Damping of giant resonances in a stochastic two-level model

We derive a theory for small amplitude motion about states in thermal equilibrium. This motion couples mean-field oscillations and occupation number relaxations. The theory contains the effects of two-body collisions treated beyond the Markov approximation. The damping of collective modes is studied in a stochastic two-level model. The widths of giant resonances in finite nuclei are estimated using sum rules.     

Chiral symmetry breaking condensates from baryonic sum rules

We analyse baryonic sum rules in order to determine chiral symmetry breaking condensates. We especially investigate the influence of the choice of the interpolating field and of the factorization hypothesis for the four quark condensate. Our results are consistent with those obtained from pseudoscalar sum rules and PCAC.     

Sum rules from boundary dispersion relations

Sum rules for inelastic reactions are derived from boundary dispersion relations. If sufficient data or a model is available for the amplitude in the direct channel, then these sum rules provide a means of studying the dynamics in the cross channel. The convergence of these sum rules is investigated, assuming they can be saturated with narrow-width resonances, and rough estimates of the coupling constants of cross-channel exchanges for the photoproduction of pseudoscalar mesons are obtained.     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters(the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.     

A semi-classical model for isoscalar giant resonances at finite temperatures

We present a study of the temperature dependence of the energies of isoscalar giant resonances with multipolarities L = 0, 2, 3 and 4, in the framework of the subtraction procedure of Bonche, Levit and Vautherin (BLV). The method is used to calculate, within a Thomas-Fermi (TF) model at finite temperatures, sum rules of the strength function in the random phase approximation (RPA). Special attention has been paid to the spurious contribution of the gas, which considerably alters the low-energy weighted sum rules, i.e. the low-energy part of the strength function; we find that when this spurious contribution is removed, the resonance energies show a weak dependence on temperature, up to the Coulomb instability onset. The temperature dependence of the nuclear incompressibilities in the scaling and in the constrained models have also been obtained.     

On QCD sum rules of the Laplace transform type and light quark masses

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ?-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given.     

QCD sum rules at finite temperature

Finite energy and Laplace transform QCD sum rules atT0 are analyzed, and predictions for vacuum condensates are compared with the low temperature expansion of the energy density and pressure. Results show a serious disagreement which indicates a breakdown of the FESR programme already at dimension four, and which invalidates Laplace transform sum rules, at least in their straightforward extension to finite temperature.     

Sum rules for SUSY gluodynamics

The sum rules analysis for SU(N) SUSY gluodynamics is presented, concerning scalar, pseudoscalar and spinor channels. The spectrum obtained is characterized by a relatively dense disposition of excitations. The applicability of the effective lagrangian method to the study of resonance properties is thus made doubtful. Some new non-trivial relations between condensates in the SUSY vacuum are also presented.     

Pion Susceptibilities of the Vacuum in a Modified Global Colour Symmetry Model

Based on a modified version of the global color symmetry model,the pion susceptibilities of vacuum needed in the QCD sum rule external-field method for the coupling of pseudoscalar current to hadron have bean calculated beyond the vacuum saturation approximation.Comparison with the previous estimations has been given.     

Model independent constraints from vacuum and in-medium QCD Sum Rules

We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the ω meson and discuss the issue of in-medium mass shifts from this viewpoint. Received: 22 December 1998 / Revised version: 13 January 1999     

Understanding light scalar meson by color-magnetic wave function in QCD sum rule

In this paper, we study the 0⁺ nonet mesons as tetraquark states with interpolating currents inspired by the color-magnetic wave function. This wave function is the eigenfunction of an effective color-magnetic Hamiltonian with the lowest eigenvalue, meaning that the state depicted by this wave function is the most stable one and is the most probable to be observed in experiments. We perform an OPE calculation up to dimension-eight condensates and find that the best QCD sum rule is achieved when the current inspired by the color-magnetic wave function is a proper mixture of the tensor and pseudoscalar diquark-antidiquark bound states. Compared with previous results, to sigma(600) and kappa(800), our results appear better, due to larger pole contribution. The direct instanton contributions are also considered, which yields a consistent result with previous OPE results. Finally, we also discuss the h￠ \eta{^\prime} problem as a possible six-quark state.     

Avoided resonance overlapping in many-channel scattering

The behaviour of interfering resonances is studied within the framework of many-channelS-matrix theory. For the case of one open channel it is shown that at high level density where one naively would expect a strong overlapping, the resonances avoid each other: one resonance accumulates almost the whole sum of the widths of all resonances while the remaining ones become nearly stable.     

Meson wave functions and SU(3) symmetry breaking

The wave functions of the pseudoscalar and vector mesons (K, ?, K¹, ?) are found using the QCD sum rules and are used for the calculation of the heavy quarkonium two-particle decay widths.     

Non-perturbative conserving approximations and Luttinger's sum rule

Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum rules at zero temperature. These properties can also be shown for variational approximations that are generated within the framework of the self-energy-functional theory without a truncation of the diagram series. Luttinger's sum rule represents an exception. We analyze the conditions under which the sum rule holds within a non-perturbative conserving approximation. Numerical examples are given for a simple but non-trivial dynamical two-site approximation. The validity of the sum rule for finite Hubbard clusters and the consequences for cluster extensions of the dynamical mean-field theory are discussed.     

Non-perturbative QCD vacuum frome +e−→I=1 hadron data

We estimate the gluon vacuum condensate α _s 〈F ²〉 from thee ⁺e^?→I=1 hadron cross-section known below 2 GeV using moment sum rules ratios. We obtain α _s 〈F ²〉= (3.9±1.0)10^?2GeV⁴. We also re-evaluate the contribution of the dimension-six vacuum condensates to the above sum rule and test the factorization hypothesis of the four-quark operator. Useful rules for the evaluation of the dimension-six vacuum condensates contributions are given.     

0++三胶子标胶球与QCD求和规则

计算了0⁺⁺三胶子标量流的两点函数,其中计及了直至量纲为6的凝聚项的贡献.在＂零宽度共振态加连续谱＂的谱函数模型中,得到了0⁺⁺三胶子标胶球的量子色动力学求和规则,由此定出了该标胶球的质量.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

A class of modified sum rules in QCD

We consider a class of modifications to the exponential QCD sum rules, replacing the energy variableq ² by (q ²) ^k withk positive integer. As a result of this modification, (i) the relative role of the condensates on the theoretical side is changed, (ii) the integral on the phenomenological side acquires a rapidly decreasing weight function and (iii) the way of approaching infinity in theq ² complex plane splits intok rays. We explicitly discuss the modified sