both using light cone expansion in the respective on-shell mesons distribution amplitudes. While the first approach allows to calculate a whole bunch of phenomenologically interesting quantities by just changing Dirac-structures of the relevant currents it has the drawback that it does not have access to the well developed twist expansion of the latter. To incorporate higher Fock-state contributions the first models for three-particle distribution amplitudes of the B-Meson have been derived. αs-corrections remain out of the scope of this work. Nevertheless does a comparison with more sophisticated methods show an encouraging numerical agreement. In the second setup all known corrections especially the never verified αs-corrections to Twist three terms have been recalculated and a competitive result for the CKM-matrixelement vertical stroke Vub vertical stroke
$\\Delta I = 1/2$ enhancement and the Glashow-Schnitzer-Weinberg sum rule
Nasrallah, N F
2000-01-01
In 1967 Glashow, Schnitzer and Weinberg derived a sum rule in the soft-pion and soft kaon limit relating the Delta I=1/2 non-leptonic K->2pi amplitude to integrals over strange and non-strange spectral functions. Using the recent ALEPH data from tau-decay, we show that the sum rule, slightly modified to reduce contributions near the cut, yields the correct magnitude decay amplitude corresponding to the Delta I=1/2 rule.
QCD sum rules for quark-gluon three-body components in the B meson
Nishikawa, Tetsuo
2011-01-01
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, $\\lambda_E$ and $\\lambda_H$, which correspond to matrix elements representing quark-gluon three-body components in the $B$-meson wavefunction. We derive the sum rules for $\\lambda_{E,H}$ calculating the new higher-order QCD corrections, i.e., the order $\\alpha_s$ radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of $\\lambda_{E,H}$. We also discuss the renormalization-group improvement for the sum rules and present update on the values of $\\lambda_{E,H}$.
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.
General solution of superconvergent sum rules for scattering of I=1 reggeons on baryons
International Nuclear Information System (INIS)
Superconvergent sum rules for reggeon-particle scattering are applied to scattering of reggeons αi (i=π, ρ, A2) with isospin I=1 on baryons with strangeness S=-1. The saturation scheme of these sum rules is determined on the basis of experimental data. Two series of baryon resonances with arbitrary isospins I and spins J=I+1/2 and J=I-1/2 are predicted. A general solution for vertices of interaction of these resonances with αi is found. Predictions for coupling vertices BαiB'(B, B'=Λ, Σ, Σ*) agree well with the experiment. It is shown that the condition of sum rules saturation by minimal number of resonances brings to saturation schemes resulting from experimental data. A general solution of sum rules for scattering of αi reggeons on Ξ and Ω hyperons is analyzed
Couplings of heavy hadrons with soft pions from QCD sum rules
International Nuclear Information System (INIS)
The couplings in the Heavy Hadron Chiral theory Lagrangian from the QCD sum rules in an external axial field are estimated. Stability of the sum rules at moderate values of the Borel parameter is poor that probably signals slow convergence of the OPE series. At large values of the Borel parameter they stabilize, and yield the couplings much lower than the constituent quark model expectations. 18 refs.; 5 figs
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 Rules of Charm CP Asymmetries beyond the SU(3)$_F$ Limit
Müller, Sarah; Schacht, Stefan
2015-01-01
We find new sum rules between direct CP asymmetries in $D$ meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies $P$ and $PA$, which cannot be determined from branching ratios. In this way we can make predictions about direct CP asymmetries in the Standard Model without ad-hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)$_F$ breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II one will identify or constrain new-physics contributions to $P$ or $PA$. The first sum rule correlates the CP asymmetries $a_{CP}^{\\mathrm{dir}}$ in $D^0\\to K^+K^-$, $D^0\\to \\pi^+\\pi^-$, and $D^0\\to \\pi^0\\pi^0$. We study the region of the $a_{CP}^{\\mathrm{dir}}(D^0\\to \\pi^+\\pi^-)$--$a_{CP}^{\\mathrm{dir}} (D^0\\to \\pi^0\\pi^0)$ plane allowed by current data and find that our sum rule excludes more than half of ...
Finite temperature effects and the validity of the Weinberg sum rules
Ayala, Alejandro; Dominguez, C. A.; Loewe, M.; Zhang, Y.
2016-05-01
Using resent independent results from QCD sum rules for the thermal evolution of hadronic parameters in the vector and the axial-vector channels, we discuss the saturation of the two Weinberg sum rules. It turn out that both sum rules are quite well satisfied in a wide range from T = 0 up to T/T c ≃ 0.7 — 0.8. At higher temperatures, coming closer to Tc , there is an asymmetry between both channels since in the vector case there is a leading order effect, proportional to T2 , due to a one loop pion contribution in the space-like region, which is absent in the axial-vector case. This leads then to a small deviation. More important, though, in this region the QCD sum rules for the hadronic parameters begin to have no solutions since the widths of the ρ and the a1-mesons diverge signaling the occurrence of deconfinement. Close to and at Tc there are no pions left in the medium and chiral symmetry is restored so that the Weinberg sum rules are trivially satisfied.
Complex deformations of Bjorken flow
Gubser, Steven S.
2013-01-01
Through a complex shift of the time coordinate, a modification of Bjorken flow is introduced which interpolates between a glasma-like stress tensor at forward rapidities and Bjorken-like hydrodynamics around mid-rapidity. A Landau-like full-stopping regime is found at early times and rapidities not too large. Approximate agreement with BRAHMS data on the rapidity distribution of produced particles at top Relativistic Heavy Ion Collider (RHIC) energies can be achieved if the complex shift of the time coordinate is comparable to the inverse of the saturation scale. The form of the stress tensor follows essentially from symmetry considerations, and it can be expressed in closed form.
Complex deformations of Bjorken flow
Gubser, Steven S
2012-01-01
Through a complex shift of the time coordinate, a modification of Bjorken flow is introduced which interpolates between a glasma-like stress tensor at forward rapidities and Bjorken-like hydrodynamics around mid-rapidity. A Landau-like full-stopping regime is found at early times and rapidities not too large. Approximate agreement with BRAHMS data on the rapidity distribution of produced particles at top RHIC energies can be achieved if the complex shift of the time coordinate is comparable to the inverse of the saturation scale. The form of the stress tensor follows essentially from symmetry considerations, and it can be expressed in closed form.
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M.; Robinett, R. W.
2009-02-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).
Charmonium spectrum at finite temperature from a Bayesian analysis of QCD sum rules
Directory of Open Access Journals (Sweden)
Morita Kenji
2012-02-01
Full Text Available Making use of a recently developed method of analyzing QCD sum rules, we investigate charmonium spectral functions at finite temperature. This method employs the Maximum Entropy Method, which makes it possible to directly obtain the spectral function from the sum rules, without having to introduce any strong assumption about its functional form. Finite temperature effects are incorporated into the sum rules by the change of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which are extracted from lattice QCD. As a result, J/ψ and ηc dissolve into the continuum already at temperatures around 1.0 ~ 1.1 Tc.
Nuclear magnetic polarizability and the slope of the Thomas-Reiche-Kuhn-Levinger-Bethe sum rule
Gorchtein, Mikhail
2015-01-01
Thomas-Reiche-Kuhn-Levinger-Bethe sum rule that relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of elementary scatterers-protons within that nucleus by means of a subtracted forward dispersion relation. I extend this dispersion relation consideration to the case of virtual photons and show that the size of the magnetic polarizability of a nucleus, under the assumption of a separation between the nuclear and hadronic scales, may be related to the slope of the transverse virtual photoabsorption cross section integrated over the energy. I check this approximate sum rule for the deuteron where necessary data is available, discuss possible applications and connection with other sum rules postulated in the literature.
Extended M1 sum rule for excited symmetric and mixed-symmetry states in nuclei
Smirnova, N A; Leviatan, A; Ginocchio, J N; Fransen, C
2002-01-01
A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the first and second $2^+$ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and in-between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio $nd(0^+_1)/nd(2^+_2) \\approx 0.6$ is obtained in a largely parameter-independent way
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 $|V_{ub}|$.
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.
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.
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.
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).
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 ...
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.
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.
Exact zero-momentum sum rules in d=3 gauge theory
International Nuclear Information System (INIS)
We derive, for non-abelian pure gauge theory, an infinite set of sum rules for connected zero-momentum matrix elements of the condensate operator Σ(Gaij)2(x) in d=3; these are equivalent to an effective action for this operator. These sum rules are analogous to similar ones derived, at the one-loop level, for d=4 gauge theory and predict a non-zero positive value of left angle G2ij right angle and a negative vacuum energy. Some applications to effective glueball couplings and approximations to the evaluation of left angle G2ij right angle are discussed. (orig.)
The influence of gluonic operators on QCD sum rules for baryons
International Nuclear Information System (INIS)
In this thesis the operator product expansion (OPE) is extended up to operators of dimension d=10. The coefficient functions are calculated only up to order αsub(s). Thereby the performation of the OPE by means of the Schwinger operator formalism is extensively described. In the final section the sum rules for nucleon and delta are discussed. (orig./HSI)
Sum rules study and a scaling property of fragmentation mass yield curves
International Nuclear Information System (INIS)
Information obtained in mass yield distributions produced in protons and heavy ions induced reactions has been analyzed with two model independent sum rules. The average number of fragments of different sizes produced in one collision has been extracted. A scaling law for the mass yield has been deduced. (orig.)
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.
Reanalyzing Pentaquark Θ+(1540) in Framework of QCD Sum Rules Approach with Direct Instantons
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, we study the pentaquark state Θ+(1540) with a (scalar) diquark-(pseudoscalar) diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.
Analysis of the Triply Heavy Baryon States with QCD Sum Rules
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang
2012-01-01
In this article, we study the (1/2)± and (3/2)± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2) and (3/2) triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.
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 FOR MAGNETIC DICHROISM IN RARE-EARTH 4F-PHOTOEMISSION
THOLE, BT; VANDERLAAN, G
1993-01-01
We present new sum rules for magnetic dichroism in spin polarized photoemission from partly filled shells which give the expectation values of the orbital and spin magnetic moments and their correlations in the ground state. We apply this to the 4f photoemission of rare earths, where the polarizatio
In-medium QCD sum rules for {omega} meson, nucleon and D meson
Energy Technology Data Exchange (ETDEWEB)
Thomas, Ronny
2008-07-01
The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the {omega} meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the {omega} meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. (orig.)
Perturbative analysis of the energy-weighted sum rule of bilinear fermion operators
International Nuclear Information System (INIS)
It is shown that the value obtained for the energy-weighted sum rule for bilinear fermionic operators using dressed one-particle propagators plus two-body random-phase approximation corrections is preserved when any higher-order correction is introduced. This is proven through the evaluation of the corresponding perturbative diagrams
In-medium QCD sum rules for ω meson, nucleon and D meson
International Nuclear Information System (INIS)
The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the ω meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the ω meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. (orig.)
Jakubassa-Amundsen, D H
2016-01-01
Inspired by the work of Pratt and coworkers on a sum rule for the polarization correlations in electron bremsstrahlung when the outgoing electron is not observed, we derive the corresponding sum rule for the elementary process of bremsstrahlung. This sum rule is valid for arbitrary electron wavefunctions provided the electron is emitted in the reaction plane. The numerical evaluation of this sum rule within the Dirac partial-wave theory for bare inert spin-zero nuclei and collision energies in the range of 1-10 MeV reveals violations for high nuclear charge. Such violations serve as a measure of the inaccuracies in the bremsstrahlung calculations.
International Nuclear Information System (INIS)
This thesis presents an experimental study of the neutron (and 3He) spin structure with a particular emphasis in the resonance domain (experiment E94010 that took place in 1997 at Jefferson Lab (TJNAF or formerly CEBAF) in Virginia). A polarized 3He target was built in order to achieve this study since polarized 3He nuclei can be seen as polarized neutrons. This target allowed the measurement of the polarized absolute cross sections σ1/2(Q2, ν) and σ3/2(Q2, ν) from the inclusive reaction →3He(→e, e')X for incident beam energies ranging from 0.86 GeV to 5.07 GeV at a scattering angle of 15.5 deg. The Q2 evolution of the generalized Gerasimov-Drell-Hearn (GDH) integral on 3He and on neutron was measured from 0.1 GeV2 to 1.0 GeV2 in order to understand the transition between perturbative QCD and non-perturbative QCD. The integration domain in ν (the energy loss of the scattered electron) is from the pion threshold to about 2.5 GeV which covers both the resonance region and the Deep Inelastic Scattering. The high precision of our data constrains the models giving the Q2 evolution of the generalized GDH integral. The polarized quasi-elastic scattering was also measured. The cross section σTT(Q2, ν) on 3He and the spin structure functions g13He(Q2, ν) and g23He(Q2, ν) are presented. These data are an indication that the higher-twists are small in our kinematics domain and that the Bloom-Gilman duality seems to hold for the polarized spin structure functions. (author)
Constraints on Airy function zeros from quantum-mechanical sum rules
Energy Technology Data Exchange (ETDEWEB)
Belloni, M [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R W [Department of Physics, Pennsylvania State University, University Park, PA 16802 (United States)], E-mail: mabelloni@davidson.edu, E-mail: rick@phys.psu.edu
2009-02-20
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form S{sub p}(n) = {sigma}{sub k{ne}}{sub n}1/({zeta}{sub k} - {zeta}{sub n}){sup p}, for natural p > 1, where -{zeta}{sub n} is the nth zero of Ai({zeta})
$J$-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.
X-ray-absorption sum rules in jj-coupled operators and ground-state moments of actinide ions
van der Laan, G; Thole, BT
1996-01-01
Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in jj-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross
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 ...
B→A transitions in the light-cone QCD sum rules with the chiral current
Institute of Scientific and Technical Information of China (English)
SUN Yan-Jun; WANG Zhi-Gang; HUANG Tao
2012-01-01
In this article,we calculate the form-factors of the transitions B → a1(1260),b1(1235) in the leading-order approximation using the light-cone QCD sum rules.In calculations,we choose the chiral current to interpolate the B-meson,which has the outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons make no contributions,and the resulting sum rules for the form-factors suffer from far fewer uncertainties.Then we study the semi-leptonic decays B → a1(1260)l(v1),b1(1235)l(v1) (l =e,μ,Τ),and make predictions for the differential decay widths and decay widths,which can be compared with the experimental data in the coming future.
Nucleon Form Factors to Next-to-Leading Order with Light-Cone Sum Rules
Kumericki, K Passek
2008-01-01
We have calculated the leading-twist next-to-leading order (NLO), i.e., O(alpha_s), correction to the light-cone sum-rules prediction for the electromagnetic form factors of the nucleon. We have used the Ioffe nucleon interpolation current and worked in M_N=0 approximation, with M_N being the mass of the nucleon. In this approximation, only the Pauli form factor F_2 receives a correction and the calculated correction is quite sizable (cca 60%). The numerical results for the proton form factors show the improved agreement with the experimental data. We also discuss the problems encountered when going away from M_N=0 approximation at NLO, as well as, gauge invariance of the perturbative results. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors.
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.
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.
Kramers-Kronig relations and sum rules in nonlinear optical spectroscopy.
Peiponen, Kai-Erik; Lucarini, Valerio; Saarinen, Jarkko J; Vartiainen, Erik
2004-05-01
The full potential of the Kramers-Kronig relations and sum rules for nonlinear susceptibilities has unfortunately drawn relatively little attention in nonlinear optical spectra analysis. In this feature article a simple treatment of an anharmonic oscillator model in description of the nonlinear susceptibility of media and holomorphic properties of the nonlinear susceptibility were utilized. Using such concepts, conventional Kramers-Kronig, multiply-subtractive Kramers-Kronig, and generalized Kramers-Kronig dispersion relations can be derived. We demonstrate how in practice the variety of different Kramers-Kronig relations mentioned above, as well as various sum rules, can be applied in nonlinear optical spectra analysis. As an example we treat the third-harmonic wave generation spectrum from a polymer.
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.
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.
Sum rules for meson and baryon production in the quark recombination model
International Nuclear Information System (INIS)
A quark recombination model with quark distributions according to a generalized Kuti-Weisskopf model is used. Mesons are formed by v-s (valence-sea) and s-s recombination, baryons by vvv, vvs, vss and sss recombination. Sum rules for energy momentum concervation, baryon number, valence and sea quarks are shown to constrain the recombination parameters of the model significantly. The resulting model is consistent with experimental data. (author)
Adler-type sum rule, charge symmetry and neutral current in general multi-triplet model
International Nuclear Information System (INIS)
We derive Adler-type sum rule extended to general multi-triplet model. Paying attention to roles of the colour degree of freedom, we discuss the charge symmetry property of the weak charged current and the structure functions for ν(ν-)+N→l(l-)+X, and also the structure of the neutral current. A comment is given on implications in our theory of Koike and Konuma's result on the neutral hadronic current. (auth.)
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.
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.
New identities from quantum-mechanical sum rules of parity-related potentials
Ayorinde, O A; Belloni, M; Robinett, R W
2010-01-01
We apply quantum mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, $V(x) = V(-x)$, and their parity-restricted partners, ones with $V(x)$, but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, $V(z) = F|z|$ and find new classes of constraints on the zeros of the Airy function, $Ai(z)$, and its derivative $Ai'(z)$. We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrleated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-clas...
New identities from quantum-mechanical sum rules of parity-related potentials
Energy Technology Data Exchange (ETDEWEB)
Ayorinde, O A; Chisholm, K; Belloni, M [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R W, E-mail: seayorinde@davidson.ed, E-mail: kechisholm@davidson.ed, E-mail: mabelloni@davidson.ed, E-mail: rick@phys.psu.ed [Department of Physics, Pennsylvania State University, University Park, PA 16802 (United States)
2010-06-11
We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai({zeta}), and its derivative, Ai'({zeta}). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.
New identities from quantum-mechanical sum rules of parity-related potentials
Ayorinde, O. A.; Chisholm, K.; Belloni, M.; Robinett, R. W.
2010-06-01
We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai(ζ), and its derivative, Ai'(ζ). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.
A resolution of the inclusive flavor-breaking sum rule $\\tau$ $V_{us}$ puzzle
Maltman, K; Lewis, R; Wolfe, C E; Zanotti, J
2015-01-01
A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $\\tau$ decay data. Results for $V_{us}$ obtained using assumptions for $D>4$ OPE contributions employed in previous conventional implementations of this approach are shown to display significant unphysical dependences on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest the necessity of a new implementation of the flavor-breaking sum rule approach, in which not only $\\vert V_{us}\\vert$, but also $D>4$ effective condensates are fit to data. Lattice results also provide a means of quantifying the truncation error for the slowly converging $D=2$ OPE series. The new implementation is shown to produce $\\vert V_{us}\\vert$ results free of unphysical $s_0$- and $w$-dependences and typically $\\sim 0.0020$ higher than the (unstable) ...
Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
International Nuclear Information System (INIS)
The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lepton scattering was based merely on a valence picture and is modified both by perturbative and by non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/Nc2, relative to those for higher moments, we propose that this suppression persists at higher orders and also applies to higher-twist effects. Moreover, we propose that the differences between the corresponding radiative corrections to higher non-singlet moments in charged-lepton and neutrino deep inelastic scattering are suppressed by 1/Nc2, in all orders of perturbation theory. For the first moment, in the Gottfried sum rule, the substantial discrepancy between the measured value and the valence-model expectation may be attributed to an intrinsic isospin asymmetry in the nucleon sea, as is indeed the case in a chiral-soliton model, where the discrepancy persists in the limit Nc→∞
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...
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.
QCD corrections to B→π form factors from light-cone sum rules
Directory of Open Access Journals (Sweden)
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.
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.
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.
Low-energy sum rules and large-N$_{c}$ consistency conditions
Broniowski, W
1994-01-01
The large-$N_c$ consistency conditions for axial vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of low-energy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial vector and isovector magnetic coupling constants get corrections only at the order $1/N_c^2$ follows from the $N_c$-counting of appropriate cross sections. This counting is performed using various approaches at the quark and hadronic level. Other implications of our method are also presented.
Analysis of 1/2+ baryon states containing fourth-family quarks from QCD sum rules
Institute of Scientific and Technical Information of China (English)
YOU Fu-Yi; WANG Zhi-Gang; WAN Shao-Long
2012-01-01
When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks,the hadrons made up from these quarks can be long-lived enough.We analyze the 1/2+ baryon statescontaining fourth-generation quarks and standard-model quarks,i.e.the charm or bottom quarks,in the QCD sum rules approach.Considering the perturbative and two gluon condensate contributions in the calculation,we give the numerical results of the masses and pole residues.
B ---> pi and B ---> K transitions from QCD sum rules on the light cone
Energy Technology Data Exchange (ETDEWEB)
Ball, Patricia
1998-09-01
I calculate the form factors describing semileptonic and penguin-induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be \\sim 15%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer.
Sum rules for meson and baryon production in the quark recombination model
International Nuclear Information System (INIS)
A quark-recombination model with quark distributions according to a generalized Kuti-Weisskopf model is used. Mesons are formed by v-s (valence-sea) and s-s recombination, baryons by vvv, vvs, vss and sss recombination. Sum rules for energy momentum conservation, baryon number, valence and sea quarks are shown to constrain the recombination parameters of the model significantly. The resulting model is consistent with experimental data. While the sss recombination into baryons is found to be quite normal we find a strong enhancement of ss recombination into mesons. This enhanced ss term represents in the model the central meson production via gluons. (author)
Bath-symmetries and hybridization sum-rules for CDMFT and DCA
International Nuclear Information System (INIS)
In the Hamiltonian formulation of CDMFT and DCA, the point symmetries of the cluster imply symmetries of the hybridization, which can substantially reduce the number of independent parameters to fit the bath Green function. We review these symmetries and derive general sum-rules for the hybridizations, which allow to check the quality of a fit using a finite set of bath sites and imply what hybridizations vanish. As examples we discuss calculations for the Hubbard model in one-dimension and for 2 x 2 clusters
In-medium QCD sum rules for D mesons: A projection method for higher order contributions
Buchheim, Thomas; Kampfer, Burkhard
2014-01-01
D mesons serve as excellent probes of hot and/or dense strongly interacting matter. They can provide insight into the restoration of chiral symmetry. The chiral condensate as well as other chirally odd condensates, such as certain four-quark condensates, are linked to order parameters of spontaneous chiral symmetry breaking. Thus, the evaluation of these higher order condensate contributions in the framework of QCD sum rules is of high interest. We present a general method for projecting Lorentz indices of ground state expectation values providing a crucial step towards a comprehensive calculation of higher order corrections to the operator product expansion of hadrons, especially D mesons, in a strongly interacting medium.
The relation between the photonuclear E1 sum rule and the effective orbital g-factor
Bentz, W
2004-01-01
The connection between the enhancement factor (1+kappa) of the photonuclear E1 sum rule and the orbital angular momentum g-factor (gl) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the kappa-gl relation. By identifying the physical processes which are taken into account in kappa and gl, the validity and limitations of this relation are discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown.
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.
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Aliev, T M
2015-01-01
The magnetic moment of the $\\Lambda \\to \\Sigma^0$ transition between negative parity, baryons is calculated in framework of the QCD sum rules approach, using the general form of the interpolating currents. The pollution arising from the positive--to--positive, and positive to negative parity baryons are eliminated by constructing the sum rules for different Lorentz structures. Nonzero value of the considered magnetic moment can be attributed to the violation of the $SU(3)$ symmetry.
New approach for calculating heavy-to-light form factors with QCD sum rules on the light-cone
Weinzierl, Stefan; Yakovlev, Oleg
2000-01-01
We suggest a new approach for calculating heavy-to-light form factors. The method is based on light cone sum rules (LCSR) and covers the whole kinematical range of momentum transfer. The derivation of the new sum rule uses a suitable combination of double and single dispersion integrals. As an example we give numerical results for the form factor f^+ for the B -> pion transition.
New Sum Rule Determination of the Mass and Strangeness Content of the Nucleon
Nasrallah, Nasrallah F
2013-01-01
A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1=2+ and 1=2- continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling. For standard values of the condensates, the prediction of the nucleon mass in the chiral limit is mN = (830+/-50)MeV. With the pion-nucleon sigma-term given by chiral perturbation theory and the strange sigma-term estimated by the Zweig rule we get mN = (990+/-50)MeV.
Isospin breaking in the decay constants of heavy mesons from QCD sum rules
Lucha, Wolfgang; Simula, Silvano
2016-01-01
We present a study of the strong isospin-breaking (IB) effect, due in QCD to the difference between $u$- and $d$-quark masses, in the leptonic decay constants of charmed and beauty pseudoscalar and vector mesons using the method of QCD sum rules. We apply the sum-rule analysis to the decay constants of mesons containing one heavy quark and one light quark with the light mass in the range from the average $u/d$ quark mass to the strange-quark mass. We then analyse the dependence of the decay constants on the light-quark mass and extract with good accuracy the IB ratios of decay constants at leading order in the mass difference $(m_d - m_u)$, obtaining: $(f_{D^+} - f_{D^0}) / f_{D} = 0.0046 (6)$, $(f_{D^{*+}} - f_{D^{*0}}) / f_{D^*} = 0.0067 (9)$, $(f_{B^0} - f_{B^+}) / f_{B} = 0.0048 (6)$, and $(f_{B^{*0}} - f_{B^{*+}}) / f_{B^*} = 0.0045 (5)$, which yield: $f_{D^+} - f_{D^0} = 0.95 \\pm 0.13$ MeV, $f_{D^{*+}} - f_{D^{*0}} = 1.69 \\pm 0.27$ MeV, $f_{B^0} - f_{B^+} = 0.92 \\pm 0.13$ MeV, $f_{B^{*0}} - f_{B^{*+}} =...
Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we study the $C\\gamma_5\\otimes \\gamma_5C$ type and $C\\otimes C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $M_{C\\gamma_5\\otimes \\gamma_5C}=3.89\\pm 0.05\\,\\rm{GeV}$ and $M_{C\\otimes C}=5.48\\pm0.10\\,\\rm{GeV}$ support assigning the $X(3915)$ to be the ground state $C\\gamma_5\\otimes \\gamma_5C$ type tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the $X(4700)$ to be the ground state $C\\otimes C$ type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$ and $X(4500)$ to be the 1S and 2S $C\\gamma_5\\otimes \\gamma_5C$ type scalar $cs\\bar{c}\\bar{s}$ tetraquark states respectively, and obtain the 1S mass $M_{\\rm 1S}=3.85^{+0.18}_{-0.17}\\,\\rm{GeV}$ and 2S mass $M_{\\rm 2S}=4.35^{+0.10}_{-0.11}\\,\\rm{GeV}$ from the QCD sum rules, which support assigning the $X(3915)$ to be the 1S $C\\gamma_5\\oti...
QCD corrections to $B \\to \\pi$ form factors from light-cone sum rules
Wang, Yu-Ming
2015-01-01
We compute perturbative corrections to $B \\to \\pi$ 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 $f_{B \\pi}^{+}(q^2)$ and $f_{B \\pi}^{0}(q^2)$ at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an explorato...
Mass sum rule of the effective action on vacua with broken rigid N=1 supersymmetry
Directory of Open Access Journals (Sweden)
H. Itoyama
2015-04-01
Full Text Available We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model consisting of adjoint scalar superfields and vector superfields possessing a Kähler potential, a set of gauge coupling functions (second prepotential derivatives and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to extend these analyses to the cases where superfields in (anti-fundamental representation are present. The supertrace is shown to vanish in those cases where underlying geometry is special Kähler and theory under concern is anomaly free. Simple phenomenological application is given, providing an upper bound for gaugino masses. We discuss that the effects of the D and/or F condensates can be represented as a set of soft breaking terms with their strengths predicted by the scales.
XYZ-like Spectra from Laplace Sum Rule at N2LO in the Chiral Limit
Albuquerque, R; Fanomezana, F; Rabemananjara, A; Rabetiarivony, D; Randriamanatrika, G
2016-01-01
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-like states at lowest order (LO) of perturbative (PT) QCD and up to $d=8$ condensates of the Operator Product Expansion (OPE). Then, we improve previous LO results from QCD spectral sum rules (QSSR), on the $XYZ$-like masses and decay constants (which suffer from the ill-defined heavy quark mass) by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria with respect to the variations of the $\\tau$-Laplace sum rule (LSR) variable, QCD continuum threshold $t_c $ and subtraction constant $\\mu$ are summarized in Tables 11 to 14. We conclude that the masses of the $XZ$ observed states are compatible with (almost) pure $J^{PC}=1^{...
Study of the $D^*\\rho$ system using QCD sum rules
Torres, A Martinez; Nielsen, M; Navarra, F S; Oset, E
2013-01-01
In this talk I present a study of the $D^* \\rho$ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three $D^*$ mesons with isospin $I=1/2$, spin $S=0$, $1$, $2$ and with masses $2500\\pm 67$ MeV, $2523\\pm60$ MeV, and $2439\\pm119$ MeV, respectively. The last state can be related to $D^*_2(2460)$ (spin 2) listed by the Particle Data Group, while one of the first two might be associated with $D^*(2640)$, whose spin-parity is unknown. In the case of $I=3/2$ we also find evidences of three states with spin 0, 1 and 2, respectively, with masses $2467\\pm82$ MeV, $2420\\pm128$ MeV, and $2550\\pm56$ MeV.
SCET Sum Rules for B to P and B to V Transition Form Factors
Energy Technology Data Exchange (ETDEWEB)
De Fazio, Fulvia; /INFN, Bari; Feldmann, Thorsten; /Siegen U.; Hurth, Tobias; /CERN /SLAC
2007-12-18
We investigate sum rules for heavy-to-light transition form factors at large recoil derived from correlation functions with interpolating currents for light pseudoscalar or vector fields in soft-collinear effective theory (SCET). We consider both, factorizable and nonfactorizable contributions at leading power in the {Lambda}/m{sub b} expansion and to first order in the strong coupling constant {alpha}{sub s}, neglecting contributions from 3-particle distribution amplitudes in the B-meson. We pay particular attention to various sources of parametric and systematic uncertainties. We also discuss certain form factor ratios where part of the hadronic uncertainties related to the B-meson distribution amplitude and to logarithmically enhanced {alpha}{sub s} corrections cancel.
Searching for hidden-charm baryonium signals in QCD sum rules
Chen, Hua-Xing; Chen, Wei; Liu, Xiang; Zhu, Shi-Lin
2016-01-01
We give an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content $u\\bar u d\\bar d c\\bar c$, spin $J=0/1/2/3$, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, and find that these currents can couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion. The masses of the lowest-lying hidden-charm baryonium states with quantum numbers $J^P=2^-/3^-/0^+/1^+/2^+$ are evaluated to be around 5.0 GeV, so we suggest to search for hidden-charm baryonium states in the $D$-wave $J/\\psi \\pi \\pi$ and $S$-wave $J/\\psi \\rho$ and $J/\\psi \\omega$ channels in this energy region.
Masses of Open-Flavour Heavy-Light Hybrids from QCD Sum-Rules
Ho, J; Steele, T G
2016-01-01
We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid's constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract mass predictions for all $J^P\\in\\{0^{\\pm},\\,1^{\\pm}\\}$. Within theoretical uncertainties, we find degeneracy between the heavy-nonstrange and heavy-strange hybrids in all $J^P$ channels. Also, our mass predictions are nearly degenerate under parity flips. For the charm-light hybrids there is a clear mass hierarchy of heavier scalar states which becomes less pronounced for the bottom-light hybrids. Possible effects of mixing with conventional quark-antiquark mesons are also explored.
QCD sum rule study of a charged bottom-strange scalar meson
Zanetti, C. M.; Nielsen, M.; Khemchandani, K. P.
2016-05-01
Using the QCD sum rule approach, we investigate the possible four-quark structure for the new observed Bs0π± narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of ms in full QCD, without relying on 1 /mQ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.
International Nuclear Information System (INIS)
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them
Reanalysis of the (0+, 1+) states Bs1 with QCD sum rules
International Nuclear Information System (INIS)
We calculate the masses and decay constants of the P-wave strange-bottomed mesons Bs0 and Bs1 with the QCD sum rules, and observe that the central values of the masses Bs0 and Bs1 are smaller than the corresponding BK and B*K thresholds respectively, the strong decays Bs0→ BK and Bs1 → B*K are kinematically forbidden. They can decay through the isospin violation processes Bs0 → Bsη → BaΠ0 and Bs1 → Bs*η → Bs*π0. The bottomed mesons Bs0 and Bs1, just like their charmed cousins Ds0 (2317) and Ds1 (2460), may be very narrow. (author)
Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we take the $X(4140)$ as the diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass and pole residue with the QCD sum rules in details by constructing two types interpolating currents. The numerical results $M_{X_{L,+}}=3.95\\pm0.09\\,\\rm{GeV}$ and $M_{X_{H,+}}=5.00\\pm0.10\\,\\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type tetraquark state. Furthermore, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark states as a byproduct. The present predictions can be confronted to the experimental data in the future.
QCD Sum Rules for the {lambda}{sub b} semileptonic decay
Energy Technology Data Exchange (ETDEWEB)
Marques de Carvalho, R.S.; Nielsen, M. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica. Grupo de Fisica Nuclear Teorica e Fenomenologia de Particulas Elementares
2001-07-01
We use the QCD Sum Rule approach to evaluate the form factors and decay rates of {lambda}{sub b} {yields} {lambda}{sub c}{sup +} + l + {nu}-bar{sub l} decay. This decay is represented by a three point function of the weak transition current and the interpolating fields of {lambda}{sub b} and {lambda}{sub c}. 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)
D+→η(')l+νl semileptonic decays in light-cone sum rules
Institute of Scientific and Technical Information of China (English)
LI Jing-Wu; XUE Dan-Qing; XU Qing-Qiang; WU Xiang-Yao
2011-01-01
We calculate the D→η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D →η lν decays with the experimental data. By comparing the difference between the results of the branching ratios of D+ →ηlν from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η' mixing angle from the dependence of the branching ratios of D →ηlν decays on the η-η' mixing angle.
Reanalysis of the (0+,1+) States Bs0 and Bs1 with QCD Sum Rules
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang
2008-01-01
We calculate the masses and decay constants of the P-wave strange-bottomed mesons Bs0 and Bs1 with the QCD sum rules, and observe that the central values of the masses Bs0 and Bs1 are smaller than the corresponding BK and B* K thresholds respectively, the strong decays Bs0 → BK and Bs1 → B* K are kinematically forbidden.They can decay through the isospin violation processes Bs0 → Bsη→, Bsπ0 and Bs1 → Bsη→, Bs*π0. The bottomed mesons Bs0 and Bs1, just like their charmed cousins Ds0(2317) and Ds1(2460), may be very narrow.
Understanding close-lying exotic charmonia states within QCD sum rules
Torres, A Martínez; Dias, J M; Navarra, F S; Nielsen, M
2016-01-01
Motivated by the experimental findings of some new exotic states decaying into channels like $J/\\psi$-phi, we investigate the formation of resonances/bound states in the $D^*_s\\bar D^*_s$ system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass varying in the range 3.8-4.2 GeV. Although the conditions of Borel stability, convergence of the OPE series and pole dominance are all well satisfied, we find the interpretation of the obtained results to be challenging.
Equivalence of post and prior sum rules for inclusive breakup reactions
International Nuclear Information System (INIS)
A critical examination of sum rules derived previously by Austern and Vincent (post form) and by Udagawa and Tamura (prior form) demonstrates that agreement between the two approaches is obtained if certain approximations implicit in the Udagawa-Tamura prior-form derivation are avoided. We examine the relation of the two approaches to singularities of the post-form distorted wave Born approximation matrix element and to the procedures for reduction of a many-body theory by use of effective operators in a model space. The two-step heuristic model is seen to be invalid for prior-form inelastic breakup; it is necessary to take account of nuclear excitations during projectile breakup. Careful treatment of the non-Hermiticity of kinetic energy operators with respect to continuum wave functions is required
Third family corrections to tri-bimaximal lepton mixing and a new sum rule
Energy Technology Data Exchange (ETDEWEB)
Antusch, Stefan [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut) Foehringer Ring 6, D-80805 Muenchen (Germany)], E-mail: antusch@mppmu.mpg.de; King, Stephen F. [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: sfk@hep.phys.soton.ac.uk; Malinsky, Michal [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: malinsky@phys.soton.ac.uk
2009-01-19
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule s=rcos{delta}+2/3 a (where s,r,a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and {delta} is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes; Falcioni, Giulio; Freitas, Abilio de
2016-05-15
We calculate analytically the flavor non-singlet O(α{sup 2}{sub s}) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F{sup ep}{sub 1,2,L}(x, Q{sup 2}) and g{sup ep}{sub 1,2}(x, Q{sup 2}) and charged current non-singlet structure functions F{sup ν(anti} {sup ν)p}{sub 1,2,3}(x, Q{sup 2}), at general virtualities Q{sup 2} in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q{sup 2} and the effects of the power corrections due to the heavy quark mass are of the size of the known O(α{sup 2}{sub s}) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q{sup 2} >> m{sup 2}{sub c,b}. We also study the target mass corrections to the above sum rules.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-01
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters λE and λH, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for λE,H calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order αs radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of λE,H.
Magnetic moment for the negative parity Λ→Σ0 transition in light cone QCD sum rules
Directory of Open Access Journals (Sweden)
T.M. Aliev
2016-07-01
Full Text Available The magnetic moment of the Λ→Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Yan, Xin-Hu; LV, Hai-Jiang; Zhu, Pengjia; Jiang, Fengjian
2014-01-01
We studied the radiation and ionization energy loss based on single arm Monte Carlo simulation for GDH sum rule experiment in Hall-A at Jefferson Lab. The radiation length and ionization energy loss calculation methods were discussed in detail for 12C elastic scattering simulation. The relative momentum ratio \\Delta p/p and 12C elastic cross section were compared without and with Radiation Energy Loss and got reasonable shape by simulation. The total energy loss distribution were obtained reasonably with landau shape for 12C elastic scattering. This simulation work will give a good support for radiation correction analysis of GDH sum rule experiment.
Institute of Scientific and Technical Information of China (English)
YAN Xin-Hu; YE Yun-Xiu; CHEN Jian-Ping; LU Hai-Jiang; ZHU Peng-Jia; JIANG Feng-Jian
2015-01-01
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at the Jefferson Lab.Radiation and ionization energy loss are discussed for 12C elastic scattering simulation.The relative momentum ratio-Ap and 12C elastic cross section are compared without and with radiative energy loss and a reasonable shape is obtained by the simulation.The total energy loss distribution is obtained,showing a Landau shape for 12C elastic scattering.This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.
Bernard, V; Meißner, Ulf G; Kubis, Bastian; Mei{\\ss}ner, Ulf-G.
2005-01-01
We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E_{0+}.
Yaouanc, Alain Le
2014-01-01
We first discuss Uraltsev's and other sum rules constraining the $B \\to D^{**}(L=1)$ weak transitions in the infinite mass limit, and compare them with dynamical approaches in the same limit. After recalling these well established facts, we discuss how to apply infinite mass limit to the physical situation. We provide predictions concerning semi-leptonic decays and non-leptonic ones, based on quark models. We then present in more detail the dynamical approaches: the relativistic quark model \\`a la Bakamjian-Thomas and lattice QCD. We summarise lattice QCD results in the infinite mass limit and compare them to the quark model predictions. We then present preliminary lattice QCD results with finite $b$ and $c$ quark masses. A systematic comparison between theory and experiment is performed. We show that some large discrepancies exist between different experiments. Altogether the predictions at infinite mass are in fair agreement with experiment for non-leptonic decays contrary to what happens for semileptonic d...
Analysis of the semileptonic Bc → D10 transition in QCD sum rules and HQET
International Nuclear Information System (INIS)
We investigate the structure of the D10(2420 [2430])(JP = 1+) mesons via analyzing the semileptonic Bc → D10lν transition in the frame work of the three-point QCD sum rules and the heavy-quark effective theory. We consider the D10 meson in three ways: as a pure vertical stroke c anti u right angle state, as a mixture of the two vertical stroke 3P1 right angle and vertical stroke 1P1 right angle states with a mixing angle θ, and as a combination of the two mentioned states with mixing angle θ = 35.3 circle in the heavy-quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the three above conditions. These form factors are numerically calculated for vertical stroke c anti u right angle and the heavy-quark limit cases. The obtained results for the form factors are used to evaluate the decay rates and the branching ratios. Also for mixed states, all of the mentioned physical quantities are plotted with respect to the unknown mixing angle θ. (orig.)
Infrared Refractive Index of Silicon: Parity and Sum-Rule Tests
Karstens, William; Inokuti, Mitio; Smith, David Y.
2012-02-01
We have resolved conflicting reports for the IR refractive index of silicon using general considerations of linear response theory. We find that use of unphysical series expansions in the analysis of channel spectra has been a significant source of systematic error. Recognition that the index is an even function of photon energy is crucial for analysis of these measurements and clarifies data presentation. In the region of high IR transparency of elemental semiconductors, the index may be expanded in a rapidly convergent Taylor series. Coefficients of terms in the (2n)^th power of energy are proportional to the (2n+1)^th inverse moment of the electronic absorption spectrum. In the favorable case of intrinsic Si, the electronic absorption is sufficiently well known that independent values of the intercept, slope and curvature of plots of index vs. the square of photon energy may be calculated. Index data sets with parameters significantly different from these suffer from systematic errors or refer to impure samples. Using these parity and sum-rule tests we have prepared a composite index data set for intrinsic silicon that represents a best fit to reliable measurements from microwaves to the visible. Applications to germanium and diamond will be discussed.
Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA
Bohr, Jakob
2013-01-01
The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Molecules that are intrinsically chiral, such as double-stranded DNA, is one example. They exhibit a non-vanishing strain-twist coupling, which depends on the local geometry, i.e. on curvature and torsion, yet the paths of closed loops are restricted by White's theorem. We suggest that the reciprocation of these principles leads to a twist neutrality condition. I.e. to a zero sum rule for the incremental change in the rate of winding along the curve. This has direct implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. A first estimate of this minimum length is 120 base pairs. This is not far from the 80 base pairs which is about the smallest length observed in experimental studies. Slightly longer microDNAs are better described as an ellipse and a relationship between length and eccentricity for these ...
Precise f_{D*,B*} and f_{B_c} from QCD spectral sum rules
Narison, Stephan
2014-01-01
Anticipating future precise measurements of the B-like leptonic decays for alternative determinations of the CKM mixing angles or/and for predicting their semi-leptonic and hadronic decays, we pursue our program on the B-like mesons by improving the estimates of f_D* and f_B* [analogue to f_\\pi=130.4(2) MeV] using suitable ratios of the well-established (inverse) Laplace sum rules less affected by the systematics and known to N2LO pQCD and where the full d=6 non-perturbative condensate contributions are included. An estimate of the N3LO terms based on geometric growth of the pQCD series is included in the error calculations. Our optimal results based on stability criteria and on an (in)dependence on the choice of the QCD subtraction point read: f_D*/f_D=1.209(22),f_B*/f_B=1.031(8) which imply : f_D*=246(7) MeV and f_B*=212(8) MeV if we use our recent results in [1] for f_D and f_B. We complete the analysis by a direct estimate of f_Bc using the complete NLO + N2LO for massless m_c pQCD expression and complete...
Medium modifications of the bound nucleon GPDs and the quark contribution to the spin sum rule
Energy Technology Data Exchange (ETDEWEB)
Guzey, Vadim; Thomas, Anthony; Tsushima, Kazuo
2009-01-01
We estimate the nuclear medium modifications of the quark contribution to the bound nucleon spin sum rule, $J^{q^{\\ast}}$, as well the separate helicity, $\\Delta \\Sigma^{\\ast}$, and the angular momentum, $L^{q^{\\ast}}$, contributions to $J^{q^{\\ast}}$. For the calculation of the bound nucleon GPDs, we use as input the bound nucleon elastic form factors predicted in the quark-meson coupling model. Our model for the bound nucleon GPDs is relevant for incoherent DVCS with nuclear targets. We find that the medium modifications increase $J^{q^{\\ast}}$ and $L^{q^{\\ast}}$ and decrease $\\Delta \\Sigma^{\\ast}$ compared to the free nucleon case. The effect is large and increases with increasing nuclear density $\\rho$. For instance, at $\\rho=\\rho_0=0.15$ fm$^{-3}$, $J^{q^{\\ast}}$ increases by 7\\%, $L^{q^{\\ast}}$ increases by 20\\% and $\\Delta \\Sigma^{\\ast}$ decreases by 17\\%. These in-medium modifications of the bound nucleon spin properties may be understood qualitatively
Mass modification of /D-meson at finite density in QCD sum rule
Hayashigaki1, A.
2000-08-01
We evaluate the mass shift of isospin-averaged /D-meson in the nuclear medium. Borel-transformed QCD sum rules are used to describe an interaction between the /D-meson and a nucleon by taking into account all the lowest dimension-4 operators in the operator product expansion (OPE). We find at normal matter density the /D-meson mass shift is about /10 times (/~50 MeV) larger than that of /J/ψ. This originates from the fact that the dominant contribution in the OPE for the /D-meson is the nucleon matrix element of mcq¯q, where mc is the charm-quark mass and /q denotes light quarks. We also discuss that the mass shift of the /D-meson in nuclear matter may cause the level crossings of the charmonium states and the /DD¯ threshold. This suggests an additional mechanism of the /J/ψ suppression in high energy heavy-ion collisions.
Light quark masses from QCD sum rules with minimal hadronic bias
Domínguez, C A; Röntsch, R H; Schilcher, R
2009-01-01
The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are $m_u(Q= 2 {GeV}) = 2.9 \\pm 0.2 {MeV}$, $m_d(Q= 2 {GeV}) = 5.3 \\pm 0.4 {MeV}$, and $m_s(Q= 2 {GeV}) = 102 \\pm 8 {MeV}$, for $\\Lambda = 381 \\pm 16 {MeV}$, corresponding to $\\alpha_s(M_\\tau^2) = 0.344 \\pm0.009$. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in $\\Lambda$, the unknown six-loop PQ...
Light quark masses from QCD sum rules with minimal hadronic bias
Energy Technology Data Exchange (ETDEWEB)
Dominguez, C.A. [Centre for Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700 (South Africa); Department of Physics, Stellenbosch University, Stellenbosch 7600 (South Africa); Nasrallah, N.F. [Faculty of Science, Lebanese University, Tripoli (Lebanon); Roentsch, R.H. [Centre for Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch 7700 (South Africa); Schilcher, K. [Institut fuer Physik, Johannes Gutenberg-Universitaet, Staudingerweg 7, D-55099 Mainz (Germany)
2009-01-15
The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are m{sub u}(Q=2 GeV)=2.9{+-}0.2 MeV, m{sub d}(Q=2 GeV)=5.3{+-}0.4 MeV, and m{sub s}(Q=2 GeV)=102{+-}8 MeV, for {lambda}=381{+-}16 MeV, corresponding to {alpha}{sub s}(M{sub {tau}}{sup 2})=0.344{+-}0.009. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in {lambda}, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement.
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
Baru, V; Hoferichter, M; Kubis, B; Nogga, A; Phillips, D R
2011-01-01
We use chiral perturbation theory (ChPT) to calculate the $\\pi^- d$ scattering length with an accuracy of a few percent, including isospin-violating corrections both in the two- and three-body sector. In particular, we provide the technical details of a recent letter, where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths $a^+$ and $a^-$. We study isospin-breaking contributions to the three-body part of $a_{\\pi^-d}$ due to mass differences, isospin violation in the $\\pi N$ scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in $a_{\\pi^- d}$ due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the p...
Renormalization group improved bottom mass from {Upsilon} sum rules at NNLL order
Energy Technology Data Exchange (ETDEWEB)
Hoang, Andre H.; Stahlhofen, Maximilian [Wien Univ. (Austria). Fakultaet fuer Physik; Ruiz-Femenia, Pedro [Wien Univ. (Austria). Fakultaet fuer Physik; Valencia Univ. - CSIC (Spain). IFIC
2012-09-15
We determine the bottom quark mass from non-relativistic large-n {Upsilon} sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of {alpha}{sub s} ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic {alpha}{sub s} ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling ({alpha}{sub s}(M{sub Z})=0.1183{+-}0.0010) we obtain M{sub b}{sup 1S}=4.755{+-}0.057{sub pert} {+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.
QCD sum rule analysis for light vector and axial-vector mesons in vacuum and nuclear matter
Leupold, Stefan
2001-01-01
Extending previous work we study the constraints of QCD sum rules on mass and width of light vector and axial-vector mesons in vacuum and in a medium with finite nuclear density. For the latter case especially the effect of nuclear pions leading to vector-axial-vector mixing is included in the analysis.
Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang
2013-01-01
In this article,we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way,and make reasonable predictions for their masses in the vacuum and in the nuclear matter.
D^＋→η^（＇）l＋ν_l semileptonic decays in light-cone sum rules
Institute of Scientific and Technical Information of China (English)
李竞武; 薛丹青; 除庆强; 吴向尧
2011-01-01
We calculate the D → η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D＋ → η^（＇）l＋νl decays with the experimental data. By compa
Institute of Scientific and Technical Information of China (English)
WU Xing-Gang; YU Yao; CHEN Gu; HAN Hua-Yong
2011-01-01
The B-meson decay constant fB is an important component for studying the B-meson decays, which can be studied through QCD sum rules.We make a detailed discussion on fB from two sum rules up to next-to-leading order, i.e.sum rules Ⅰ and Ⅱ, which are derived from the conventional correlator and the correlator with chiral currents respectively.It is found that these two sum rules are consistent with each other.The sum rules Ⅱ involves less non-perturbative condensates as that of sum rules Ⅰ, and in principle, it can be more accurate if we know the dimensionfour gluon condensate well.It is found that fB decreases with the increment of mb, and to compare with the Belle experimental data on fB, both sum rules Ⅰ and Ⅱ prefer smaller pole b-quark mass, mb = 4.68 ± 0.07 GeV.By varying all the input parameters within their reasonable regions and by adding all the uncertainties in quadrature, we obtain fB = 172+23-25 MeV for sum rules Ⅰ and fB = 214+26-34 MeV for sum rules Ⅱ.PACS numbers: 11.55.Hx, 12.38.-t, 13.20.He, 12.38.Lg
Becirevic, D; Le Yaouanc, A; Oliver, L; Pène, O; Raynal, J C
2003-01-01
The introduction of an explicit negative radial excitation contribution in the hadronic side of the light cone QCD sum rule (LCSR) of Belyaev, Braun, Khodjamirian and Ruckl, can explain the large experimental value of g(D*Dpi), recently measured by CLEO. At the same time, it considerably improves the stability of the sum rule when varying the Borel parameter.
Magnetic moment of $X_Q$ state with $J^{PC}=1^{+\\pm}$ in light cone QCD sum rules
Agamaliev, A K; Savcı, M
2016-01-01
The magnetic moments of the recently observed resonance $X_b(5568)$ by DO Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetra--quark states with quantum numbers $J^{PC}=1^{+\\pm}$. The magnetic moment can play critical role in determination of the quantum numbers, as well as giving useful information about the inner structure of these mesons.
How Precisely can we Determine the $\\piNN$ Coupling Constant from the Isovector GMO Sum Rule?
Loiseau, B; Thomas, A W
1999-01-01
The isovector GMO sum rule for zero energy forward pion-nucleon scattering iscritically studied to obtain the charged pion-nucleon coupling constant usingthe precise negatively charged pion-proton and pion-deuteron scattering lengthsdeduced recently from pionic atom experiments. This direct determination leadsto a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09(statistic) +- 0.17 (systematic). We obtain also accurate values for thepion-nucleon scattering lengths.
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.; Rittinger, J.
2012-01-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available...
General proof of the saturation of the Adler-Weisberger sum rule in a quark shell model
International Nuclear Information System (INIS)
The exact saturation of the Adler-Weisberger sum rule is demonstrated in a model of Dirac particles bound by a central potential. We use a method similar in spirit to the P→infinity approach, suitably modified to deal with a static potential. The pair contribution corresponding to exotic intermediate states is shown to be nonvanishing, but in a nonrelativistic expansion it vanishes order by order as found in low orders by the approach of the previous paper
Determination of αs from Gross-Llewellyn Smith sum rule by accounting for infrared renormalon
International Nuclear Information System (INIS)
We recapitulate the method which resums the truncated perturbation series of a physical observable in a way which takes into account the structure of the leading infrared renormalon. We apply the method to the Gross-Llewellyn Smith (GLS) sum rule. By confronting the obtained result with the experimentally extracted GLS value, we determine the value of the QCD coupling parameter, which turns out to agree with the present world average
A QCD sum rule calculation of the X± (5568) → Bs0 π± decay width
Dias, J. M.; Khemchandani, K. P.; Martínez Torres, A.; Nielsen, M.; Zanetti, C. M.
2016-07-01
To understand the nature of the X (5568), recently observed in the mass spectrum of the Bs0 π± system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. We found that it is possible to obtain a stable value of the mass compatible with the D0 result, although a rigorous QCD sum rule constrained analysis led to a higher value of mass. As a continuation of our investigation, we calculate the width of the tetraquark state with same quark content as X (5568), to the channel Bs0 π±, using the three-point QCD sum rule. We obtain a value of (20.4 ± 8.7) MeV for the mass ∼ 5568 MeV, which is compatible with the experimental value of 21.9 ± 6.4 (sta)-2.5+5.0 (syst) MeV /c2. We find that the decay width to Bs0 π± does not alter much for a higher mass state.
Majewski, M
2003-01-01
Mass formulae for light meson multiplets derived by means of the exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the CMSR give the well known mass formulae for real masses (Gell-Mann-Okubo, Schwinger and ideal mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths - width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for the S nonet that the points (m,GAMMA) form a rectilinear stitch (RS) on the complex mass plane. For low-mass nonets the WSR are strongly violated due to ''kinematical'' suppression of the particle decays, but the violation decreases as the mass increases and disappears above propor to 1.5 GeV. The slope k sub s of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value -0.5. If k sub s is known for a nonet, w...
Lattice QCD and QCD sum rule determination of the decay constants of ηc, J/ψ and hc states
Bečirević, Damir; Duplančić, Goran; Klajn, Bruno; Melić, Blaženka; Sanﬁlippo, Francesco
2014-01-01
We compute the decay constants of the lowest cc¯ -states with quantum numbers JPC=0−+ ( ηc ), 1−− ( J/ψ ), and 1+− ( hc ) by using lattice QCD and QCD sum rules. We consider the coupling of J/ψ to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched ( Nf=2 ) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate...
The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths
DEFF Research Database (Denmark)
Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens;
1999-01-01
approximation. For an incomplete (computational) basis, some guidelines are developed for constructing higher angular momentum contributions to bases that will optimize the sum of generalized oscillator strengths and thus make the basis well suited for the calculation of stopping cross sections....
Kivel, N A
2000-01-01
We applied QCD Light Cone Sum Rules to estimate power corrections to the helicity-conserving amplitude in the process $\\gamma^*\\gamma\\to \\pi\\pi$. We found that above $Q^2 \\sim 4$ GeV$^2$ power corrections are numerically small and the twist-2 part dominates.The amplitude can be reliably calculated in this region using models of $2 \\pi$ distribution amplitudes as an input. We found that the magnitude of the NLO corrections depends rather strongly on the normalization of the gluonic distribution amplitude.
Koike, Y
1996-01-01
A new QCD sum rule analysis on the spin-isospin averaged $\\rho$, $\\omega$ and constraint relation on the the low energy limit of the vector-current nucleon forward scattering amplitude, we get $a_\\rho=-0.47\\pm 0.05$ fm, $a_\\omega=-0.41\\pm 0.05$ fm and $a_\\phi=-0.15\\pm 0.02$ fm, which suggests that these $V-N$ interactions are attractive. It is also proved that the previous studies on the mass shift of these vector mesons in the nuclear medium are essentially the ones obtained from these scattering lengths in the linear density approximation.
Calculation of the K^0-\\bar{K}^0 mixing parameter via the QCD sum rules at finite energies
Chetyrkin, K. G.; Kataev, A. L.; Krasulin, A. B.; Pivovarov, A. A.
2001-01-01
The QCD finite energy sum rules method is used to show that the parameter of the K^0-\\bar{K}_0 mixing \\hat{B} is mainly determined by the value of g m_s and the vacuum expectation values of four-quark operators. Assuming the hypothesis of vacuum dominance and/or unitarity symmetry to estimate latter, it is found that \\hat{B}=1.2\\pm 0.1. (The updated (March 2001) prediction reads \\hat{B} = 1.0 +- 0.1 (for more details, see Comments after the main text).
A measurement of $\\alpha_{s}$ (M$_{Z}^{2}$) from the Gross Llewellyn Smith sum rule
Harris, D A; Auchincloss, P S; De Barbaro, P; Bazarko, A O; Bernstein, R H; Bodek, A; Bolton, T; Budd, H; Conrad, J; Drucker, R B; Johnson, R A; Kim, J H; King, B J; Kinnel, T; Koizumi, G; Koutsoliotas, S; Lamm, M J; Lefmann, W C; Marsh, W; McFarland, K S; McNulty, C; Mishra, S R; Naples, D; Nienaber, P; Nussbaum, M; Oreglia, M J; Perera, L; Quintas, P Z; Romosan, A; Sakumoto, W K; Schumm, B A; Sciulli, F J; Seligman, W G; Shaevitz, M H; Smith, W H; Spentzouris, P; Steiner, R; Stern, E G; Vakili, M; Yang, U K
1995-01-01
The Gross Llewellyn Smith sum rule has been measured at different values of four-momentum transfer squared (Q^{2}) by combining the precise CCFR neutrino data with data from other deep-inelastic scattering experiments at lower values of Q^{2}. A comparison with the {\\cal O}(\\alpha^{3}_{s}) predictions of perturbative QCD yields a determination of \\alpha_{s} and its dependence on Q^{2} in the range 1\\,GeV^2 < Q^{2} < 20 \\,GeV^{2}. Low \\qsq\\ tests have greater sensitivity to \\alfs(\\mztwo) than high \\qsq\\ tests, since at low Q^2, \\alpha_s is large and changing rapidly.
Aliev, T M
2016-01-01
The strong coupling constants of the $\\pi$ and $K$ mesons with negative parity octet baryons are estimated within the light cone QCD sum rules. It is observed that all strong coupling constants, similar to the case for the positive parity baryons, can be described in terms of three invariant functions, where two of them correspond to the well known $F$ and $D$ couplings in the $SU(3)_f$ symmetry, and the third function describes the $SU(3)_f$ symmetry violating effects. We compare our predictions on the strong coupling constants of pseudoscalar mesons of negative parity baryons with those corresponding to the strong coupling constants for the positive parity baryons.
Ikawa, Shun-ichi; Yamazaki, Shuichi; Kimura, Masao
1981-06-01
Another form of the sum rule for dipolar absorptions has been derived by means of quantum statistics. The difference between this and usually used form results from a quantum effect on the molecular rotational motion. By the joint use of the two forms, average rotational kinetic energies of water molec in the liquid and solid phases and some dipolar molecules in solutions have been estimated. It has been shown that the average rotational kinetic energ larger than the value expected from the classical equipartition rule, with an increase in the hindering potential for the rotational motion of the mole The dipole moments of water molecules in liquid and solid water have been estimated. These are considerably smaller than the gas-phase value.
Perturbative Corrections to $\\Lambda_b \\to \\Lambda$ Form Factors from QCD Light-Cone Sum Rules
Wang, Yu-Ming
2015-01-01
We compute radiative corrections to $\\Lambda_b \\to \\Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\\Lambda_b$-baryon correlation function is justified at leading power in $\\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\\cal O}(\\alpha_s)$ shift the $\\Lambda_b \\to \\Lambda$ from factors at large recoil significantly and the dominant contribution originat...
Improved QCD sum rule study of $Z_{c}(3900)$ as a $\\bar{D}D^{*}$ molecular state
Zhang, Jian-Rong
2013-01-01
In the framework of QCD sum rules, we present an improved study of our previous work [Phys. Rev. D {\\bf80}, 056004 (2009)] particularly on the $\\bar{D}D^{*}$ molecular state to investigate that the possibility of the newly observed $Z_{c}(3900)$ as a $S$-wave $\\bar{D}D^{*}$ molecular state. To ensure the quality of QCD sum rule analysis, contributions of up to dimension nine are calculated to test the convergence of operator product expansion (OPE). We find that the two-quark condensate $$ is very large and makes the standard OPE convergence (i.e. the perturbative at least larger than each condensate contribution) happen at very large values of Borel parameters. By releasing the rigid OPE convergence criterion, one could find that the OPE convergence is still under control. We arrive at the numerical result $3.86\\pm0.27 {GeV}$ for $\\bar{D}D^{*}$, which agrees with the mass of $Z_{c}(3900)$ and could support the explanation of $Z_{c}(3900)$ in terms of a $S$-wave $\\bar{D}D^{*}$ molecular state.
Determination of Baryon wave functions of the ground-state octet by means of QCD sum rules
International Nuclear Information System (INIS)
In this work we investigate the wave functions of the baryons in the ground state octet by using the QCD sum rules technique, especially referring to the formalism of Chernyak and Zhitnitsky. The moments of the quark distibution amplitudes of the proton, Σ+ and Ξ- are determined by evaluating their sum rules graphically. For the necessary algebraic calculations we have developed a computer program package based on standard REDUCE, such that the Wilson coefficients could be calculated automatically. The contributions of the quark and gluon condensates up to energy dimension 6 have been taken into account. The corresponding quark distribution amplitudes of the cited baryons are plotted. Our results do not agree with those of a paper recently published by Chernyak, Ogloblin and Zhitnitsky and show, that the effects of the SU(3)F symmetry breaking by the mass of the strange quark are unexpectedly large. The electromagnetic form factors of the considered baryons are determined for an intermediate momentum transfer of several GeV. (orig.)
International Nuclear Information System (INIS)
Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non-forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1)nξ(n)(1) ≥ ((2n+1)!!/22n). Moreover, for the curvature we find ξ''(1) ≥ (1/5)[4ρ2 + 3(ρ2)2] where ρ2 = -ξ'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λ-barξ(w) and the sums n ΔEj(n)τj(n)(1)τj(n)(w) (j = (1/2), (3/2)), that involve leading quantities, Isgur-Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi · v', vf · v', vi · vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute ((1/2)+, (3/2)+). We also obtain new sum rules involving the elastic subleading form factors χi(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (jP, JP) = ((1/2)-, 1-),((3/2)-, 1-) that enter in the 1/mQ2 corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -δ1/m2(A1) in terms of the χi(w) and the shape of the elastic IW function ξ(w). An important theoretical implication is that χ1'(1), χ2(1) and χ3'(1) (χ1(1) = χ3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values ρ2 → (3/4), σ2 → (15/16). These constraints
Jugeau, F.; Le Yaouanc, A.; Oliver, L.; Raynal, J.-C.
2006-01-01
Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non-forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1)nξ(n)(1) ⩾ (2n+1)!!/22n. Moreover, for the curvature we find ξ″(1) ⩾ 1/5[4ρ2 + 3(ρ2)2] where ρ2 = -ξ'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λ¯ξ(w) and the sums ∑ n ΔEj(n)τj(n)(1)τj(n)(w) (j = 1/2, 3/2), that involve leading quantities, Isgur-Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi ṡ v', vf ṡ v', vi ṡ vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute (1/2+, 3/2+). We also obtain new sum rules involving the elastic subleading form factors χi(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (jP, JP) = (1/2-, 1-),(3/2-, 1-) that enter in the 1/mQ2 corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -δ1/m2(A1) in terms of the χi(w) and the shape of the elastic IW function ξ(w). An important theoretical implication is that χ1'(1), χ2(1) and χ3'(1)(χ1(1) = χ3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values ρ2 → 3/4, σ2 → 15/16. These constraints should be taken
Chiral sum rules for scrL(6)WZ parameters and its application to π0,η,η' decays
International Nuclear Information System (INIS)
The chiral expansion of the low-energy processes π0→γγ and η→γγ is reconsidered with particular emphasis on the question of the evaluation of the two low-energy parameters from scrL(6)WZ which are involved at chiral order six. It is shown how extensive use of sum rules and saturation with resonances as well as constraints from asymptotic QCD effectively determine their values. Predictions for the widths are presented for both standard and nonstandard values of the quark mass ratio ms/m. A precise relation is established between the usual phenomenological η-η' mixing parameters and those of the chiral expansion. The large size of the chiral correction to the η decay can be understood on the basis of a simple counting rule: O(1/Nc)∼O(mq). It is shown how this counting rule eventually allows one to include the η' into the effective Lagrangian in a consistent and systematic way
Estimating the mass of the hidden charm 1{sup +}(1{sup +}) tetraquark state via QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Qiao, Cong-Feng; Tang, Liang [University of Chinese Academy of Sciences, Department of Physics, Beijing (China)
2014-10-15
By using QCD sum rules, the mass of the hidden charm tetraquark [cu][ anti c anti d] state with I{sup G}(J{sup P}) = 1{sup +}(1{sup +}) (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance Z{sub c}{sup +} (3900). In the calculation, contributions up to dimension eight in the operator product expansion (OPE) are taken into account. We find m{sup c}{sub 1+} = (3912{sub -153}{sup +306}) MeV, which is consistent,within the errors, with the experimental observation of Z+ c (3900). Extending to the b-quark sector, m{sup b}{sub 1+} = (10561{sub -163}{sup +395})MeV is obtained. The calculational result strongly supports the tetraquark picture for the ''exotic'' states of Z{sub c}{sup +} (3900) and Z{sub b}{sup +} (10610). (orig.)
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions. PMID:16321073
Analysis of the (1)/(2){sup ±} pentaquark states in the diquark model with QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China); Huang, Tao [Chinese Academy of Sciences, Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Beijing (China)
2016-01-15
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future. (orig.)
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
Pion Form Factor in QCD Sum Rules with Nonlocal Condensates and in the Local-Duality Approach
Bakulev, Alexander P; Stefanis, N G
2009-01-01
We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(\\alpha_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(\\alpha_s^2)$ contribution to the pion's form factor.
F-wave heavy-light meson spectroscopy in QCD sum rules and heavy quark effective theory
Zhou, Dan; Geng, Li-Sheng; Liu, Xiang; Zhu, Shi-Lin
2015-01-01
We study the F-wave c_bar s heavy meson doublets (2+,3+) and (3+,4+). They have large orbital excitations L=3, and may be good challenges (tests) for theoretical studies. To study them we use the method of QCD sum rule in the framework of heavy quark effective theory. Their masses are predicted to be m_{(2+,3+)} = (3.45 \\pm 0.25, 3.50 \\pm 0.26) GeV and m_{(3+,4+)} = (3.20 \\pm 0.22, 3.26 \\pm 0.23) GeV, with mass splittings Delta m_{(2+,3+)} = m_{3+} - m_{2+} = 0.046 \\pm 0.030 GeV and Delta m_{(3+,4+)} = 0.053 \\pm 0.044 GeV, respectively.
Analysis of the (1)/(2)± pentaquark states in the diquark-diquark-antiquark model with QCD sum rules
International Nuclear Information System (INIS)
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the JP = (1)/(2)± hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ = √(MP2-(2Mc)2) to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S = 0, -1, -2, -3, which can be confronted with the experimental data in the future. (orig.)
Adler function, sum rules and Crewther relation of order O(αs4): The singlet case
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.; Rittinger, J.
2012-07-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 [1]), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 [2], Baikov et al., 2010 [3]) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e- annihilation into hadrons in a general gauge theory.
Adler function, sum rules and Crewther relation of order O(αs4): The singlet case
International Nuclear Information System (INIS)
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 ), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 , Baikov et al., 2010 ) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e- annihilation into hadrons in a general gauge theory.
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
Baikov, by P A; Kühn, J H; Rittinger, J
2012-01-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\\cal O}(\\alpha_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\\cal O}(\\alpha_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.
D → a1, f1 transition form factors and semileptonic decays via 3-point QCD sum rules
Zuo, Yabing; Hu, Yue; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-07-01
By using the 3-point QCD sum rules, we calculate the transition form factors of D decays into the spin triplet axial vector mesons a1(1260), f1(1285), f1(1420). In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of a1(1260) is one, we calculate the D+ → a 10(1260) and D0 → a 1‑(1260) transition form factors separately. In the case of f1(1285), f1(1420), the mixing between light flavor SU(3) singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
$D \\rightarrow a_1, f_1$ transition form factors and semileptonic decays via 3-point QCD sum rules
Zuo, Yabing; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-01-01
By using the 3-point QCD sum rules, we calculate the transition form factors of $D$ decays into the spin triplet axial vector mesons $a_1(1260)$, $f_1(1285) $, $f_1(1420)$. In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of $a_1(1260)$ is one, we calculate the $D^+ \\rightarrow a_1^0 (1260)$ and $D^0 \\rightarrow a_1^- (1260)$ transition form factors separately. In the case of $ f_1(1285), f_1(1420)$, the mixing between light flavor $SU(3)$ singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules
Wang, Zhi-Gang
2016-09-01
In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity JP = 0+, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value MX = (5.57±0.12) GeV, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state. Supported by National Natural Science Foundation under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017
Shen, Yue-Long; Lü, Cai-Dian
2016-01-01
Within the framework of $B$-meson light-cone sum rules, we compute the one-loop level QCD corrections to $B\\to \\pi$ transition form factors at small $ q^{2}$ region, in implement of a complete renormalization group equation evolution. To solve the renormalization group equations, we work at the "dual" space where the anomalous dimensions of the jet function and the light-cone distribution amplitudes are diagonal. With the complete renormalization group equation evolution, the form factors are almost independent of the factorization scale, which is shown numerically. We also extrapolate the results of the form factors to the whole $q^2$ region, and compare their behavior with other studies.
Relation between (e,e') sum rules in 6,7Li and 4He nuclei.Experiment and cluster model
Efros, V D; Buki, A Yu
2016-01-01
The sums over (e,e') spectra of 6Li and 7Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the alpha-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm^{-1} the relations expressing the A=6 or 7 sum in terms of the A=4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm^{-1} the longitudinal correlation functions of 6Li and 7Li nuclei are found to be close to that of the alpha-particle. The experimental longitudinal sums in the range between 0.450 and 1.625 fm^{-1} are employed to perform comparison with those calculated in the framework of cluster models. Out of the mentioned experimental sums, those in the range between 0.750 and 1.000 fm^{-1} in the 6Li case ...
Energy Technology Data Exchange (ETDEWEB)
Deur, A
2000-10-01
This thesis presents an experimental study of the neutron (and {sup 3}He) spin structure with a particular emphasis in the resonance domain (experiment E94010 that took place in 1997 at Jefferson Lab (TJNAF or formerly CEBAF) in Virginia). A polarized {sup 3}He target was built in order to achieve this study since polarized {sup 3}He nuclei can be seen as polarized neutrons. This target allowed the measurement of the polarized absolute cross sections {sigma}{sub 1/2}(Q{sup 2}, {nu}) and {sigma}{sub 3/2}(Q{sup 2}, {nu}) from the inclusive reaction {sup {sup {yields}}{sup 3}He}({sup {yields}}e, e')X for incident beam energies ranging from 0.86 GeV to 5.07 GeV at a scattering angle of 15.5 deg. The Q{sup 2} evolution of the generalized Gerasimov-Drell-Hearn (GDH) integral on {sup 3}He and on neutron was measured from 0.1 GeV{sup 2} to 1.0 GeV{sup 2} in order to understand the transition between perturbative QCD and non-perturbative QCD. The integration domain in {nu} (the energy loss of the scattered electron) is from the pion threshold to about 2.5 GeV which covers both the resonance region and the Deep Inelastic Scattering. The high precision of our data constrains the models giving the Q{sup 2} evolution of the generalized GDH integral. The polarized quasi-elastic scattering was also measured. The cross section {sigma}{sup TT}(Q{sup 2}, {nu}) on {sup 3}He and the spin structure functions g{sub 1}{sup {sup 3}He}(Q{sup 2}, {nu}) and g{sub 2}{sup {sup 3}He}(Q{sup 2}, {nu}) are presented. These data are an indication that the higher-twists are small in our kinematics domain and that the Bloom-Gilman duality seems to hold for the polarized spin structure functions. (author)
Energy Technology Data Exchange (ETDEWEB)
Yazici, E.; Sundu, H.; Veliev, E.V. [Kocaeli University, Department of Physics, Izmit (Turkey)
2016-02-15
The strong form factor of the B{sub c}B{sub c}J/ψ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T ≅ 100 MeV but slightly increases after this point. After T ≅ 160 MeV, the form factor suddenly decreases up to T ≅ 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q{sub 2} = -m{sup 2}{sub offshell} at T = 0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments. (orig.)
Aliev, T M; Savcı, M
2016-01-01
The light cone sum rules method is used in studying the radiative decays $\\Sigma_Q \\to \\Lambda_Q \\gamma$ and $\\Xi^\\prime_Q \\to \\Xi_Q \\gamma$. Firstly, the sum rules for the form factor $F_2(Q^2=0)$ responsible for these transitions is constructed. Using this result the decay widths of the above--mentioned decays are calculated and analyzed. A comparison of our predictions on the decay widths of considered transitions with the predictions of the other approaches is presented.
Kondratyuk, S; Myhrer, F; Scholten, O
2004-01-01
The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: 1) by evaluating of the scattering amplitude at the corresponding low-energy kinematics and 2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the $\\Delta$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.
Analysis of the strong decays $D_{s3}^*(2860)\\to DK$, $D^{*}K$ with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we assign the $D_{s3}^*(2860)$ to be a D-wave $c\\bar{s}$ meson, study the vertices $D_{s3}^*(2860)DK$ and $D_{s3}^*(2860)D^*K$ in details to select the pertinent tensor structures, calculate the hadronic coupling constants $G_{D_{s3}^*(2860)DK}$ and $G_{D_{s3}^*(2860)D^*K}$ with the three-point QCD sum rules and obtain the decay widths $\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)$ and $\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)$. The predicted ratio $R=\\Gamma\\left(D_{s3}^*(2860)\\to D^{*}K\\right)/\\Gamma\\left(D_{s3}^*(2860)\\to DK\\right)=0.57\\pm0.38$ cannot reproduce the experimental data $R={\\rm Br}\\left(D_{sJ}^*(2860)\\to D^{*}K\\right)/{\\rm Br}\\left(D_{sJ}^*(2860)\\to DK\\right)=1.10 \\pm 0.15 \\pm 0.19$.
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Energy Technology Data Exchange (ETDEWEB)
Baru, V. [Institut fuer Theoretische Physik II, Ruhr-Universitaet Bochum, D-44870 Bochum (Germany); Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Theoretical and Experimental Physics, B. Cheremushinskaya 25, 117218 Moscow (Russian Federation); Hanhart, C. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany); Hoferichter, M., E-mail: hoferichter@hiskp.uni-bonn.de [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, OH 45701 (United States); Kubis, B. [Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universitaet Bonn, D-53115 Bonn (Germany); Nogga, A. [Institut fuer Kernphysik and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany)
2011-12-15
We use chiral perturbation theory (ChPT) to calculate the {pi}{sup -}d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a{sup +} and a{sup -}. We study isospin-breaking contributions to the three-body part of a{sub {pi}}{sup -}{sub d} due to mass differences, isospin violation in the {pi}N scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a{sub {pi}}{sup -}{sub d} due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Interpretation of Z{sub c}(4025) as the hidden charm tetraquark states via QCD Sum Rules
Energy Technology Data Exchange (ETDEWEB)
Qiao, Cong-Feng [Graduate University of Chinese Academy of Sciences, School of Physics, Beijing (China); CAS Center for Excellence in Particle Physics, Beijing (China); Tang, Liang [Graduate University of Chinese Academy of Sciences, School of Physics, Beijing (China)
2014-03-15
By using QCD Sum Rules, we found that the charged hidden charm tetraquark [cu][ anti c anti d] states with J{sup P} = 1{sup -} and 2{sup +}, which are possible quantum numbers of the newly observed charmonium-like resonance Z{sub c}(4025), have masses of m{sup c}{sub 1-} = (4.54 ± 0.20) GeV and m{sup c}{sub 2+} = (4.04 ± 0.19) GeV. The contributions up to dimension eight in the operator product expansion were taken into account in the calculation. The tetraquark mass of J{sup P} = 2{sup +} state was consistent with the experimental data of Z{sub c}(4025), suggesting the Z{sub c}(4025) state to possess the quantum number of J{sup P} = 2{sup +}. Extending to the b-quark sector, the corresponding tetraquark masses m{sup b}{sub 1-} = (10.97 ± 0.25) GeV and m{sup b}{sub 2+} = (10.35 ± 0.25) GeV were obtained, which values are testable in future B-factories. (orig.)
Precision calculation of threshold π−d scattering, πN scattering lengths, and the GMO sum rule
International Nuclear Information System (INIS)
We use chiral perturbation theory (ChPT) to calculate the π−d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion–nucleon scattering lengths a+ and a−. We study isospin-breaking contributions to the three-body part of aπ−d due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in aπ−d due to virtual photons. Finally, we discuss the validity of the Goldberger–Miyazawa–Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion–nucleon coupling constant.
Kondratyuk, S; Kubodera, K; Myhrer, F; Scholten, O
2004-01-01
The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: (1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and (2) by
Hudspith, R J; Maltman, K; Wolfe, C E; Zanotti, J
2015-01-01
Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{us}$ using inclusive hadronic $\\tau$ decay data. Results for $V_{us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\\vert V_{us}\\vert$, but also $D>4$ effective condensates, fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging $D=2$ OPE series. The new sum rule implementation yields $\\vert V_{us}\\vert$ results free of unphysical $s_0$- and $w$-dependences and $\\sim 0.0020$ higher than that obtained using the conventional implementation. With preliminary new experimental results for the $K\\pi$ branching frac...
Kontturi, Ville; Silfsten, Pertti; Peiponen, Kai-Erik
2011-07-01
Absorption spectra from colloids containing different concentrations of spherical gold nanoparticles in water were measured with a spectrophotometer. The absorption spectra were used to calculate the number density of nanoparticles (NPs) with the aid of an unconventional finite spectral band f-sum rule applied for gold colloid. Good correlation between the number density of dispersion electrons, obtained from the f-sum rule, and the number density of nanoparticles was found. The effective absolute refractive index of the gold colloid was obtained with the aid of a singly subtractive Kramers-Kronig relation, and in addition the refractive index change due to the nanoparticles was obtained with the aid of a conventional Kramers-Kronig relation. Such optical properties are valuable in studies of light interaction with nanoparticles.
A QCD sum rule calculation of the $X^\\pm(5568) \\to B_{s}^0\\pi^\\pm$ decay width
Dias, J M; Torres, A Martínez; Nielsen, M; Zanetti, C M
2016-01-01
To understand the nature of the $X(5568)$, recently observed in the mass spectrum of the $B_{s}^0\\pi^\\pm$ system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. The result found for its mass agrees well with the experimental value. Encouraged by this finding we now extend our calculations to obtain the decay width of $X(5568)$ to $B_{s}^0\\pi^\\pm$ using the three-point QCD sum rule. We obtain a value of $(20.4\\pm8.7)\\MeV$, which, on comparing with the experimental value of $21.9\\pm6.4 (\\mbox{sta})^{+5.0}_{-2.5}(\\mbox{syst}) \\MeV/c^2$, reinforces the scalar four quark nature of $X(5568)$.
Energy Technology Data Exchange (ETDEWEB)
Hilger, Thomas Uwe
2012-04-11
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
International Nuclear Information System (INIS)
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes Ds and D*0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
International Nuclear Information System (INIS)
The computer program LIMES is based on an improved version of the extended sum-rule model for light and intermediate-mass fragment emission in heavy ion reactions. It includes a code for dynamical calculations of the critical angular momentum for fusion following the suggestions. The report briefly describes the use of this program, the necessary input for the calculations of the element distribution and partial cross sections and gives a Fortran listing. Using the fitting routine FITEX the program provides an option for fast parameter adjustments. The use is demonstrated by an application to a specific example. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research
2007-03-15
We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
Representations of the U$_{q}$(u$_{4,1}$) and a q-polynomial that determines baryon mass sum rules
Gavrilik, A M; Tertychnyj, A V; Gavrilik, A M; Kachurik, I I; Tertychnyj, A V
1995-01-01
With quantum groups U_q(su_n) taken as classifying symmetries for hadrons of n flavors, we calculate within irreducible representation D^+_{12}(p-1,p-3,p-4;p,p-2) (p \\in {\\bf Z}) of 'dynamical' quantum group U_q(u_{4,1}) the masses of baryons {1\\over 2}^+ that belong to {\\it 20}-plet of U_q(su_4). The obtained q-analog of mass relation (MR) for U_q(su_3)-octet contains unexpected mass-dependent term multiplied by the factor {A_q\\over B_q} where A_q, B_q are certain polynomials (resp. of 7-th and 6-th order) in the variable q+q^{-1}\\equiv [2]_q. Both values q=1 and q=e^{i\\pi \\over 6} turn the polynomial A_q into zero. But, while q=1 results in well-known Gell-Mann--Okubo (GMO) baryon MR, the second root of A_q reduces the q-MR to some novel mass sum rule which has irrational coefficients and which holds, for empirical masses, even with better accuracy than GMO mass sum rule.
Bréhamet, Lionel
2008-01-01
Efficiency of intrinsic operator techniques (using only products and ranks of tensor operators) is first evidenced by condensed proofs of already known $\\bigtriangledown$-triangle sum rules of su(2)/su$_q$(2). {\\em A new compact} su$_q$(2)-{\\em expression} is found, using a $q$-series $\\Phi$, with $\\Phi(n)_{| q=1}=1$. This success comes from an ultimate identification process over monomials like $(c_0)^p$. For osp(1$|$2), analogous principles of calculation are transposed, involving a second parameter $d_0$. Ultimate identification process then must be done over binomials like ${(c_{0}+{d_{0}}^{2})}^{\\Omega -m} ({d_{0}}^{2})^{m}$. {\\em Unknown} polynomials ${\\cal P}$ are introduced as well as their expansion coefficients, $x$, over the binomials. It is clearly shown that a hypothetical super-triangle sum rule requires super-triangles $\\bigtriangleup^{S}$, instead of $\\bigtriangledown$ for su(2)/su$_q$(2). Coefficients $x$ are integers ({\\em conjecture 1}). Massive unknown advances are done for intermediate st...
Analysis of the $D_{s3}^*(2860)$ as a D-wave $c\\bar{s}$ meson with QCD sum rules
Wang, Zhi-Gang
2016-01-01
In this article, we take the $D_{s3}^*(2860)$ as a D-wave $c\\bar{s}$ meson, and study the mass and decay constant of the $D_{s3}^*(2860)$ with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-6 in the operator product expansion. The predicted mass $M_{D_{s3}^*}=(2.86\\pm0.10)\\,\\rm{GeV}$ is in excellent agreement with the experimental value $M_{D_{s3}^*}=(2860.5\\pm 2.6 \\pm 2.5\\pm 6.0)\\,\\rm{ MeV}$ from the LHCb collaboration. The prediction supports assigning the $D_{s3}^*(2860)$ to be the D-wave $c\\bar{s}$ meson.
Analysis of the strong coupling form factors of $\\Sigma_bNB$ and $\\Sigma_c ND$ in QCD sum rules
Yu, Guo Liang; Li, Zhen Yu
2016-01-01
In this article, we study the strong interaction of the vertexes $\\Sigma_bNB$ and $\\Sigma_c ND$ using the three-point QCD sum rules under two different dirac structures. Considering the contributions of the vacuum condensates up to dimension $5$ in the operation product expansion, the form factors of these vertexes are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant. Our analysis indicates that the coupling constant for these two vertexes are $G_{\\Sigma_bNB}=0.43\\pm0.01GeV^{-1}$ and $G_{\\Sigma_cND}=3.76\\pm0.05GeV^{-1}$.
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-03-15
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the J{sup P} = (1)/(2){sup ±} hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ = √(M{sub P}{sup 2}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S = 0, -1, -2, -3, which can be confronted with the experimental data in the future. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-02-15
In this article,we construct the diquark-diquark- antiquark type interpolating currents, and we study the masses and pole residues of the J{sup P} = (3)/(2){sup -} and (5)/(2){sup +} hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula μ = √(M{sup 2}{sub P{sub c}}-(2M{sub c}){sup 2}) to determine the energy scales of the QCD spectral densities. The present predictions favor assigning P{sub c}(4380) and P{sub c}(4450) to be the (3)/(2){sup -} and (5)/(2){sup +} pentaquark states, respectively. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Johnson, R.A.; Vakili, M. [University of Cincinnati, Cincinnati, Ohio 45221 (United States); Kim, J.H.; Arroyo, C.G.; Bazarko, A.O.; Conrad, J.; King, B.J.; Lefmann, W.C.; McNulty, C.; Mishra, S.R.; Quintas, P.Z.; Romosan, A.; Schellman, H.; Sciulli, F.J.; Seligman, W.G.; Shaevitz, M.H.; Spentzouris, P.; Stern, E.G. [Columbia University, New York, New York 10027 (United States); Bernstein, R.H.; Lamm, M.J.; Marsh, W.; McFarland, K.S.; Yu, J. [Fermi National Accelerator Laboratory, Batavia, Illinois 60510 (United States); Bolton, T.; Naples, D. [Kansas State University, Manhattan, Kansas 66506 (United States); de Barbaro, L. [Northwestern University, Evanston, Illinois 60208 (United States); Harris, D.A.; de Barbaro, P.; Bodek, A.; Budd, H.; Sakumoto, W.K.; Yang, U.K. [University of Rochester, Rochester, New York 14627 (United States); Kinnel, T.; Smith, W.H. [University of Wisconsin, Madison, Wisconsin 53706 (United States)
1998-10-01
We extract a set of values for the Gross{endash}Llewellyn Smith sum rule at different values of 4-momentum transfer squared (Q{sup 2} ), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for 1{lt}Q{sup 2}{lt}15 GeV{sup 2}/c{sup 2} . A comparison with the order {alpha}{sup 3}{sub s} theoretical predictions yields a determination of {alpha}{sub s} at the scale of the Z -boson mass of 0.114{plus_minus}{sup 0.009}{sub 0.012} . This measurement provides a new and useful test of perturbative QCD at low Q{sup 2} , because of the low uncertainties in the higher order calculations. {copyright} {ital 1998} {ital The American Physical Society }
Application of the QCD light cone sum rule to tetraquarks: The strong vertices XbXbρ and XcXcρ
Agaev, S. S.; Azizi, K.; Sundu, H.
2016-06-01
The full version of the QCD light-cone sum rule method is applied to tetraquarks containing a single heavy b or c quark. To this end, investigations of the strong vertices XbXbρ and XcXcρ are performed, where Xb=[s u ][b ¯ d ¯ ] and Xc=[s u ][c ¯d ¯] are the exotic states built of four quarks of different flavors. The strong coupling constants GXbXbρ and GXcXcρ corresponding to these vertices are found using the ρ -meson leading- and higher-twist distribution amplitudes. In the calculations, Xb and Xc are treated as scalar bound states of a diquark and antidiquark.
Analysis of the strong decay X(5568) → B{sub s}{sup 0}π{sup +} with QCD sum rules
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2016-05-15
In this article, we take the X(5568) to be the scalar diquark-antidiquark type tetraquark state, study the hadronic coupling constant g{sub XB{sub sπ}} with the three-point QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension-6 and including both the connected and the disconnected Feynman diagrams; then we calculate the partial decay width of the strong decay X(5568) → B{sub s}{sup 0}π{sup +} and obtain the value Γ{sub X} = (20.5 ± 8.1) MeV, which is consistent with the experimental data Γ{sub X} = (21.9 ± 6.4{sup +5.0}{sub -2.5}) MeV from the D0 collaboration. (orig.)
Dynamical simulation of disoriented chiral condensate formation in Bjorken rods
International Nuclear Information System (INIS)
Using a semiclassical treatment of the linear σ model, we simulate the dynamical evolution of an initially hot cylindrical rod endowed with a longitudinal Bjorken scaling expansion (a ''Bjorken rod''). The field equation is propagated until full decoupling has occurred and the asymptotic many-body state of free pions is then obtained by a suitable Fourier decomposition of the field and a subsequent stochastic determination of the number of quanta in each elementary mode. The resulting transverse pion spectrum exhibits visible enhancements below 200 MeV due to the parametric amplification caused by the oscillatory relaxation of the chiral order parameter. Ensembles of such final states are subjected to various event-by-event analyses. The factorial moments of the multiplicity distribution suggest that the soft pions are nonstatistical. Furthermore, their emission patterns exhibit azimuthal correlations that have a bearing on the domain size in the source. Finally, the distribution of the neutral pion fraction shows a significant broadening for the soft pions which grows steadily as the number of azimuthal segments is increased. All of these features are indicative of disoriented chiral condensates and it may be interesting to apply similar analyses to actual data from high-energy nuclear collision experiments. (c) 2000 The American Physical Society
International Nuclear Information System (INIS)
Deep inelastic neutrino-deuteron scattering in the covariant approach in the light-cone variables is considered. The deuteron structure function F3D(x,Q2) is calculated in the relativistic impulse approximation on the basis of the relativistic wave function. The results are compared with available experimental data. The nuclear effect of relativistic Fermi motion described by the ratio RFD/N = F3D/F3N is estimated. The dependence of the ratio on x and Q2 is investigated. The dependence of the Gross-Llewellyn Smith integral SGLS(x,Q2) on x and Q2 is considered. On the basis of the QCD analysis of the xF3N structure function the correction for SGLS(x,Q2) due to the nuclear effect is estimated and it is shown that the nuclear effect should be taken into account to verify the Gross-Llewellyn Smith sum rule. 25 refs., 4 figs., 2 tabs
Energy Technology Data Exchange (ETDEWEB)
Mirez, Carlos; Trevisan, Luis A.; Tomio, Lauro [Universidade Estadual Paulista (IFT/UNESP), Sao Paulo, SP (Brazil). Inst. de Fisica Teorica
2010-07-01
In the present work the method used in ref. [1] is considered to obtain the function structure of pion F{sub 2}{sup {pi}}2 , In that model, it was needed an initial quark distribution and the observed distribution in the hadron. This method provides information about the sea quark distribution of mesons that are out of reach experimentally. The pion structure is determined fairly acc urated. The initial distribution for the anti-d quark may given by the thermal model ref. [2,3]. We compare our results with other models to describe the pion structure function ref. [4,5] and with the experimental data on pion structure. We also studied if there is a relation between the q{sup 2} and the measured violation of the Gottfried sum rule. Also, a comparison between the relations Gott x q{sup 2} and Gott x T, where the T is the temperature given by a statistical model ref.[1,2] is done. On this way, it is expected to understand if there is a relation q{sup 2} x T [3,4], that would mean that the scattering heats the hadron. (author)
Bakulev, A P; Pimikov, A V; Stefanis, N G
2011-01-01
A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.
Mikhailov, S V; Stefanis, N G
2016-01-01
We consider the calculation of the pion-photon transition form factor $F^{\\gamma^*\\gamma\\pi^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale $M^2$, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for $F^{\\gamma^*\\gamma\\pi^0}(Q^2)$ are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the $Q^2$ range between 1 and 5 GeV$^2$, thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical p...
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2016-06-01
We consider the calculation of the pion-photon transition form factor Fγ*γπ0(Q2) within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M2, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for Fγ*γπ0(Q2) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q2 range between 1 and 5 GeV2 , thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
Kataev, A L; Andrei L Kataev; Aleksander V Sidorov
1994-01-01
We present the results of our QCD analysis of the recent CCFR data for the structure function $xF_3 (x,Q^2)$ of the deep-inelastic neutrino--nucleon scattering. The analysis is based on the Jacobi polynomials expansion of the structure functions. The concrete results for the parameter $\\Lambda_{\\overline {MS}}^{(4)}$ and the shape of quark distributions are determined. At the reference scale $|Q_0 ^2|$=3 $GeV^2$ our results are in satisfactory agreement with the ones obtained by the CCFR group with the help of another method. The $Q_0^{2}$-dependence of the experimental data for the Gross--Llewellyn Smith sum rule is extracted in the wide region of high-momentum transfer. Within systematical experimental uncertainties the results obtained are consistent with the perturbative QCD predictions. We reveal the effect of the discrepancy between our results and the analysed perturbative QCD predictions at the level of the statistical error bars. The importance of taking account, in our procedure, of a still unknown ...
New Constraints on the 18F(p,alpha) 15O Rate in Novae from (d,p) Reaction Sum Rules
Kozub, R L; Batchelder, J C; Blackmon, J C; Brune, C R; Champagne, A E; Cizewski, J A; Davinson, T; Greife, U; Gross, C J; Jewett, C C; Livesay, R J; Ma, Z; Moazen, B H; Nesaraja, C D; Sahin, L; Scott, J P; Shapira, D; Smith, M S; Thomas, J S; Woods, P J
2004-01-01
The degree to which the (p,gamma) and (p,alpha) reactions destroy 18F at temperatures 1-4x10^8 K is important for understanding the synthesis of nuclei in nova explosions and for using the long-lived radionuclide 18F, a target of gamma-ray astronomy, as a diagnostic of nova mechanisms. The reactions are dominated by low-lying proton resonances near the 18F+p threshold (E_x=6.411 MeV in 19Ne). To gain further information about these resonances, we have used a radioactive 18F beam from the Holifield Radioactive Ion Beam Facility to selectively populate corresponding mirror states in 19F via the inverse d(18F,p)19F neutron transfer reaction. Neutron spectroscopic factors were measured for states in 19F in the excitation energy range 0-9 MeV and appropriately scaled to conform to sum rule limits. The results would suggest significantly lower 18F(p,gamma)19Ne and 18F(p,alpha)15O reaction rates than reported previously, thereby increasing the prospect of observing the 511-keV annihilation radiation associated with ...
Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics
Roy, Victor; Rezzolla, Luciano; Rischke, Dirk
2015-01-01
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $\\tau$ is the same as for the time-honored "Bjorken flow" without magnetic field. Furthermore, when the magnetic field is assumed to decay $\\sim \\tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the...
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2014-05-15
In this article, we distinguish the charge conjugations of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and we study the masses and pole residues of the J{sup PC} = 1{sup -±} hidden charmed tetraquark states with the QCD sum rules. We suggest a formula μ = √(M{sup 2}{sub X/Y/Z}-(2M{sub c}){sup 2}) with the effective mass M{sub c} = 1.8 GeV to estimate the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, which works very well. The numerical results disfavor assigning the Z{sub c}(4020), Z{sub c}(4025), and Y(4360) as the diquark-antidiquark (with the Dirac-spinor structure C - Cγ{sub μ}) type vector tetraquark states, and they favor assigning the Z{sub c}(4020), Z{sub c}(4025) as the diquark-antidiquark type 1{sup +-} tetraquark states. While the masses of the tetraquark states with symbolic quark structures c anti cs anti s and c anti c(u anti u + d anti d)/√(2) favor assigning the Y(4660) as the 1{sup --} diquark-antidiquark type tetraquark state, more experimental data are still needed to distinguish its quark constituents. There are no candidates for the positive charge conjugation vector tetraquark states; the predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II. (orig.)
Two views on the Bjorken scenario for ultra-relativistic heavy-ion collisions
Maire, Antonin
2011-01-01
The sketch describes the Bjorken scenario foreseen for the collision of ultra-relativistic heavy-ions, leading to the creation of strongly-interacting hot and dense deconfined matter, the so-called Quark-Gluon Plasma (QGP).
A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
Akamatsu, Yukinao; Teaney, Derek
2016-01-01
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations. We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\\propto \\omega^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid. Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, evaluating the contribution of thermal noise from the earliest moments and at late times. In the Bjorken case, the solution to the kinetic equations determines the coefficient of the first fractional power of the gradient expansion ($\\propto 1/(\\tau T)^{3/2}$) for the expanding system. Numerically, we find that the contribution to the longitudinal pressure from hydrodynamic fluctuations is larger than second order hyd...
International Nuclear Information System (INIS)
Using recent experimental results on Compton scattering by 208Pb at energies below pion threshold we explore the effects of enhancement due to mesonic currents and isovector vibrations on the giant resonances of nuclei. Quantitative information is given for the enhancements of the electric polarizability, the diamagnetic susceptibility and the energy-weighted quadrupole sum rule. It is shown that the average of results available from different laboratories on the ''nonretarded'' enhancement constant κGDR in the A = 197-209 mass range favours an effective nucleon mass of m*/m = 3/4. Some new results for the amplitude of Compton scattering by the giant resonances of nuclei are presented which allow a treatment of the retardation problem in a zero-order approximation. ((orig.))
Transverse flow induced by inhomogeneous magnetic fields in the Bjorken expansion
Pu, Shi
2016-01-01
We investigate the magnetohydrodynamics in the presence of an external magnetic field following the power-law decay in proper time and having spatial inhomogeneity characterized by a Gaussian distribution in one of transverse coordinates under the Bjorken expansion. The leading-order solution is obtained in the weak-field approximation, where both energy density and fluid velocity are modified. It is found that the spatial gradient of the magnetic field results in transverse flow, where the flow direction depends on the decay exponents of the magnetic field. We suggest that such a magnetic-field-induced effect might influence anisotropic flow in heavy ion collisions.
Bjorken flow from an anti-de Sitter space Schwarzschild black hole.
Alsup, James; Siopsis, George
2008-07-18
We consider a large black hole in asymptotically anti-de Sitter spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions. PMID:18764245
International Nuclear Information System (INIS)
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
Beautiful mesons from QCD spectral sum rules
Energy Technology Data Exchange (ETDEWEB)
Narison, S.
1988-08-18
We apply q/sup 2/ = 0 moments within n (number of derivatives) and t/sub c/ (continuum threshold) stability criteria to the beautiful-meson systems. The optimal predictions are reached for the same ranges of n and t/sub c/ values leading to the previous estimate of the decay constant f/sub B/. The QCD scales (b-quark 'physical' mass, mixed and four-quark condensates) are strongly constrained by the observed B and B/sup */ masses. The predictions for the S- and P-state splittings are much affected by the definition of the b-quark mass (pole or euclidian) entering into the Wilson coefficients of the non-perturbative condensates. The size of the SU(3)/sub F/ breaking on the mass splittings cannot be accurately predicted due to the imprecise value of the
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang [North China Electric Power University, Department of Physics, Baoding (China)
2014-07-15
In this article, we calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and study the J{sup PC} = 0{sup ++}, 1{sup +-}, 2{sup ++} D{sup *} anti D{sup *}, D{sub s}{sup *} anti D{sub s}{sup *}, B{sup *} anti B{sup *}, B{sub s}{sup *} anti B{sub s}{sup *} molecular states with the QCD sum rules. In the calculations, we use the formula μ = √(M{sup 2}{sub X/Y/Z}-(2M{sub Q}){sup 2}) to determine the energy scales of the QCD spectral densities. The numerical results favor assigning the Z{sub c}(4020) and Z{sub c}(4025) to the J{sup PC} = 0{sup ++}, 1{sup +-} or 2{sup ++} D{sup *} anti D{sup *} molecular states, the Y(4140) to the J{sup PC} = 0{sup ++} D{sub s}{sup *} anti D{sub s}{sup *} molecular state, the Z{sub b}(10650) to the J{sup PC} = 1{sup +-} B{sup *} anti B{sup *} molecular state, and they disfavor assigning the Y(3940) to the (J{sup PC} = 0{sup ++}) molecular state. The present predictions can be confronted with the experimental data in the future. (orig.)
Wang, Z G
2006-01-01
In this article, we analyze the vertexes $D^*D_sK$, $D^*_sDK$, $D_0D_sK$ and $D_{s0}DK$ within the framework of the light-cone QCD sum rules approach in an unified way. The strong coupling constants $G_{D^*D_sK}$ and $G_{D^*_sDK}$ are important parameters in evaluating the charmonium absorption cross sections in searching for the quark-gluon plasmas, our numerical values for the $G_{D^*D_sK}$ and $G_{D^*_sDK}$ are compatible with the existing estimations although somewhat smaller, the SU(4) symmetry breaking effects are very large, about 60%. For the charmed scalar mesons $D_0$ and $D_{s0}$, we take the point of view that they are the conventional $c\\bar{u}$ and $c\\bar{s}$ mesons respectively, and calculate the strong coupling constants $G_{D_0 D_s K}$ and $G_{D_{s0} D K}$ with the vector interpolating currents. The numerical values for the scalar-$D_sK$ and -$DK$ coupling constants $G_{D_0 D_s K}$ and $G_{D_{s0} D K}$ are compatible with the existing estimations, the large values support the hadronic dressin...
International Nuclear Information System (INIS)
The QCD sum rule approach of Chernyak and Zhitnitsky for calculating the quark distribution amplitudes is applied to the lowest lying nucleon resonance of spin 3/2 and positive parity, namely the Δ(1232). With the help of an especially developed REDUCE computer program package the sum rules for the first few moments of the wavefunction are calculated. It is found that no fiducial region exists, where the sum rules can be saturated such that the amount of the nonperturbative and continuum contributions are acceptable. A detailed analysis shows that the reasons for this defect are the spin-mixing on the light-cone and the canonical choice of the baryonic currents in connection with their correlation function. We show however that with the considered currents the sum rules can be saturated accurately by a dominating baryon resonance with a mass around 1600 MeV. The resulting quark distribution amplitude of this resonance, which is identified as the Δ(1600) with 1/2 and negative parity, is compatible with its asymptotic form and shows no asymmetry in the quark momenta. Its magnetic transition form factor at momentum transfer of several GeV is calculated refering to the perturbative QCD results of Carlson and Poor. (orig.)
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Fu, Hai-Bing; Wu, Xing-Gang; Ma, Yang; Cheng, Wei; Zhong, Tao
2016-08-01
We present a detailed calculation on the B\\to {K}* transition form factors (TFFs), {A}{0,1,2}, V and {T}{1,2,3}, within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude {φ }2;{K*}\\perp provides over 90% contribution, thus those TFFs provide good platforms for testing the property of {φ }2;{K*}\\perp . We suggest a model for {φ }2;{K*}\\perp , in which two parameters {B}2;{K*}\\perp and {C}2;{K*}\\perp dominantly control its longitudinal distribution. With a proper choice of {B}2;{K*}\\perp and {C}2;{K*}\\perp , our predictions on B\\to {K}* TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay B\\to {K}*{μ }+{μ }-. The predicted differential branching fraction {{d}}{B}/{{d}}{q}2(B\\to {K}*{μ }+{μ }-) is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q 2-region, we get the branching fraction, {B}(B\\to {K}*{μ }+{μ }-)=≤ft({1.088}-0.205+0.261\\right)× {10}-6, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of {φ }2;{K*}\\perp .
Measurement of neutral current cross-sections at high Bjorken- with the ZEUS detector at HERA
Indian Academy of Sciences (India)
Inderpal Singh; on behalf of the ZEUS Collaboration
2012-11-01
A new method is employed to measure the neutral current cross-section up to Bjorken values of 1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb-1 of electron–proton collisions and 142 pb-1 of positron–proton collisions, at a centre-of-mass energy of 318 GeV. Cross-sections have been extracted for 2 > 575 GeV2. A much improved precision with respect to the previous ZEUS publication, which used only 16.7 pb-1 of electron–proton collisions and 65.1 pb-1 of positron–proton collisions, is achieved, owing to the large data sample and improved kinematic reconstruction methods. The measurement is well-described by different theory predictions.
Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
Floerchinger, Stefan
2015-01-01
Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane and rapidity. We examine how the time evolution of linear perturbations depends on the equation of state as well as on shear viscosity, bulk viscosity and heat conductivity for modes with different azimuthal, radial and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.
Inclusive Dijet Production at Low Bjorken-x in Deep Inelastic Scattering
Aktas, A; Anthonis, T; Asmone, A; Babaev, A; Backovic, S; Bähr, J; Baranov, P; Barrelet, E; Bartel, Wulfrin; Baumgartner, S; Becker, J; Beckingham, M; Behnke, O; Behrendt, O; Belousov, A; Berger, C; Berndt, T; Bizot, J C; Böhme, J; Boenig, M O; Boudry, V; Bracinik, J; Braunschweig, W; Brisson, V; Broker, H B; Brown, D P; Bruncko, Dusan; Büsser, F W; Bunyatyan, A; Buschhorn, G; Bystritskaya, L; Campbell, A J; Caron, S; Cassol-Brunner, F; Chekelian, V; Clarke, D; Collard, Caroline; Contreras, J G; Coppens, Y R; Coughlan, J A; Cousinou, M C; Cox, B E; Cozzika, G; Cvach, J; Dainton, J B; Dau, W D; Daum, K; Delcourt, B; Delerue, N; Demirchyan, R; de Roeck, A; De Wolf, E A; Diaconu, C; Dingfelder, J; Dodonov, V; Dowell, John D; Dubak, A; Duprel, C; Eckerlin, G; Efremenko, V; Egli, S; Eichler, R; Eisele, F; Ellerbrock, M; Elsen, E; Erdmann, M; Erdmann, W; Faulkner, P J W; Favart, L; Fedotov, A; Felst, R; Ferencei, J; Fleischer, M; Fleischmann, P; Fleming, Y H; Flucke, G; Flügge, G; Fomenko, A; Foresti, I; Formánek, J; Franke, G; Frising, G; Gabathuler, Erwin; Gabathuler, K; Garvey, J; Gassner, J; Gayler, J; Gerhards, R; Gerlich, C; Ghazaryan, S; Görlich, L; Gogitidze, N; Gorbounov, S; Grab, C; Grabskii, V; Grässler, Herbert; Greenshaw, T; Gregori, M; Grindhammer, G; Haidt, Dieter; Hajduk, L; Haller, J; Heinzelmann, G; Henderson, R C W; Henschel, H; Henshaw, O; Heremans, R; Herrera-Corral, G; Herynek, I; Hildebrandt, M; Hiller, K H; Hladky, J; Hoting, P; Hoffmann, D; Horisberger, R P; Hovhannisyan, A; Ibbotson, M; Jacquet, M; Janauschek, L; Janssen, X; Jemanov, V; Jönsson, L B; Johnson, C; Johnson, D P; Jung, H; Kant, D; Kapichine, M; Karlsson, M; Katzy, J; Keil, F; Keller, N; Kennedy, J; Kenyon, I R; Kiesling, C; Klein, M; Kleinwort, C; Kluge, T; Knies, G; Koblitz, B; Kolya, S D; Korbel, V; Kostka, P; Koutouev, R; Kropivnitskaya, A; Kroseberg, J; Kueckens, J; Kuhr, T; Landon, M P J; Lange, W; Lastoviicka, T; Laycock, P; Lebedev, A; Leiner, B; Lemrani, R; Lendermann, V; Levonian, S; List, B; Lobodzinska, E; Loktionova, N A; López-Fernandez, R; Lubimov, V; Lüders, H; Lüders, S; Lüke, D; Lytkin, L; Makankine, A; Malden, N; Malinovskii, E I; Mangano, S; Marage, P; Marks, J; Marshall, R; Martyn, H U; Martyniak, J; Maxfield, S J; Meer, D; Mehta, A; Meier, K; Meyer, A B; Meyer, H; Meyer, J; Michine, S; Mikocki, S; Milstead, D; Moreau, F; Morozov, A; Morozov, I; Morris, J V; Müller, K; Murn, P; Nagovizin, V; Naroska, Beate; Naumann, J; Naumann, T; Newman, P R; Niebergall, F; Niebuhr, C B; Nikitin, D K; Nowak, G; Nozicka, M; Olivier, B; Olsson, J E; Ossoskov, G; Ozerov, D; Pascaud, C; Patel, G D; Peez, M; Pérez, E; Petrukhin, A; Pitzl, D; Pöschl, R; Povh, B; Raicevic, N; Rauschenberger, J; Reimer, P; Reisert, B; Risler, C; Rizvi, E; Robmann, P; Roosen, R; Rostovtsev, A A; Rusakov, S V; Rybicki, K; Sankey, D P C; Sauvan, E; Schatzel, S; Scheins, J; Schilling, F P; Schleper, P; Schmidt, S; Schmitt, S; Schneider, M; Schoeffel, L; Schöning, A; Schröder, V; Schultz-Coulon, H C; Schwanenberger, C; Sedlak, K; Sefkow, F; Shevyakov, I; Shtarkov, L N; Sirois, Y; Sloan, T; Smirnov, P; Soloviev, Yu; South, D; Spaskov, V; Specka, A; Spitzer, H; Stamen, R; Stella, B; Stiewe, J; Strauch, I; Straumann, U; Thompson, G; Thompson, P D; Tomasz, F; Traynor, D; Truöl, P; Tsipolitis, G; Tsurin, I; Turnau, J; Turney, J E; Tzamariudaki, E; Uraev, A; Urban, M; Usik, A; Valkár, S; Valkárová, A; Vallée, C; Van Mechelen, P; Vargas-Trevino, A; Vasilev, S; Vazdik, Ya A; Veelken, C; Vest, A; Vichnevski, A; Vinokurova, S; Volchinski, V; Wacker, K; Wagner, J; Waugh, B; Weber, G; Weber, R; Wegener, D; Werner, C; Werner, N; Wessels, M; Wessling, B; Winde, M; Winter, G G; Wissing, C; Woerling, E E; Wünsch, E; Zaicek, J; Zaleisak, J; Zhang, Z; Zhokin, A; Zomer, F; Zur Nedden, M
2003-01-01
Dijet production in deep inelastic ep scattering is investigated in the region of low values of the Bjorken-variable x (10^-4 < x < 10^-2) and low photon virtualities Q^2 (5 < Q^2 < 100 GeV^2). The measured dijet cross sections are compared with perturbative QCD calculations in next-to-leading order. For most dijet variables studied, these calculations can provide a reasonable description of the data over the full phase space region covered, including the region of very low x. However, large discrepancies are observed for events with small separation in azimuth between the two highest transverse momentum jets. This region of phase space is described better by predictions based on the CCFM evolution equation, which incorporates k_t factorized unintegrated parton distributions. A reasonable description is also obtained using the Color Dipole Model or models incorporating virtual photon structure.
Vyawahare, Anant
2006-01-01
This paper deals with the sums of products of first n natural numbers, taken r at a time. Many interesting results about the summations are obtained. Ramasubramanian has already made some work in this direction. This paper is an extension of his work. In next part, the sums of odd and even natural numbers are discussed, and also of natural numbers, not necessarily beginning with one. After that, properties of sequences, arising out of these sums are obtained. Interest...
U.S. Geological Survey, Department of the Interior — The GIS layer "Census_sum_15" provides a standardized tool for examining spatial patterns in abundance and demographic trends of the southern sea otter (Enhydra...
The extraction of the spin structure function, g2 (and g1) at low Bjorken x
International Nuclear Information System (INIS)
The Spin Asymmetries of the Nucleon Experiment (SANE) used the Continuous Electron Beam Accelerator Facility at Jefferson Laboratory in Newport News, VA to investigate the spin structure of the proton. The experiment measured inclusive double polarization electron asymmetries using a polarized electron beam, scattered off a solid polarized ammonia target with target polarization aligned longitudinal and near transverse to the electron beam, allowing the extraction of the spin asymmetries A1 and A2, and spin structure functions g1 and g2. Polarized electrons of energies of 4.7 and 5.9 GeV were used. The scattered electrons were detected by a novel, non-magnetic array of detectors observing a four-momentum transfer range of 2.5 to 6.5 GeV*V. This document addresses the extraction of the spin asymmetries and spin structure functions, with a focus on spin structure function, g2 (and g1) at low Bjorken x. The spin structure functions were measured as a function of x and W in four Q square bins. A full understanding of the low x region is necessary to get clean results for SANE and extend our understanding of the kinematic region at low x.
The Hadronic Final State in Deep Inelastic ep Scattering at Low Bjorken-x at HERA
International Nuclear Information System (INIS)
The electron-proton collider HERA with centre of mass system energy of about 300 GeV has extended the available kinematic regime in deep inelastic scattering to low values of Bjorken-x (10-5-10-3) and made possible studies of the QCD dynamics in this region. The processes in which partons carry a very small fraction of the proton momentum may show deviations from the standard DGLAP dynamics and it is believed that their correct description is provided by the BFKL evolution formalism. Low x phenomena have been initially studied with the HERA data on F2 structure function and later with more exclusive measurements of the hadronic final state. In this report recent results of these studies and especially dedicated measurements of jets and π0 mesons, produced close to the proton remnant, are reviewed. The data are used to discriminate between QCD models with different parton evolution approximations. For completeness, measurements at e+e- and p-p colliders sensitive to the BFKL dynamics are also described. (author)
Quantum measurements without sums
Coecke, B; Coecke, Bob; Pavlovic, Dusko
2006-01-01
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product. The corresponding axioms define classical spaces as objects that allow copying and deleting data. Indeed, the information exchange between the quantum and the classical worlds is essentially determined by their distinct capabilities to copy and delete data. The sums turn out to be an implicit implementation of this capabilities. Realizing it through explicit axioms not only dispenses with the unnecessary structural baggage, but also allows a simple and intuitive graphical calculus. In category-theoretic terms, classical data types are dagger-compact Frobenius algebras, and quantum spectra underlying quantum measurements are Eilenberg-Moore coalgebras induced by these Frobenius algebras.
Multiparty Symmetric Sum Types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Factorization of numbers with Gauss sums: I. Mathematical background
Wölk, S.; Merkel, W.; Schleich, W. P.; Averbukh, I.Sh.; Girard, B
2012-01-01
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.
Factorization of numbers with Gauss sums: I. Mathematical background
Energy Technology Data Exchange (ETDEWEB)
Woelk, S; Merkel, W; Schleich, W P [Institut fuer Quantenphysik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89081 Ulm (Germany); Averbukh, I Sh [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Girard, B, E-mail: sabine.woelk@uni-ulm.de [Laboratoire de Collisions, Agregats, Reactivite, IRSAMC (Universite de Toulouse/UPS, CNRS) Toulouse (France)
2011-10-15
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.
Multiparty Symmetric Sum Types
Directory of Open Access Journals (Sweden)
Lasse Nielsen
2010-11-01
Full Text Available This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs. Processes using the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient implementation of a prototypical tool for CPGs which automatically translates the original CPG specifications from a representation called the Process Matrix to symmetric sum types, type checks programs and executes them.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
Institute of Scientific and Technical Information of China (English)
贺丽; 余增强
2016-01-01
Sum rules for the dynamic structure factors are powerful tools to explore the collective behaviors in many-body systems at zero temperature as well as at finite temperatures. The recent remarkable realization of synthetic spin-orbit (SO) coupling in quantum gases is opening up new perspective to study the intriguing SO effects with ultracold atoms. So far, a specific type of SO coupling, which is generated by a pair of Raman laser beams, has been experimentally achieved in Bose-Einstein condensates of 87Rb and degenerate Fermi gases of 40K and 6Li. In the presence of SO coupling, the dynamic structure factors for the density fluctuation and spin fluctuation satisfy different sum rules. In particular, in the two-component quantum gases with inter-species Raman coupling, the f-sum rule for the spin fluctuation has an additional term proportional to the transverse spin polarization. Due to the coupling between the momentum and spin, the first moment of the dynamic structure factor does not necessarily possess the inversion symmetry, which is in strong contrast to the conventional system without SO coupling. Such an asymmetric behavior could be observed in both Fermi gases and Bose gases with Raman coupling. As a demonstration, we focus on the uniform case at zero temperature in this work. For the non-interacting Fermi gases, the asymmetric first moment appears only when the Raman detuning is finite. The asymmetric amplitude is quite limited, and it vanishes at both zero detuning and infinite detuning. For the weakly interacting Bose gases, the first moment is asymmetric in momentum space even at zero detuning, when the ground state spontaneously breaks the Z2 symmetry in the plane-wave condensation phase. Using the Bogoliubov method, the dynamic structure factor and its first moment are explicitly calculated for various interaction parameters. We find that the asymmetric behavior in the spin channel could be much more significant than in the density channel, and the
Aktay, Metin
2000-01-01
Goldbach`s Conjecture, "every even number greater than 2 can be expressed as the sum of two primes" is renamed Goldbach`s Rule for it can not be otherwise. The conjecture is proven by showing that the existence of prime pairs adding to any even number greater than 2 is a natural by-product of the existence of the prime sequence less than that even number. First it is shown that the remainder of cancellations process which identifies primes less than an even number also remainders prime pairs ...
Sums of multiplicative characters analogue of Kloosterman sums
Xi, Ping
2010-01-01
Let $q$ be a positive integer, $\\chi$ a nontrivial character mod $q$. In this paper the authors prove some estimates for the character sum which is analogue of incomplete Kloostermann sums\\[\\sum_{\\substack{a\\in\\mathcal{I}\\\\ \\gcd(a,q)=1}}\\chi(ma+n\\overline{a}),\\] where $\\overline{a}$ is the multiplicative inverse of $a\\bmod q$, and $\\mathcal{I}$ is a subinterval of $[x+1,x+q]$ for certain integer $x.$
Measurement of neutral current e{sup {+-}}p cross sections at high Bjorken x with the ZEUS detector
Energy Technology Data Exchange (ETDEWEB)
Abramowicz, H. [Tel Aviv Univ. (Israel). School of Physics; Max-Planck-Institute for Physics, Munich (Germany); Abt, I. [Max-Planck-Institute for Physics, Munich (Germany); Adamczyk, L. [AGH-Univ. of Science and Technology, Krakow (Poland). Faculty of Physics and Applied Computer Science; Collaboration: ZEUS Collaboration; and others
2013-12-15
The neutral current e{sup {+-}}p cross section has been measured up to values of Bjorken x{approx_equal}1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb{sup -1} of e{sup -}p and 142 pb{sup -1} of e{sup +}p collisions at {radical}(s)=318 GeV. Differential cross sections in x and Q{sup 2}, the exchanged boson virtuality, are presented for Q{sup 2}{>=}725 GeV{sup 2}. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.
Measurement of neutral current e±p cross sections at high Bjorken x with the ZEUS detector
International Nuclear Information System (INIS)
The neutral current e±p cross section has been measured up to values of Bjorken x≅1 with the ZEUS detector at HERA using an integrated luminosity of 187 pb-1 of e-p and 142 pb-1 of e+p collisions at √(s)=318 GeV. Differential cross sections in x and Q2, the exchanged boson virtuality, are presented for Q2≥725 GeV2. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-x region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.
Social Security Administration — Staging Instance for all SUMs Counts related projects including: Redeterminations/Limited Issue, Continuing Disability Resolution, CDR Performance Measures, Initial...
On exponential sums of digital sums related to Gelfond's theorem
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.
Generation of symmetric exponential sums
Sergeyev, Yaroslav D.
2011-01-01
In this paper, a new method for generation of infinite series of symmetric identities written for exponential sums in real numbers is proposed. Such systems have numerous applications in theory of numbers, chaos theory, algorithmic complexity, dynamic systems, etc. Properties of generated identities are studied. Relations of the introduced method for generation of symmetric exponential sums to the Morse-Hedlund sequence and to the theory of magic squares are established.
Comment concerning Leonardo's rule
Sotolongo-Costa, O; Oseguera-Manzanilla, T; Díaz-Guerrero, D S
2016-01-01
In this comment we propose a novel explanation for the Leonardo's rule concerning the tree branching. According to Leonardo's notebooks he observed that if one observes the branches of a tree, the squared radius of the principal branch is equal to the sum of the squared radius of the branch daughters.
Character Sums Over The Prime Numbers
Carella, N. A.
2012-01-01
A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.
Sum rules for the T-odd fragmentation functions
Schäfer, A
2000-01-01
The conservation of the intrinsic transverse momentum during parton fragmentation imposes non-trivial constraints on T-odd fragmentation functions. These significantly enhance the differences between the favoured and unfavoured fragmentation functions, which could be relevant to understand the azimuthal asymmetries of charged pion production observed recently by the HERMES collaboration.
Euler Sums of Hyperharmonic Numbers
Dil, Ayhan; Khristo N. Boyadzhiev
2012-01-01
The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\\sigma}(r,m)=\\sum_{n=1}^{\\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of series of Hurwitz zeta function values. This is a generalization of a result of Mez\\H{o} and Dil. We also provide an explicit evaluation of {\\sigma}(r,m) in a closed form in terms of zeta values and Stirling numbers of the first kind. Furthermore, we evalu...
EXTENSIONS OF EULER HARMONIC SUMS
Directory of Open Access Journals (Sweden)
Djurdje Cvijović
2012-10-01
Full Text Available Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Euler’s famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Ablinger, Jakob; Raab, Clemens G; Schneider, Carsten
2014-01-01
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Determinant Sums for Undirected Hamiltonicity
Björklund, Andreas
2010-01-01
We present a Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in $O^*(1.657^{n})$ time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for TSP almost fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the first open problem in Woeginger's 2003 survey on exact algorithms for NP-hard problems. For bipartite graphs, we improve the bound to $O^*(1.414^{n})$ time. Both the bipartite and the general algorithm can be implemented to use space polynomial in $n$. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for $k$-Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle covers over a finite field of characteristic two. We reduce Hamiltonicity to Labeled ...
New continuity estimates of geometric sums
Directory of Open Access Journals (Sweden)
Evgueni Gordienko
2002-01-01
Full Text Available The paper deals with sums of a random number of independent and identically distributed random variables. More specifically, we compare two such sums, which differ from each other in the distributions of their summands. New upper bounds (inequalities for the uniform distance between distributions of sums are established. The right-hand sides of these inequalities are expressed in terms of Zolotarev's and the uniform distances between the distributions of summands. Such a feature makes it possible to consider these inequalities as continuity estimates and to apply them to the study of the stability (continuity of various applied stochastic models involving geometric sums and their generalizations.
Decompounding random sums: A nonparametric approach
DEFF Research Database (Denmark)
Hansen, Martin Bøgsted; Pitts, Susan M.
Observations from sums of random variables with a random number of summands, known as random, compound or stopped sums arise within many areas of engineering and science. Quite often it is desirable to infer properties of the distribution of the terms in the random sum. In the present paper we...... review a number of applications and consider the nonlinear inverse problem of inferring the cumulative distribution function of the components in the random sum. We review the existing literature on non-parametric approaches to the problem. The models amenable to the analysis are generalized considerably...
Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers
Directory of Open Access Journals (Sweden)
E. Kılıç
2011-01-01
Full Text Available By considering Melham's sums (Melham, 2004, we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−12+1 involving the generalized Fibonacci and Lucas numbers.
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
Directory of Open Access Journals (Sweden)
Shaofeng Ru
2014-01-01
Full Text Available The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
A hybrid mean value related to the Dedekind sums and Kloosterman sums
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The main purpose of this paper is using the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums,and give some interesting mean value formulae and identities for it.
International Nuclear Information System (INIS)
Let D be a t-(v, k, λ) design and let Ni(D), for 1 ≤ i ≤ t, be the higher incidence matrix of D, a (0, 1)-matrix of size (v/i) x b, where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N1(D). A zero-sum k-flow of D is a zero-sum flow with values in {±,...,±(k-1)}. In this paper we show that every non-symmetric design admits an integral zero-sum flow, and consequently we conjecture that every non-symmetric design admits a zero-sum 5-flow. Similarly, the definition of zero-sum flow can be extended to Ni(D), 1 ≤ i ≤ t. Let D = t-(v,k, (v-t/k-t)) be the complete design. We conjecture that Nt(D) admits a zero-sum 3-flow and prove this conjecture for t = 2. (author)
Private Decayed Sum Estimation under Continual Observation
Bolot, Jean; Muthukrishnan, S; Nikolov, Aleksandar; Taft, Nina
2011-01-01
Motivated by monitoring applications, recently, Dwork et al. initiated the study of differential privacy as data is continually updated over time. They abstracted the problem of running sums that is applicable widely, and proved upper and lower bounds on accuracy of \\epsilon - differentially private algorithms for this problem. We continue their study, but we are motivated by the reality that in many monitoring applications, recent data is more important than distant data. Thus, we study the sums problem for well known decay models of data, from window to exponential and polynomial decay. Such "decayed sums" are challenging because (a) while we want accuracy in analysis with respect to the window or decayed sum, we still want differential privacy; (b) sums within windows and decayed sums in general are not monotonic or even near-monotonic as studied in the work of Dwork et al. We present algorithms for decayed sum in each model which are \\epsilon-differentially private, and are accurate. For window and expone...
Sums-of-Products and Subproblem Independence
Stearns, Richard E.; Hunt, Harry B.
Sums-of-products provide a basis for describing certain computational problems, particularly problems related to constraint satisfaction including SAT, MAX SAT, and #SAT. They also can be used to describe many problems arising from graph theory. By modeling a problem as a sum-of-products problem, the concept of “subproblem independence” takes on a clear meaning. Subproblem independence has immediate computational implications since it can be used to create programs with reduced levels of nesting and programs which exploit memoization. The concept of subproblem independence also extends to quantified sums.
A method to compute periodic sums
Gumerov, Nail A
2013-01-01
In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even though the finite sum can be efficiently computed via fast summation algorithms, such as the fast multipole method (FMM), the periodized extension is usually treated via a different algorithm, Ewald summation, accelerated via the fast Fourier transform (FFT). A different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper. The method splits the periodized sum in to two parts. The first, comprising the contribution of all points outside a large sphere enclosing the box, and some of its neighbors, is approximated inside the box by a collection of kernel functions ("sources") placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions. The second part, compri...
SANE's Measurement of the Proton's Virtual Photon Spin Asymmetry, A^{p}_{1}, at Large Bjorken x
Energy Technology Data Exchange (ETDEWEB)
Mulholland, Jonathan [Univ. of Virginia, Charlottesville, VA (United States)
2012-05-01
The experiment SANE (Spin Asymmetries of the Nucleon Experiment) measured inclusive double polarization electron asymmetries on a proton target at the Continuous Electron Beam Accelerator Facility at the Thomas Jefferson National Laboratory in Newport News Virgina. Polarized electrons were scattered from a solid ^{14}NH_{3} polarized target provided by the University of Virginia target group. Measurements were taken with the target polarization oriented at 80 degrees and 180 degrees relative to the beam direction, and beam energies of 4.7 and 5.9 GeV were used. Scattered electrons were detected by a multi-component novel non-magnetic detector package constructed for this experiment. Asymmetries measured at the two target orientations allow for the extraction of the virtual Compton asymmetries A_{1}^{p} and A_{2}^{p} as well as the spin structure functions g_{1}^{p} and g_{2}^{p}. This work addresses the extraction of the virtual Compton asymmetry A_{1}^{p} in the deep inelastic regime. The analysis uses data in the kinematic range from Bjorken x of 0.30 to 0.55, separated into four Q^{2} bins from 1.9 to 4.7 GeV^{2}.
Exponential sums over primes in short intervals
Institute of Scientific and Technical Information of China (English)
LIU; Jianya
2006-01-01
[1]Vinogradov,I.M.,Estimation of certain trigonometric sums with prime variables,Izv.Acad.Nauk.SSSR,1939,3:371-398.[2]Zhan,T.,On the representation of large odd integer as a sum of three almost equal primes,Acta Math.Sin.,1991,7:259-272.[3]Ren,X.M.,On exponential sums over primes and application in the Waring-Goldbach problem,Sci.China,Ser.A-Math.,2005,48(6):785-797.[4]Liu,J.Y.,Wooley,T.D.,Yu,G.,The quadratic Waring-Goldbach problem,J.Number Theory,2004,107:298-321.[5]Hua,L.K.,Some results in the additive prime number theory,Quart.J.Math.(Oxford),1938,9:68-80.[6]Liu,J.Y.,Zhan,T.,On sums of five almost equal prime squares,Acta Arith.,1996,77:369-383.[7]Bauer,C.,A note on sums of five almost equal prime squares,Arch.Math,1997,69:20-30.[8]Liu,J.Y.,Zhan,T.,Sums of five almost equal prime squares,Science in China,Ser.A,1998,41:710-722.[9]Liu,J.Y.,Zhan,T.,Hua's theorem on prime squares in short intervals,Acta Math.Sin.,2000,16:1-22.[10]Bauer,C.,Sums of five almost equal prime squares,Acta Math.Sin.,2005,21(4):833-840.[11]Lü,G.S.,Hua's Theorem with five almost equal prime variables,Chin.Ann.Math.,Ser.B,2005,26(2):291-304.[12]Vinogradov,I.M.,Elements of Number Theory,Dover Publications,1954.[13]Titchmarsh,E.C.,The Theory of the Riemann Zeta-function,2nd ed.,Oxford:Oxford University Press,1986.
Skew quantum Murnaghan-Nakayama rule
Konvalinka, Matjaz
2011-01-01
In this paper, we extend recent results of Assaf and McNamara on skew Pieri rule and skew Murnaghan-Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf-McNamara's original proof, and one via Lam-Lauve-Sotille's skew Littlewood-Richardson rule. We end with some conjectures for skew rules for Hall-Littlewood polynomials.
On Learning Ring-Sum-Expansions
DEFF Research Database (Denmark)
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only. Moreover, it is proved that 2-term-RSE is learnable by a conjunction...... of a 2-CNF and a 1-DNF. Finally the paper presents learning (on-line prediction) algorithms for k-RSE that are optimal with respect to the sample size (worst case mistake bound)...
Dowker, J S
2015-01-01
The finite sums of powers of cosecs occur in numerous situations, both physical and mathematical, examples being the Casimir effect, Renyi entropy, Verlinde's formula and Dedekind sums. I here present some further discussion which consists mainly of a reprise of early work by H.M.Jeffery in 1862-64 which has fallen by the wayside and whose results are being reproduced up to the present day. The motivation is partly historical justice and partly that, because of the continuing appearance of the sums, his particular methods deserve re--exposure. For example, simple trigonometric generating functions are found and these have a field theoretic, Green function significance and I make a few comments in the topic of R\\'enyi entropies.
Separating OR, SUM, and XOR Circuits
Find, Magnus; Göös, Mika; Järvisalo, Matti; Kaski, Petteri; Koivisto, Mikko; Korhonen, Janne H.
2013-01-01
Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on \\emph{separating} these models in terms of their circuit complexities. We give three results towards this goal: (1) We prove a direct sum type theorem on the monotone complexity of ...
The Ronkin number of an exponential sum
Silipo, James
2011-01-01
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
Demonstration of a Quantum Nondemolition Sum Gate
DEFF Research Database (Denmark)
Yoshikawa, J.; Miwa, Y.; Huck, Alexander;
2008-01-01
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature...
Sum and product in dynamic epistemic logic
Van Ditmarsch, H. P.; Ruan, J.; Verbrugge, R.
2008-01-01
The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the
Sums of Integer Squares: A New Look.
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
Zero-Sum Problems with Subgroup Weights
Indian Academy of Sciences (India)
S D Adhikari; A A Ambily; B Sury
2010-06-01
In this note, we generalize some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider $\\mathbb{Z}^d_p$ for a general and subgroups of $Z^∗_p$ as weights.
RIORDAN MATRICES AND SUMS OF HARMONIC NUMBERS
Directory of Open Access Journals (Sweden)
Emanuele Munarini
2011-10-01
Full Text Available We obtain a general identity involving the row-sums of a Riordan matrixand the harmonic numbers. From this identity, we deduce several particular identities involving numbers of combinatorial interest, such as generalized Fibonacci and Lucas numbers, Catalan numbers, binomial and trinomial coefficients and Stirling numbers.
Fibonacci Identities via the Determinant Sum Property
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
Large- quantum chromodynamics and harmonic sums
Indian Academy of Sciences (India)
Eduardo De Rafael
2012-06-01
In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is discussed.
Improved approach to the heavy-to-light form factors in the light-cone QCD sum
Huang, Tao; Li, Zuo-Hong; Wu, Xiang-Yao
2000-01-01
A systematic analysis shows that the main uncertainties in the form factors are due to the twist-3 wave functions of the light mesons in the light-cone QCD sum rules. We propose an improved approach, in which the twist-3 wave functions doesn't make any contribution and therefore the possible pollution by them can be avoided, to re-examine $B \\to \\pi$ semileptonic form factors. Also, a comparison between the previous and our results from the light-cone QCD sum rules is made. Our method will be...
A New Generalization of Hardy-Berndt Sums
Indian Academy of Sciences (India)
Muhammet Cihat Dağli; Mümün Can
2013-05-01
In this paper, we construct a new generalization of Hardy–Berndt sums which are explicit extensions of Hardy–Berndt sums. We express these sums in terms of Dedekind sums $s_r(h,k:x,y|)$ with ==0 and obtain corresponding reciprocity formulas.
Transition Mean Values of Shifted Convolution Sums
Petrow, Ian
2011-01-01
Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let \\lambda(n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues \\lambda(n) after averaging over many shifts h and obtain asymptotic estimates. The result is somewhat surprising: one encounters a transition region depending on the ratio of the square of the length of the average over h to the length of the shifted convolution sum. The phenomenon is similar to that encountered by Conrey, Farmer and Soundararajan in their 2000 paper Transition Mean Values of Real Characters, and the connection of both results to Eisenstein series and multiple Dirichlet series is discussed.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
Gao's Conjecture on Zero-Sum Sequences
Indian Academy of Sciences (India)
B Sury; R Thangadurai
2002-08-01
In this paper, we shall address three closely-related conjectures due to van Emde Boas, W D Gao and Kemnitz on zero-sum problems on $\\mathbf{Z}_p \\oplus \\mathbf{Z}_p$. We prove a number of results including a proof of the conjecture of Gao for the prime = 7 (Theorem 3.1). The conjecture of Kemnitz is also proved (Propositions 4.6, 4.9, 4.10) for many classes of sequences.
A 2-categorical state sum model
Energy Technology Data Exchange (ETDEWEB)
Baratin, Aristide, E-mail: abaratin@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario N2L 3G1 (Canada); Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Str. N, Waterloo, Ontario N2L 2Y5 (Canada)
2015-01-15
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.
A 2-categorical state sum model
Baratin, Aristide; Freidel, Laurent
2015-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027-2060 (2007)] which was shown to lead after gauge-fixing to Korepanov's invariant of 4-manifolds.
A 2-categorical state sum model
Baratin, Aristide
2014-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6$j$-symbols. These weights solve an hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in [1], which was shown to lead after gauge-fixing to ...
Theorems of Forming and Summing of Natural Numbers and Their Application
Manaye Getu Tsige
2013-01-01
This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular...
26 CFR 1.1502-36 - Unified loss rule.
2010-04-01
... (including rules for transfers of S stock between members), definitions, and an anti-abuse rule, respectively... is the sum of S's net operating and capital loss carryovers, deferred deductions, money, and basis in assets other than money, reduced by the amount of S's liabilities. For this purpose, S's basis in...
The information content of rules and rule sets and its application
Institute of Scientific and Technical Information of China (English)
HU Dan; LI HongXing; YU XianChuan
2008-01-01
The information content of rules is categorized into inner mutual information content and outer impartation information content. Actually, the conventional objective interestingness measures based on information theory are all inner mutual informarion, which represent the confidence of rules and the mutual information between the antecedent and consequent. Moreover, almost all of these measures lose sight of the outer impartation information, which is conveyed to the user and help the user to make decisions. We put forward the viewpoint that the outer impartation information content of rules and rule sets can be represented by the relations from input universe to output universe. By binary relations, the interaction of rules in a rule set can be easily represented by operators: union and intersection. Based on the entropy of relations, the outer impartation information content of rules and rule sets are well measured. Then, the conditional information content of rules and rule sets, the independence of rules and rule sets and the inconsistent knowledge of rule sets are defined and measured. The properties of these new measures are discussed and some interesting results are proven, such as the information content of a rule set may be bigger than the sum of the information content of rules in the rule set, and the conditional information content of rules may be negative. At last, the applications of these new measures are discussed. The new method for the appraisement of .rule mining algorithm, and two rule pruning algorithms, λ-choice and RPCIC, are put forward. These new methods and algorithms havepredominance in satisfying the need of more efficient decision information.
Nucleon spin structure at low momentum transfers
Pasechnik, Roman; Teryaev, Oleg
2010-01-01
The generalized Gerasimov-Drell-Hearn (GDH) sum rule is known to be very sensitive to QCD radiative and power corrections. We improve the previously developed QCD-inspired model for the $Q^2$-dependence of the GDH sum rule. We take into account higher order radiative and higher twist power corrections extracted from precise Jefferson Lab data on the lowest moment of the spin-dependent proton structure function $\\Gamma_1^{p}(Q^2)$ and on the Bjorken sum rule $\\Gamma_1^{p-n}(Q^2)$. By using the singularity-free analytic perturbation theory we demonstrate that the matching point between chiral-like positive-$Q^2$ expansion and QCD operator product $1/Q^2$-expansion for the nucleon spin sum rules can be shifted down to rather low $Q\\simeq\\Lambda_{QCD}$ leading to a good description of recent proton, neutron, deuteron and Bjorken sum rule data at all accessible $Q^2$.
Nucleon spin structure at low momentum transfers
Pasechnik, Roman S.; Soffer, Jacques; Teryaev, Oleg V.
2010-10-01
The generalized Gerasimov-Drell-Hearn sum rule is known to be very sensitive to QCD radiative and power corrections. We improve the previously developed QCD-inspired model for the Q2 dependence of the Gerasimov-Drell-Hearn sum rule. We take into account higher order radiative and higher-twist power corrections extracted from precise Jefferson Lab data on the lowest moment of the spin-dependent proton structure function Γ1p(Q2) and on the Bjorken sum rule Γ1p-n(Q2). By using the singularity-free analytic perturbation theory we demonstrate that the matching point between chiral-like positive-Q2 expansion and QCD operator product 1/Q2 expansion for the nucleon spin sum rules can be shifted down to rather low Q≃ΛQCD leading to a good description of recent proton, neutron, deuteron, and Bjorken sum rule data at all accessible Q2.
Generalizations of some Zero Sum Theorems
Indian Academy of Sciences (India)
M N Chintamani; B K Moriya
2012-02-01
Given an abelian group of order , and a finite non-empty subset of integers, the Davenport constant of with weight , denoted by $D_A(G)$, is defined to be the least positive integer such that, for every sequence $(x_1,\\ldots,x_t)$ with $x_i\\in G$, there exists a non-empty subsequence $(x_{j_1},\\ldots,x_{j_l})$ and $a_i\\in A$ such that $\\sum^l_{i=1}a_ix_{j_i}=0$. Similarly, for an abelian group of order $n,E_A(G)$ is defined to be the least positive integer such that every sequence over of length contains a subsequence $(x_{j_1},\\ldots,x_{j_n})$ such that $\\sum^n_{i=1}a_ix_{j_i}=0$, for some $a_i\\in A$. When is of order , one considers to be a non-empty subset of $\\{1,\\ldots,n-1\\}$. If is the cyclic group $\\mathbb{Z}/n\\mathbb{Z}$, we denote $E_A(G)$ and $D_A(G)$ by $E_A(n)$ and $D_A(n)$ respectively. In this note, we extend some results of Adhikari et al(Integers 8(2008) Article A52) and determine bounds for $D_{R_n}(n)$ and $E_{R_n}(n)$, where $R_n=\\{x^2:x\\in(\\mathbb{Z}/n\\mathbb{Z})^∗\\}$. We follow some lines of argument from Adhikari et al(Integers 8 (2008) Article A52) and use a recent result of Yuan and Zeng (European J. Combinatorics 31 (2010) 677–680), a theorem due to Chowla (Proc. Indian Acad. Sci. (Math. Sci.) 2 (1935) 242–243) and Kneser’s theorem (Math. Z.58(1953) 459–484;66(1956) 88–110;61(1955) 429–434).
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Dedekind zeta-functions and Dedekind sums
Institute of Scientific and Technical Information of China (English)
陆洪文; 焦荣政; 纪春岗
2002-01-01
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel's. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =1/45(26n3-41n±9), n ≡±2(mod 5), where K=Q( q),prime q=4n2+1, and the class number of quadratic number field K2=Q(q) is 1.
Exponential sums over primes in short intervals
Institute of Scientific and Technical Information of China (English)
LIU Jianya; L(U) Guangshi; ZHAN Tao
2006-01-01
In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p21 +p22 +p23 +p24 +p25, with |pj - √N/5| ≤ U = N1/2-1/20+ε,where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.
Sums of two-dimensional spectral triples
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval....
Some Zero-Sum Constants with Weights
Indian Academy of Sciences (India)
S D Adhikari; R Balasubramanian; F Pappalardi; P Rath
2008-05-01
For an abelian group , the Davenport constant () is defined to be the smallest natural number such that any sequence of elements in has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to $(\\mathbb{Z}/n\\mathbb{Z})^d$, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of $(\\mathbb{Z}/n\\mathbb{Z})^2$ where is an odd integer.
Sum-SINR/sum-capacity optimal multisignature spread-spectrum steganography
Wei, Lili; Pados, Dimitris A.; Batalama, Stella N.; Medley, Michael J.
2008-04-01
For any given digital host image or audio file (or group of hosts) and any (block) transform domain of interest, we find an orthogonal set of signatures that achieves maximum sum-signal-to-interference-plus-noise ratio (sum- SINR) spread-spectrum message embedding for any fixed embedding amplitude values. We also find the sumcapacity optimal amplitude allocation scheme for any given total distortion budget under the assumption of (colored) Gaussian transform-domain host data. The practical implication of the results is sum-SINR, sumcapacity optimal multiuser/multisignature spread-spectrum data hiding in the same medium. Theoretically, the findings establish optimality of the recently presented Gkizeli-Pados-Medley multisignature eigen-design algorithm.
The Infinite Sum of Reciprocal of the Fibonacci Numbers
Institute of Scientific and Technical Information of China (English)
Guo Jie ZHANG
2011-01-01
In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.
7 CFR 42.132 - Determining cumulative sum values.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Determining cumulative sum values. 42.132 Section 42... Determining cumulative sum values. (a) The parameters for the on-line cumulative sum sampling plans for AQL's... 3 1 2.5 3 1 2 1 (b) At the beginning of the basic inspection period, the CuSum value is set equal...
VerSum: Verifiable Computations over Large Public Logs
van den Hooff, Jelle; Kaashoek, M. Frans; Zeldovich, Nickolai
2014-01-01
VerSum allows lightweight clients to outsource expensive computations over large and frequently changing data structures, such as the Bitcoin or Namecoin blockchains, or a Certificate Transparency log. VerSum clients ensure that the output is correct by comparing the outputs from multiple servers. VerSum assumes that at least one server is honest, and crucially, when servers disagree, VerSum uses an efficient conflict resolution protocol to determine which server(s) made a mistake and thus ob...
Interpreting the Four Types of Sums of Squares in SPSS.
Tanguma, Jesus; Speed, F. M.
This paper analyzes three possible research designs using each of the four types of sums of squares in the Statistical Package for the Social Sciences (SPSS). When the design is balanced (i.e., each cell has the same number of observations), all of the SPSS types of sums of squares yield equivalent results (testable hypotheses and sums of squares)…
Logical consistency and sum-constrained linear models
van Perlo -ten Kleij, Frederieke; Steerneman, A.G.M.; Koning, Ruud H.
2006-01-01
A topic that has received quite some attention in the seventies and eighties is logical consistency of sum-constrained linear models. Loosely defined, a sum-constrained model is logically consistent if the restrictions on the parameters and explanatory variables are such that the sum constraint is a
22 CFR 19.13-1 - Lump-sum credit.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the...
Tinbergen Rules the Taylor Rule
Thomas R. Michl
2008-01-01
This paper elaborates a simple model of growth with a Taylor-like monetary policy rule that includes inflation-targeting as a special case. When the inflation process originates in the product market, inflation-targeting locks in the unemployment rate prevailing at the time the policy matures. Although there is an apparent NAIRU and Phillips curve, this long-run position depends on initial conditions; in the presence of stochastic shocks, it would be path dependent. Even with an employment ta...
On Zero Sum Subsequences of Restricted Size
Indian Academy of Sciences (India)
B K Moriya
2010-09-01
Let be a finite abelian group with $\\exp(G)=e$. Let $s(G)$ be the minimal integer with the property that any sequence of elements in contains an -term subsequence with sum zero. Let , and be positive integers and ≥ 3. Furthermore, $(C^r_m)=a_r(m-1)+1$, for some constant $a_r$ depending on and is a fixed positive integer such that $$n≥\\frac{m^r(c(r)m-a_r(m-1)+m-3)(m-1)-(m+1)+(m+1)(a_r+1)}{m(m+1)(a_r+1)}$$ and $s(C^r_n)=(a_r+1)(n-1)+1$. In the above lower bound on $n,c(r)$ is the Alon-Dubiner constant. Then $s(C^r_{nm})=(a_r+1)(nm-1)+1$.
Fractional Sums and Differences with Binomial Coefficients
Directory of Open Access Journals (Sweden)
Thabet Abdeljawad
2013-01-01
Full Text Available In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
Sum of Bernoulli Mixtures: Beyond Conditional Independence
Directory of Open Access Journals (Sweden)
Taehan Bae
2014-01-01
Full Text Available We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.
On solving equations of algebraic sum of equal powers
Institute of Scientific and Technical Information of China (English)
WANG; Xinghua; YANG; Shijun
2006-01-01
It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.
Preservation of tensor sum and tensor product continuous functions
Directory of Open Access Journals (Sweden)
C. S. Kubrusly
2011-02-01
Full Text Available This note deals with preservation of tensor sum and tensor product of Hilbert space operators. Basic operations with tensor sum are presented. The main result addresses to the problem of transferring properties from a pair of operators to their tensor sum and to their tensor product. Sufficient conditions are given to ensure that properties preserved by ordinary sum and ordinary product are preserved by tensor sum and tensor product, which are equally relevant for both finite-dimensional and infinite-dimensional spaces.
Manifestation of nuclear cluster structure in Coulomb sums
Buki, A Yu
2016-01-01
Experimental Coulomb sum values of 6^Li and 7^Li nuclei have been obtained, extending the earlier reported momentum transfer range of Coulomb sums for these nuclei up to q = 0.750 ... 1.625 fm^-1. The dependence of the Coulomb sums on the momentum transfers of 6^Li and 7^Li is shown to differ substantially from similar dependences for all the other nuclei investigated. Relationship between the nuclear cluster structure and Coulomb sums has been considered. The momentum transfer value, above which the Coulomb sum becomes constant, is found to be related to the cluster isolation parameter x, which characterizes the degree of nuclear clusterization.
Institute of Scientific and Technical Information of China (English)
尉志武; 周蕊; 刘芸
2002-01-01
A solubility-related rule, nonzero solubility rule, is introduced in this paper. It is complementary to the existing rules such as the "like dissolves like" rule and can be understood on the basis of classical chemical thermodynamics.
Energy Technology Data Exchange (ETDEWEB)
Merkel, W; Woelk, S; Schleich, W P [Institut fuer Quantenphysik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89081 Ulm (Germany); Averbukh, I Sh [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Girard, B [Laboratoire de Collisions, Agregats, Reactivite, IRSAMC (Universite de Toulouse/UPS, CNRS), Toulouse (France); Paulus, G G, E-mail: sabine.woelk@uni-ulm.de [Institut fuer Optik und Quantenelektronik, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)
2011-10-15
We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series (Woelk et al 2011 New J. Phys. 13 103007): (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems, we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules on how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.
Multireflection sum frequency generation vibrational spectroscopy.
Zhang, Chi; Jasensky, Joshua; Chen, Zhan
2015-08-18
We developed a multireflection data collection method in order to improve the signal-to-noise ratio (SNR) and sensitivity of sum frequency generation (SFG) spectroscopy, which we refer to as multireflection SFG, or MRSFG for short. To achieve MRSFG, a collinear laser beam propagation geometry was adopted and trapezoidal Dove prisms were used as sample substrates. An in-depth discussion on the signal and SNR in MRSFG was performed. We showed experimentally, with "m" total internal reflections in a Dove prism, MRSFG signal is ∼m times that of conventional SFG; SNR of the SFG signal-to-background is improved by a factor of >m(1/2) and
Level-1 Jets and Sums Trigger Performance
CMS Collaboration
2016-01-01
After the first long shutdown, the LHC has restarted at a centre-of-mass energy of 13 TeV. The LHC is expected to achieve an instantaneous luminosity larger than $10^{34} \\rm{cm}^{-2} \\rm{s}^{-1}$ and an average number of pile-up interactions of at least 40. The CMS Level-1 trigger architecture has undergone a full upgrade in order to maintain and improve the trigger performance under these new conditions. It will allow CMS to keep the trigger rate under control and to avoid a significant increase in trigger thresholds that would have a negative impact on the CMS physics programme. First studies of the performance of the calorimeter trigger upgrade for jets and energy sums are shown. Details of the algorithms and commissioning may be found in CMS-DP-2015-051 and the CMS Technical Design Report for the Level-1 Trigger upgrade: CERN-LHCC-2013-011, CMS-TDR-12 (2013)
$N_c$-counting rules and the axial vector coupling constant of the constituent quark
Broniowski, W; Steiner, A
1993-01-01
Instead of using a simple reggeon-exchange model, we provide a model-independent estimate of high-energy contribution to the Adler-Weisberger sum-rule. Results and conclusions of the paper remain unchanged.
Central Binomial Sums, Multiple Clausen Values and Zeta Values
Borwein, J M; Kamnitzer, J
2000-01-01
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K.
Resonance sum rules from large $N_C$ and partial wave dispersive analysis
Guo, Zhi-Hui
2008-01-01
Combining large $N_C$ techniques and partial wave dispersion theory to analyze the $\\pi\\pi$ scattering, without relying on any explicit resonance lagrangian, some interesting results are derived: (a) a general KSRF relation including the scalar meson contribution; (b) a new relation between resonance couplings, with which we have made an intensive analysis in several specific models; (c) low energy constants in chiral perturbation theory related with $\\pi\\pi$ scattering in terms of the mass and decay width of resonances.
Three nucleon forces in nuclear matter in the QCD sum rules
Drukarev, E G; Sadovnikova, V A
2016-01-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N interactions. The contribution of the 3N forces to the nucleon self energies are expressed in terms of the nonlocal scalar condensate (d=3) and of the configuration of the two four-quark condensates (d=6) in which two diquark operators act on two different nucleons of the matter. The most important part of the contribution of the four-quark condensate is calculated in a model-independent way. We employed a relativistic quark model of nucleon for calculation of the rest part. The density dependence of the vector and scalar nucleon self energies and of the single-particle potential energy are obtained.
Energy Technology Data Exchange (ETDEWEB)
Lopez-Aguilar, F.; Costa-Quintana, J. (Dept. de Fisica, Grupo de Electromagnetismo, Univ. Autonoma de Barcelona, Bellaterra, E-08193 Barcelona (ES))
1992-07-10
In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method.
Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rule
Broadhurst, D J; Maxwell, C J
2001-01-01
The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the $\\bar{MS}$-scheme in the limit of a large $N_f$. We find that in the factorial growth of the coefficients due to renormalons takes over almost immediately in the euclidean region. The essential differences between the large-order growth of coefficients in the scalar case, and in the vector case are analysed.In the timelike region a stabilization of the perturbative series for the imaginary part, with $n$-loop behaviour $S_n/[\\log(s/\\Lambda^2)]^{n-1}$, where $S_n$ is essentially constant for $n\\le{6}$, is observed. Only for $n\\ge{7}$ does one discern the factorial growth and alternations of sign. Our all-orders results are used to scrutinize the performance of multiloop estimates, within the ``naive nonabelianization'' procedure, and the effective charges approach. The asymptotic behaviour of perturbative coefficients, in both large-$N_f$ and large-$N_c$ limits, is analysed. A contour-improved resummation ...
Twisted exponential sums of polynomials in one variable
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The twisted T-adic exponential sums associated to a polynomial in one variable are studied.An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential sums.This bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.
Factorization of numbers with Gauss sums: III. Algorithms with Entanglement
Wölk, S.; Schleich, W. P.
2012-01-01
We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of Gauss sums in the probability amplitudes of two entangled states.These schemes are rather efficient provided that there exists a fast algorithm that can detect a period of a function hidden in its zeros.
APPROXIMATION OF RANDOM SUMS OF RANDOM VARIABLES IN INSURANCE
Directory of Open Access Journals (Sweden)
Paweł Wlaź
2014-09-01
Full Text Available The paper deals with approximations of random sums. By random sum we mean a sum of random number of independent and identically distributed random variables. Distribution of this sum is called a compound distribution. The model is especially important in non-life insurance. There are many methods for approximating compound distributions, one of the most popular one is approximation with shifted gamma distribution. In this work we show an alternative way – using kernel density, Fast Fourier Transform and numerical optimization methods – for finding shifted gamma approximations and show results suggesting its superiority over classical method.
Nahm sums, stability and the colored Jones polynomial
Garoufalidis, Stavros
2011-01-01
Nahm sums are $q$-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements ot the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise natural in Quantum Knot Theory, namely we prove the stability of the coefficients of an alternating link and present a Nahm sum formula for the resulting power series, defined in terms of a reduced, downward diagram of an alternating link. The Nahm sum formula comes with a computer implementation, illustrated in numerous examples of proven or conjectural identities among $q$-series.
On unit root formulas for toric exponential sums
Adolphson, Alan
2010-01-01
Starting from a classical generating series for Bessel functions due to Schlomilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In particular, we express the (unique) p-adic unit root of an arbitrary exponential sum on the torus in terms of special values of the p-adic analytic continuation of a ratio of A-hypergeometric functions. In contrast with the earlier works, we use noncohomological methods and obtain results that are valid for arbitrary exponential sums without any hypothesis of nondegeneracy.
PROBABILITY INEQUALITIES FOR SUMS OF INDEPENDENT UNBOUNDED RANDOM VARIABLES
Institute of Scientific and Technical Information of China (English)
张涤新; 王志诚
2001-01-01
The tail probability inequalities for the sum of independent unbounded random variables on a probability space ( Ω , T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Ω, T, P ). The probability exponential inequalities for sums of independent unbounded random variables were given. As applications of the results, some interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.
Theorems of Forming and Summing of Natural Numbers and Their Application
Directory of Open Access Journals (Sweden)
Manaye Getu Tsige
2013-08-01
Full Text Available This paper presents the way to form other set of natural numbers from a given set of natural numbers and formulae to determine the sum of resulting numbers. The other set of natural numbers can be formed either by arranging a given natural numbers in specific order that is by using the principles of permutation rule or by using the principle of product rule provided that a given set of natural numbers should contain equal number of digits. The major areas of study to carry out this particular research work are probability rule, counting principles like permutation rule and product rule, and geometric series. Paper contains some essential theorems that help to arrive at main findings. The objective of this paper is to contribute additional knowledge to the Mathematical and Statistical science. The research results are two fundamental theorems and their applications in Mathematics, Statistics and other expected field of study. They are used to analyze complex numerical data computation and to create a password for a given numerical data with its importance to protect information flow management within a socio economic organization. The findings are foot step for the other related findings and applications that will be presented in the future. The future expected formulas or equations help to solve some difficult scientific and socio economic problems and also to derive approximation formula.
Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions
Directory of Open Access Journals (Sweden)
Yan Wang
2013-01-01
Full Text Available We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB equations for the solutions of the game. Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.
Lorenz comparisons of nine rules for the adjudication of conflicting claims.
Bosmans, Kristof; Lauwers, Luc
2007-01-01
Consider the following nine rules for adjudicating conflicting claims: the proportional, constrained equal awards, constrained equal losses, Talmud, Piniles’, constrained egalitarian, adjusted proportional, random arrival, and minimal overlap rules. For each pair of rules in this list, we examine whether or not the two rules are Lorenz comparable. We allow the comparison to depend upon whether the amount to divide is larger or smaller than the half-sum of claims. In addition, we provide Loren...
Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions
Indian Academy of Sciences (India)
BISWAJYOTI SAHA
2016-08-01
For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.
Sum formula for SL2 over imaginary quadratic number fields
Lokvenec-Guleska, H.
2004-01-01
The subject of this thesis is generalization of the classical sum formula of Bruggeman and Kuznetsov to the upper half-space H3. The derivation of the preliminary sum formula involves computation of the inner product of two specially chosen Poincar´e series in two different ways: the spectral descri
Almost Sure Central Limit Theorems for Heavily Trimmed Sums
Institute of Scientific and Technical Information of China (English)
Fang WANG; Shi Hong CHENG
2004-01-01
We obtain an almost sure central limit theorem (ASCLT) for heavily trimmed sums. We also prove a function-typed ASCLT under the same conditions that assure measurable functions to satisfy the ASCLT for the partial sums of i.i.d. random variables with EX1 = 0, EX12 = 1.
Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-01-15
In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from {+-}1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.
An Inequality for the Sum of Independent Bounded Random Variables
Dance, Christopher R.
2012-01-01
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
College Sports: The Mystery of the Zero-Sum Game
Getz, Malcolm; Siegfried, John J.
2012-01-01
In recent years, when a university may earn well over $10 million per year from fees for sports-broadcast rights, half of the teams still lose. Collegiate athletic competition is a zero sum game: The number of winners equals the number of losers. So why do universities spend growing sums of scarce resources on an activity when the odds of winning…
Finding Sums for an Infinite Class of Alternating Series
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
An electrophysiological signature of summed similarity in visual working memory
Van Vugt, Marieke K.; Sekuler, Robert; Wilson, Hugh R.; Kahana, Michael J.
2013-01-01
Summed-similarity models of short-term item recognition posit that participants base their judgments of an item's prior occurrence on that item's summed similarity to the ensemble of items on the remembered list. We examined the neural predictions of these models in 3 short-term recognition memory e
Harmonic sums, polylogarithms, special numbers, and their generalizations
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-04-15
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.
GRASP with Path Relinking for the SumCut Problem
Directory of Open Access Journals (Sweden)
Jesús Sánchez-Oro
2012-01-01
Full Text Available This paper proposes a GRASP algorithm combined with Path Relinking to solve the SumCut minimization problem. In the SumCut problem one is given a graph with n nodes and must label the nodes in a way that each node receives a unique label from the set{1,2,…,n}, in order to minimize the sum cut of the generated solution. The SumCut problem is really important in archeology (in seriation tasks and in genetics, helping in the Human Genome Project. This problem is equivalent to the Profile problem, because a solution for SumCut is reversal solution for Profile problem. Experimental results show that the GRASP and Path Relinking methods presented outperform in terms of average percentage deviation the results from the State of the Art using shorter CPU time.
Evaluation of the multi-sums for large scale problems
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, J.; Hasselhuhn, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2012-02-15
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter {epsilon} can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)
Lim, Kim-Hui,; Har, Wai-Mun
2008-01-01
The lack of academic and thinking culture is getting more worried and becomes a major challenge to our academia society this 21st century. Few directions that move academia from "cogito ergo sum" to "consumo ergo sum" are actually leading us to "the end of academia". Those directions are: (1) the death of dialectic;…
Harmonic sums and polylogarithms generated by cyclotomic polynomials
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2011-05-15
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)
Generalized sums over histories for quantum gravity (II). Simplicial conifolds
Schleich, Kristin; Witt, Donald M.
1993-08-01
This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one must have an algorithmically implementable method of generating a list of all spaces in the set to be summed over. This requirement causes well known problems in the formulation of sums over manifolds in four or more dimensions; there is no algorithmic method of determining whether or not a topological space is an n-manifold in five or more dimensions and the issue of whether or not such an algorithm exists is open in four. However, as this paper shows, conifolds are algorithmically decidable in four dimensions. Thus the set of 4-conifolds provides a starting point for a concrete implementation of euclidean sums over histories in four dimensions. Explicit algorithms for summing over various sets of 4-conifolds are presented in the context of Regge calculus.
Minkowski sum of HV-polytopes in Rn
Delos, Vincent
2014-01-01
Minkowski sums cover a wide range of applications in many different fields like algebra, morphing, robotics, mechanical CAD/CAM systems ... This paper deals with sums of polytopes in a n dimensional space provided that both H-representation and V-representation are available i.e. the polytopes are described by both their half-spaces and vertices. The first method uses the polytope normal fans and relies on the ability to intersect dual polyhedral cones. Then we introduce another way of considering Minkowski sums of polytopes based on the primal polyhedral cones attached to each vertex.
Evolution of sum-chirp in polarization multiplexed communication system
Institute of Scientific and Technical Information of China (English)
Wang Jing; Wang Zhen-Li
2004-01-01
The evolution of sum-chirp for an initially chirped Gaussian pulse is studied in the polarization multiplexed communication system, with fibre attenuation considered. The sum-chirp is found to have the character of saturation.Its value appears different along the two different polarization axes, determined by the incidence polarization angle. We also find that sum-chirp is dominated by the initial chirp at a short distance, and by the cross-phase modulation effect at long distance. And it is influenced apparently by a wavevector mismatch parameter below 10 ps/km. Further, its saturation results from the effective distance determined by fibre attenuation.
A toolbox for Harmonic Sums and their analytic continuations
International Nuclear Information System (INIS)
The package HarmonicSums implemented in the computer algebra system Mathematica is presented. It supports higher loop calculations in QCD and QED to represent single-scale quantities like anomalous dimensions and Wilson coefficients. The package allows to reduce general harmonic sums due to their algebraic and different structural relations. We provide a general framework for these reductions and the explicit representations up to weight w=8. For the use in experimental analyzes we also provide an analytic formalism to continue the harmonic sums form their integer arguments into the complex plane, which includes their recursions and asymptotic representations. The main ideas are illustrated by specific examples.
Lump-sum over Distortionary Taxation Dominance with Heterogeneous Individuals
Ramon J. Torregrosa-Montaner
2015-01-01
The dominance of lump-sum over distortionary taxation for the single consumer case is a well-known proposition in microeconomics. This result implies that if the consumer is asked about what tax she would pay to bear a given tax burden, she would choose lump-sum taxation. This paper provides a version of this dominance of lump-sum taxation for the case of several heterogeneous individuals by means of a game where the government allows each individual to choose between the two tax regimes.
Pentagon Relations in Direct Sums and Grassmann Algebras
Korepanov, Igor G.; Sadykov, Nurlan M.
2013-01-01
We construct vast families of orthogonal operators obeying pentagon relation in a direct sum of three n-dimensional vector spaces. As a consequence, we obtain pentagon relations in Grassmann algebras, making a far reaching generalization of exotic Reidemeister torsions.
On the sum of the first n prime numbers
Axler, Christian
2014-01-01
In this paper we establish a general asymptotic formula for the sum of the first n prime numbers, which leads to a generalization of the most accurate asymptotic formula given by Massias and Robin in 1996.
Summing up dynamics: modelling biological processes in variable temperature scenarios
Tijskens, L.M.M.; Verdenius, F.
2000-01-01
The interest of modelling biological processes with dynamically changing external conditions (temperature, relative humidity, gas conditions) increases. Several modelling approaches are currently available. Among them are approaches like modelling under standard conditions, temperature sum models an
Static Quark Potential from the Polyakov Sum over Surfaces
Jaskolski, Zbigniew; Meissner, Krzysztof A.
1993-01-01
Using the Polyakov string ansatz for the rectangular Wilson loop we calculate the static potential in the semiclassical approximation. Our results lead to a well defined sum over surfaces in the range $1
Limiting Behavior of Weighted Sums of NOD Random Variables
Institute of Scientific and Technical Information of China (English)
De Hua QIU; Ping Yan CHEN
2011-01-01
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5]in independent sequence case.
The Sum and Difference of Two Lognormal Random Variables
Directory of Open Access Journals (Sweden)
C. F. Lo
2012-01-01
Full Text Available We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1 the algebraic sum of N lognormals, and (2 the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.
International Nuclear Information System (INIS)
A combination is presented of the inclusive neutral current e±p scattering cross section data collected by the H1 and ZEUS collaborations during the last months of the HERA II operation period with proton beam energies Ep of 460 and 575 GeV. The kinematic range of the cross section data covers low absolute four-momentum transfers squared, 1.5 GeV2 ≤ Q2 ≤ 110 GeV2, small values of Bjorken-x, 2.8.10-5 ≤ x ≤ 1.5.10-2, and high inelasticity y ≤ 0.85. The combination algorithm is based on the method of least squares and takes into account correlations of the systematic uncertainties. The combined data are used in the QCD fits to extract the parton distribution functions. The phenomenological low-x dipole models are tested and parameters of the models are obtained. A good description of the data by the dipole model taking into account the evolution of the gluon distribution is observed. The longitudinal structure function FL is extracted from the combination of the currently used H1 and ZEUS reduced proton beam energy data with previously published H1 nominal proton beam energy data of 920 GeV. A precision of the obtained values of FL is improved at medium Q2 compared to the published results of the H1 collaboration.
Energy Technology Data Exchange (ETDEWEB)
Belov, Pavel
2013-06-15
A combination is presented of the inclusive neutral current e{sup {+-}}p scattering cross section data collected by the H1 and ZEUS collaborations during the last months of the HERA II operation period with proton beam energies E{sub p} of 460 and 575 GeV. The kinematic range of the cross section data covers low absolute four-momentum transfers squared, 1.5 GeV{sup 2} {<=} Q{sup 2} {<=} 110 GeV{sup 2}, small values of Bjorken-x, 2.8.10{sup -5} {<=} x {<=} 1.5.10{sup -2}, and high inelasticity y {<=} 0.85. The combination algorithm is based on the method of least squares and takes into account correlations of the systematic uncertainties. The combined data are used in the QCD fits to extract the parton distribution functions. The phenomenological low-x dipole models are tested and parameters of the models are obtained. A good description of the data by the dipole model taking into account the evolution of the gluon distribution is observed. The longitudinal structure function F{sub L} is extracted from the combination of the currently used H1 and ZEUS reduced proton beam energy data with previously published H1 nominal proton beam energy data of 920 GeV. A precision of the obtained values of F{sub L} is improved at medium Q{sup 2} compared to the published results of the H1 collaboration.
On Sums of Conditionally Independent Subexponential Random Variables
Foss, Serguei; Richards, Andrew
2008-01-01
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random variables, for both deterministic and random sums, using a fresh approach, by considering conditional independence structures on the random variables. We seek sufficient conditions for the results of the theory with independent random variables still to hold. For...
Factorization of numbers with truncated Gauss sums at rational arguments
Wölk, S.; Feiler, C.; Schleich, W. P.
2012-01-01
Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a one-to-one relationship. As a result the identification of factors by the maxima is unique. However, for non-integer arguments such as rational numbers this powerful instrument to find factors breaks down. We develop new strategies for factoring numbers using Gaus...
Complete Convergence for Weighted Sums of WOD Random Variables
Institute of Scientific and Technical Information of China (English)
ZHANG Ying; ZHANG Yu; SHEN Ai-ting
2016-01-01
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.
Sums of entire functions having only real zeros
Adams, Steven R.; Cardon, David A.
2006-01-01
We show that certain sums of products of Hermite-Biehler entire functions have only real zeros, extending results of Cardon. As applications of this theorem we construct sums of exponential functions having only real zeros, we construct polynomials having zeros only on the unit circle, and we obtain the three-term recurrence relation for an arbitrary family of real orthogonal polynomials. We discuss a similarity of this result with the Lee-Yang circle theorem from statistical mechanics. Also,...
The odd-number sequence: squares and sums
Leyendekkers, J. V.; Shannon, A. G.
2015-11-01
Direct study of various characteristics of integers and their interactions is readily accessible to undergraduate students. Integers obviously fall in different classes of modular rings and thus have features unique to that class which can result in a variety of formations, particularly with sums of squares. The sum of the first n odd numbers is itself the square of n within the odd number sequence, from which testing for primality within the Fibonacci sequence is investigated in this note.
Mould, Richard A
2004-01-01
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required to engage and interpret the Schrodinger solutions in individual measurements. The rules in this paper (called the nRules) do not include the Born rule that connects probability with square modulus. It is required that the rules allow all conscious observer...
International Nuclear Information System (INIS)
Scintillation signals and ionization signals produced in liquid rare gases by ionizing radiation can be simultaneously observed with high efficiencies. The fluctuation of the sum of scintillation and ionization signals is smaller than that of either of the individual signals. The present paper discusses the theoretical limit of energy resolution of the sum signals, compares it with the experimental results obtained in liquid rare gases, and presents comments recent papers treating related topics
Phonological reduplication in sign language: rules rule
Directory of Open Access Journals (Sweden)
Iris eBerent
2014-06-01
Full Text Available Productivity—the hallmark of linguistic competence—is typically attributed to algebraic rules that support broad generalizations. Past research on spoken language has documented such generalizations in both adults and infants. But whether algebraic rules form part of the linguistic competence of signers remains unknown. To address this question, here we gauge the generalization afforded by American Sign Language (ASL. As a case study, we examine reduplication (X→XX—a rule that, inter alia, generates ASL nouns from verbs. If signers encode this rule, then they should freely extend it to novel syllables, including ones with features that are unattested in ASL. And since reduplicated disyllables are preferred in ASL, such rule should favor novel reduplicated signs. Novel reduplicated signs should thus be preferred to nonreduplicative controls (in rating, and consequently, such stimuli should also be harder to classify as nonsigns (in the lexical decision task. The results of four experiments support this prediction. These findings suggest that the phonological knowledge of signers includes powerful algebraic rules. The convergence between these conclusions and previous evidence for phonological rules in spoken language suggests that the architecture of the phonological mind is partly amodal.
Institute of Scientific and Technical Information of China (English)
Filiz KANBAY
2005-01-01
We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.
Skew Schur Functions of Sums of Fat Staircases
Morin, Matthew
2010-01-01
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\\alpha_n}, {n-1}^{\\alpha_{n-1}},..., 1^{\\alpha_1})$, where $\\alpha = (\\alpha_1,...,\\alpha_n)$ is a composition, or the $180^\\circ$ rotation of such a diagram. If a diagram's skew Schur function is a linear combination of Schur functions of fat staircases, we call the diagram a sum of fat staircases. We prove a Schur-positivity result that is obtained each time we augment a sum of fat staircases with a skew diagram. We also determine conditions on which diagrams can be sums of fat staircases, including necessary and sufficient conditions in the special case when the diagram is a fat staircase skew a single row or column.
Random sum-free subsets of abelian groups
Balogh, József; Samotij, Wojciech
2011-01-01
We characterize the structure of maximum-size sum-free subsets of a random subset of an abelian group $G$. In particular, we determine the threshold $p_c \\approx \\sqrt{\\log n / n}$ above which, with high probability as $|G| \\to \\infty$, each such subset is contained in a maximum-size sum-free subset of $G$, whenever $q$ divides $|G|$ for some (fixed) prime $q$ with $q \\equiv 2 \\pmod 3$. Moreover, in the special case $G = \\ZZ_{2n}$, we determine a sharp threshold for the above property. The proof uses recent 'transference' theorems of Conlon and Gowers, together with stability theorems for sum-free sets of abelian groups.
Sums of hermitian squares and the BMV conjecture
Klep, Igor
2007-01-01
Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.
On sums involving products of three binomial coefficients
Sun, Zhi-Wei
2010-01-01
In this paper we mainly employ the Zeilberger algorithm to study congruences for sums of terms involving products of three binomial coefficients. Let $p>3$ be a prime. We prove that $$\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k^2\\binom{2k}{k+d}}{64^k}\\equiv 0\\pmod{p^2}$$ for all $d\\in\\{0,\\ldots,p-1\\}$ with $d\\equiv (p+1)/2\\pmod2$. If $p\\equiv 1\\pmod4$ and $p=x^2+y^2$ with $x\\equiv 1\\pmod4$ and $y\\equiv 0\\pmod2$, then we show $$\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k^2\\binom{2k}{k+1}}{(-8)^k}\\equiv 2p-2x^2\\pm...
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
Stiell, I.
1996-01-01
The Ottawa ankle rule project demonstrated that more than 95% of patients with ankle injuries had radiographic examinations but that 85% of the films showed no fractures. A group of Ottawa emergency physicians developed two rules to identify clinically important fractures of the malleoli and the midfoot. Use of these rules reduced radiographic examinations by 28% for the ankle and 14% for the foot.
Computation of bankruptcy rules
Saavedra, Verónica; Lopez, Marcelo; Necco, Claudia Mónica; Quintas, Luis Guillermo
2003-01-01
We implemented a system that computes bankruptcy rules. The implemented rules are: The Talmud, the Proportional, the Truncated Proportional, the Adjusted Proportional, the Constrained Equal Awards and the Random Arrival rule. The system computes, compares and graphics the different allocations to claimants. We present some applications and examples exported by the system.
Sums of class numbers and mixed mock modular forms
Bringmann, Kathrin; Kane, Ben
2013-01-01
In this paper, we consider sums of class numbers of the type $\\sum_{m\\equiv a\\pmod{p}} H(4n-m^2)$, where $p$ is an odd prime, $n\\in \\mathbb{N},$ and $a\\in \\mathbb{Z}$. By showing that these are coefficients of mixed mock modular forms, we obtain explicit formulas. Using these formulas for $p=5$ and $7$, we then prove a conjecture of Brown et al. in the case that $n=\\ell$ is prime.
IDENTITIES INVOLVING RATIONAL SUMS BY INVERSION AND PARTIAL FRACTION DECOMPOSITION
Directory of Open Access Journals (Sweden)
Helmut Prodinger
2008-03-01
Full Text Available Identities appearing recentlyin: {sc J. L. D'{i}az-Barrero, J. Gibergans-B'agu-ena, P. G. Popescu:}{it Some identities involving rational sums}. Appl. Anal. Discrete Math., {f 1} (2007, 397--402, aretreated by inverting them; the resulting sums areevaluated using partial fraction decomposition, following{sc Wenchang Chu:} {it A binomial coefficient identity associated with {B}eukers' conjectureon {A}p'ery numbers.} Electron. J. Combin., {f 11} (1: Note 15, 3 pp. (electronic, 2004.This approach produces a general formula, not only special cases.
A zero-sum monetary system, interest rates, and implications
Hanley, Brian P
2015-01-01
To the knowledge of the author, this is the first time it has been shown that interest rates that are extremely high by modern standards are necessary within a zero-sum monetary system. Extreme interest rates persisted for long periods of time in many places. Prior to the invention of banking, most money was hard-money in the form of some type of coin. Here a model is presented that examines the interest rate required to succeed as an investor in a zero-sum hard-money system. Even when the pl...
Cogito, ergo sum : induction et déduction
Jeangène Vilmer, Jean-Baptiste
2004-01-01
International audience; The cartesian “cogito, ergo sum” appears for forty years as “an Inference and a Performance” (J. Hintikka). But what kind of inference are we talking about? This paper works towards two ends : first, to point out that the real question about the inference in the cartesian cogito does not concern the internal logical relation between cogito and sum, which is an intuition, but the external one between « cogito, ergo sum » and « quicquid cogitat, est ». Then, to show that...
Experimental determination of the effective strong coupling constant
Energy Technology Data Exchange (ETDEWEB)
Alexandre Deur; Volker Burkert; Jian-Ping Chen; Wolfgang Korsch
2005-09-15
We extract an effective strong coupling constant from low Q2 data on the Bjorken sum. Using sum rules, we establish its Q2-behavior over the complete Q2-range. The result is compared to effective coupling constants extracted from different processes and to calculations based on Schwinger-Dyson equations, hadron spectroscopy or lattice QCD. Although the connection between the experimentally extracted effective coupling constant and the calculations is not clear, the results agree surprisingly well.
Early object rule acquisition.
Pierce, D E
1991-05-01
The purpose of this study was to generate a grounded theory of early object rule acquisition. The grounded theory approach and computer coding were used to analyze videotaped samples of an infant's and a toddler's independent object play, which produced the categories descriptive of three primary types of object rules; rules of object properties, rules of object action, and rules of object affect. This occupational science theory offers potential for understanding the role of objects in human occupations, for development of instruments, and for applications in occupational therapy early intervention. PMID:2048625
Safety Commission
2008-01-01
The revision of CERN Safety rules is in progress and the following new Safety rules have been issued on 15-04-2008: Safety Procedure SP-R1 Establishing, Updating and Publishing CERN Safety rules: http://cern.ch/safety-rules/SP-R1.htm; Safety Regulation SR-S Smoking at CERN: http://cern.ch/safety-rules/SR-S.htm; Safety Regulation SR-M Mechanical Equipment: http://cern.ch/safety-rules/SR-M.htm; General Safety Instruction GSI-M1 Standard Lifting Equipment: http://cern.ch/safety-rules/GSI-M1.htm; General Safety Instruction GSI-M2 Standard Pressure Equipment: http://cern.ch/safety-rules/GSI-M2.htm; General Safety Instruction GSI-M3 Special Mechanical Equipment: http://cern.ch/safety-rules/GSI-M3.htm. These documents apply to all persons under the Director General’s authority. All Safety rules are available at the web page: http://www.cern.ch/safety-rules The Safety Commission
Dardzinska, Agnieszka
2013-01-01
We are surrounded by data, numerical, categorical and otherwise, which must to be analyzed and processed to convert it into information that instructs, answers or aids understanding and decision making. Data analysts in many disciplines such as business, education or medicine, are frequently asked to analyze new data sets which are often composed of numerous tables possessing different properties. They try to find completely new correlations between attributes and show new possibilities for users. Action rules mining discusses some of data mining and knowledge discovery principles and then describe representative concepts, methods and algorithms connected with action. The author introduces the formal definition of action rule, notion of a simple association action rule and a representative action rule, the cost of association action rule, and gives a strategy how to construct simple association action rules of a lowest cost. A new approach for generating action rules from datasets with numerical attributes...
Determination of rotational temperature of AlO from the $B^{2}\\sum^{+} -X^{2}\\sum^{+}$ system
Indian Academy of Sciences (India)
M M Chaudhari; C T Londhe; S H Behere
2006-03-01
AlO molecule was excited in a DC arc in air running between two aluminium electrodes. Rotational structure of the (0,0) band of the $B^{2}\\sum^{+} -x^{2}\\sum^{+}$ system of AlO molecule was photographed in the first order of a 10.6 m concave grating spectrograph. Intensity distribution amongst the well-resolved rotational lines of R1 and R2 branches was recorded and the average rotational temperature calculated from these has been determined as 2880 ± 100 K.
A new leptogenesis scenario with predictions on \\sum m_{\
Gu, Pei-Hong
2014-01-01
In an SU(3)_c \\times SU(2)_L \\times SU(2)_R \\times U(1)_L \\times U(1)_R left-right symmetric framework with spontaneous breaking U(1)_L \\times U(1)_R \\rightarrow U(1)_{B-L}, we present a new leptogenesis scenario to predict low limits on neutrinos' mass scale \\sum m_{\
Efficient simulation of tail probabilities of sums of correlated lognormals
DEFF Research Database (Denmark)
Asmussen, Søren; Blanchet, José; Juneja, Sandeep;
We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be eff...
Pointwise Approximation for the Iterated Boolean Sums of Bernstein Operators
Institute of Scientific and Technical Information of China (English)
HUO Xiao-yan; LI Cui-xiang; YAO Qiu-mei
2013-01-01
In this paper,with the help of modulus of smoothness ω2r(4)(f,t),we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator Bnn and obtain direct and inverse theorems when 1-1/r ≤ λ ≤ 1,r ∈ N.
27 CFR 25.93 - Penal sum of bond.
2010-04-01
... quantity of beer used in the production of concentrate during a calendar year. The brewer shall add this... OF THE TREASURY LIQUORS BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... during the period of the bond on beer: (i) Removed for transfer to the brewery from other breweries...
Standardization of I-125. Sum-Peak Coincidence Counting
Energy Technology Data Exchange (ETDEWEB)
Grau Carles, A.; Grau Malonda, A.
2011-07-01
I-125 is a nuclide which presents difficulties for standardization. The sum-peak method is one of the procedures used to standardize this radionuclide. Initially NaI (Tl)detectors and then the semiconductor detectors with higher resolution have been used.This paper describes the different methods based on the sum-peak procedure and the different expressions used to calculate the activity are deduced. We describe a general procedure for obtaining all of the above equations and many more. We analyze the influence of uncertainties in the used parameters in the uncertainty of the activity. We give a complete example of the transmission of uncertainty and the effects of correlations in the uncertainty of the activity of the sample. High-resolution spectra show an unresolved doublet of 62.0 keV and 62.8 keV. The paper presents two approaches to solve this problem. One is based on the calculation of area ratio and the sum of peak areas obtained from atomic and nuclear data, in the other we modify the equations so that the sum of the peak areas doublet, rather than its components, is present. (Author) 19 refs.
Time- vs. frequency-domain femtosecond surface sum frequency generation
Roke, S.; Kleyn, A. W.; Bonn, M.
2003-01-01
We present an experimental and theoretical investigation into time- vs. frequency-domain ferntosecond sum frequency spectroscopy at the metal-liquid interface. Although frequency and time-domain measurements are theoretically equivalent it is demonstrated here experimentally that the two approaches
A Solution to Weighted Sums of Squares as a Square
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Sum uncertainty relations based on Wigner-Yanase skew information
Chen, Bin; Fei, Shao-Ming; Long, Gui-Lu
2016-06-01
We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.
Using the Finite Difference Calculus to Sum Powers of Integers.
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
Stability of character sums for positive-depth, supercuspidal representations
DeBacker, Stephen; Spice, Loren
2013-01-01
We re-write the character formul{\\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's conjectural positive-depth, unramified, toral supercuspidal L-packets.
Lump Sum Moving Cost and Aggregate Office Space Use
G. Romijn
1997-01-01
textabstractWhen firms decide to change office space use, in many instances this involves relocation. Relocation involves sizable costs to the firm that can to a large extent be characterized as lump sum, i.e. independent of the change in demand. In this paper we propose and solve a model of the dem
On some Vongruence with Application to Exponential Sums
Indian Academy of Sciences (India)
Soon-Mo Jung
2004-02-01
We will study the solution of a congruence, $x≡ g^{(1/2)_g(2^n)}\\mathrm{mod} 2^n$, depending on the integers and , where $_g(2^n)$ denotes the order of modulo $2^n$. Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.
The Sensitive Infrared Signal Detection by Sum Frequency Generation
Wong, Teh-Hwa; Yu, Jirong; Bai, Yingxin
2013-01-01
An up-conversion device that converts 2.05-micron light to 700 nm signal by sum frequency generation using a periodically poled lithium niobate crystal is demonstrated. The achieved 92% up-conversion efficiency paves the path to detect extremely weak 2.05-micron signal with well established silicon avalanche photodiode detector for sensitive lidar applications.
Measuring interesting rules in Characteristic rule
Warnars, Spits
2010-01-01
Finding interesting rule in the sixth strategy step about threshold control on generalized relations in attribute oriented induction, there is possibility to select candidate attribute for further generalization and merging of identical tuples until the number of tuples is no greater than the threshold value, as implemented in basic attribute oriented induction algorithm. At this strategy step there is possibility the number of tuples in final generalization result still greater than threshold value. In order to get the final generalization result which only small number of tuples and can be easy to transfer into simple logical formula, the seventh strategy step about rule transformation is evolved where there will be simplification by unioning or grouping the identical attribute. Our approach to measure interesting rule is opposite with heuristic measurement approach by Fudger and Hamilton where the more complex concept hierarchies, more interesting results are likely to be found, but our approach the simple...
Mould, R A
2004-01-01
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required to engage and interpret the Schrodinger solutions in individual measurements. The rules in this paper (called the nRules) do not include the Born rule that connects probability with square modulus. It is required that the rules allow all conscious observers to exist inside the system without empirical ambiguity, reflecting our own unambiguous experience in the universe. This requirement is satisfied by the nRules. They allow both objective and observer measurements, so state reduction can occur with or without an observer being present. Keywords: brain states, consciousness, decoherence, epistemology, measurement, ontology, stochastic, state reduction, wave collapse.
International Nuclear Information System (INIS)
An important source of knowledge for technical experts is the state of the art reflected by catalogues of technical rules. Technical rules may also achieve importance in law due to a legal transformation standard. Here, rigid and flexible reference are controversial with regard to their admissibility from the point of view of constitutional law. In case of a divergence from the generally accepted technical rules, it is assumed - refutably - that the necessary care had not been taken. Technical rules are one out of several sources of information; they have no normative effect. This may result in a duty of anyone applying them to review the state of technology himself. (orig.)
Linguistic Valued Association Rules
Institute of Scientific and Technical Information of China (English)
LU Jian-jiang; QIAN Zuo-ping
2002-01-01
Association rules discovering and prediction with data mining method are two topics in the field of information processing. In this paper, the records in database are divided into many linguistic values expressed with normal fuzzy numbers by fuzzy c-means algorithm, and a series of linguistic valued association rules are generated. Then the records in database are mapped onto the linguistic values according to largest subject principle, and the support and confidence definitions of linguistic valued association rules are also provided. The discovering and prediction methods of the linguistic valued association rules are discussed through a weather example last.
Gauss Sum of Index 4: (2) Non-cyclic Case
Institute of Scientific and Technical Information of China (English)
Jing YANG; Shi Xin LUO; Ke Qin FENG
2006-01-01
Assume that m≥2,p is a prime number,(m,p(p-1))=1,-1(∈)(∈)((Z)/m(Z))* and [((z)/m(Z)*:]=4.In this paper,we calculate the value of Gauss sum G(χ)=∑x(F)*qχ(x)ζTp(x) over (F)q,where q=pf,(f)=(ψ)(m)/4,χ is a multiplicative character of (F)q and T is the trace map from (F)q to (F)p.Under our assumptions,C(χ) belongs to the decomposition field K of p in (Q)(ζm) and K is an imaginary quartic abelian number field.When the Galois group Gal(K/(Q)) is cyclic,we have studied this cyclic case in another paper:"Gauss sums of index four:(1) cyclic case" (accepted by Acta Mathematica Sinica,2003).In this paper we deal with the non-cyclic case.
Approximating amoebas and coamoebas by sums of squares
Theobald, Thorsten
2011-01-01
Amoebas and coamoebas are the logarithmic images of algebraic varieties and the images of algebraic varieties under the arg-map, respectively. We present new techniques for computational problems on amoebas and coamoebas, thus establishing new connections between (co-)amoebas, semialgebraic and convex algebraic geometry and semidefinite programming. Our approach is based on formulating the membership problem in amoebas (respectively coamoebas) as a suitable real algebraic feasibility problem. Using the real Nullstellensatz, this allows to tackle the problem by sums of squares techniques and semidefinite programming. Our method yields polynomial identities as certificates of non-containedness of a point in an amoeba or comaoeba. As main theoretical result, we establish some degree bounds on the polynomial certificates. Moreover, we provide some actual computations of amoebas based on the sums of squares approach.
Limit law of the iterated logarithm for -valued trimmed sums
Indian Academy of Sciences (India)
Ke-Ang Fu; Yuyang Qiu; Yeling Tong
2015-05-01
Given a sequence of i.i.d. random variables $\\{X,X_{n};n≥ 1\\}$ taking values in a separable Banach space $(B,\\|\\cdot \\|)$ with topological dual *, let $X^{(r)}_{n}=X_{m}$ if $\\| X_{m}\\|$ is the -th maximum of $\\{\\| X_{k}\\|; 1≤ k≤ n\\}$ and $^{(r)}S_{n}=S_{n}-(X^{(1)}_{n}+\\cdots+X^{(r)}_{n})$ be the trimmed sums when extreme terms are excluded, where $S_{n}=\\sum^{n}_{k=1}X_{k}$. In this paper, it is stated that under some suitable conditions, $$ \\lim\\limits_{n→ ∞}\\frac{1}{\\sqrt{2\\log \\log n}}\\max\\limits_{1≤ k≤ n}\\frac{\\| {}^{(r)}S_{k}\\|}{\\sqrt{k}}=(X)\\quad\\text{a.s.,} $$ where $^{2}(X)=\\sup_{f\\in B^{*}_{1}}\\text{\\sf E}f^{2}(X)$ and $B^{*}_{1}$ is the unit ball of *.
The partially alternating ternary sum in an associative dialgebra
Energy Technology Data Exchange (ETDEWEB)
Bremner, Murray R [Department of Mathematics and Statistics, University of Saskatchewan (Canada); Sanchez-Ortega, Juana, E-mail: bremner@math.usask.c, E-mail: jsanchez@agt.cie.uma.e [Department of Algebra, Geometry and Topology, University of Malaga (Spain)
2010-11-12
The alternating ternary sum in an associative algebra, abc - acb - bac + bca + cab - cba, gives rise to the partially alternating ternary sum in an associative dialgebra with products dashv and vdash by making the argument a the center of each term. We use computer algebra to determine the polynomial identities in degree {<=}9 satisfied by this new trilinear operation. In degrees 3 and 5, these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.
Strategy complexity of two-player, zero-sum games
DEFF Research Database (Denmark)
Ibsen-Jensen, Rasmus
This dissertation considers two-player, zero-sum games with a focus on how complicated they are to play; a notion I will call strategy complexity. Often, knowing good bounds on the strategy complexity indicates bounds on the run time of various algorithms. In such cases I will also derive bounds...... on the algorithms. I consider a wide assortment of different two-player, zero-sum game classes, e.g. matrix games, uni-chain concurrent mean-payoff games, concurrent mean-payoff games, concurrent reachability games and one-clock priced timed games. In all game classes considered, except for one-clock priced timed......, which show that they require double exponential much patience. I use this to show that two classic algorithms for concurrent reachability games run slowly. I will also present an exponential (both upper and lower) bound on patience for uni-chain concurrent mean-payoff games and for matrix games...
Eisenhardt, K M; Sull, D N
2001-01-01
The success of Yahoo!, eBay, Enron, and other companies that have become adept at morphing to meet the demands of changing markets can't be explained using traditional thinking about competitive strategy. These companies have succeeded by pursuing constantly evolving strategies in market spaces that were considered unattractive according to traditional measures. In this article--the third in an HBR series by Kathleen Eisenhardt and Donald Sull on strategy in the new economy--the authors ask, what are the sources of competitive advantage in high-velocity markets? The secret, they say, is strategy as simple rules. The companies know that the greatest opportunities for competitive advantage lie in market confusion, but they recognize the need for a few crucial strategic processes and a few simple rules. In traditional strategy, advantage comes from exploiting resources or stable market positions. In strategy as simple rules, advantage comes from successfully seizing fleeting opportunities. Key strategic processes, such as product innovation, partnering, or spinout creation, place the company where the flow of opportunities is greatest. Simple rules then provide the guidelines within which managers can pursue such opportunities. Simple rules, which grow out of experience, fall into five broad categories: how- to rules, boundary conditions, priority rules, timing rules, and exit rules. Companies with simple-rules strategies must follow the rules religiously and avoid the temptation to change them too frequently. A consistent strategy helps managers sort through opportunities and gain short-term advantage by exploiting the attractive ones. In stable markets, managers rely on complicated strategies built on detailed predictions of the future. But when business is complicated, strategy should be simple. PMID:11189455
Path Integral Solution by Sum Over Perturbation Series
Lin, De-Hone
1999-01-01
A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method. Different from the earlier treatment based on the space-time transformation and infinite multiple-valued trasformation of Kustaanheimo-Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simpl...
Stream sampling for variance-optimal estimation of subset sums
Cohen, Edith; Duffield, Nick; Kaplan, Haim; Lund, Carsten; Thorup, Mikkel
2008-01-01
From a high volume stream of weighted items, we want to maintain a generic sample of a certain limited size $k$ that we can later use to estimate the total weight of arbitrary subsets. This is the classic context of on-line reservoir sampling, thinking of the generic sample as a reservoir. We present an efficient reservoir sampling scheme, $\\varoptk$, that dominates all previous schemes in terms of estimation quality. $\\varoptk$ provides {\\em variance optimal unbiased estimation of subset sum...
Broadband sum frequency generation via chirped quasi-phase-matching
Rangelov, A. A.; Vitanov, N. V.
2011-01-01
An efficient broadband sum frequency generation (SFG) technique using the two collinear optical parametric processes \\omega 3=\\omega 1+\\omega 2 and \\omega 4=\\omega 1+\\omega 3 is proposed. The technique uses chirped quasi-phase-matched gratings, which, in the undepleted pump approximation, make SFG analogous to adiabatic population transfer in three-state systems with crossing energies in quantum physics. If the local modulation period %for aperiodically poled quasi-phase-matching first makes ...
LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMPS
Institute of Scientific and Technical Information of China (English)
WU Zhen; YU Zhi-yong
2005-01-01
The existence and uniqueness of the solutions for one kind of forwardbackward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
Factors of binomial sums from the Catalan triangle
Guo, Victor J W
2009-01-01
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers $n_1, ..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, the expression
On sums involving the number of distinct prime factors function
Wakhare, Tanay
2016-01-01
The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\\omega(n)$, where $\\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria for these series. The approach of this paper is use polynomial theorems to prove several factorization identities for arbitrary complex numbers, then apply these identities with arbitrary primes and values of multiplicative functions evaluated at primes. This...
A linear upper bound in zero-sum Ramsey theory
Directory of Open Access Journals (Sweden)
Yair Caro
1994-01-01
Full Text Available Let n, r and k be positive integers such that k|(nr. There exists a constant c(k,r such that for fixed k and r and for every group A of order kR(Knr,A≤n+c(k,r,where R(Knr,A is the zero-sum Ramsey number introduced by Bialostocki and Dierker [1], and Knr is the complete r-uniform hypergraph on n-vertices.
A Gaussian-sum filter for vertex reconstruction
International Nuclear Information System (INIS)
A vertex reconstruction algorithm was developed based on the Gaussian-sum filter and implemented in the framework of the CMS reconstruction program. While linear least-squares estimators are optimal in case all observation errors are Gaussian-distributed, a GSF offers a better treatment of non-Gaussian distributions of track parameter errors when these are modeled by Gaussian mixtures. Results are compared to the Kalman filter
Scaled unscented transform Gaussian sum filter: theory and application
Luo, Xiaodong; Moroz, Irene M.; Hoteit, Ibrahim
2010-01-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is a...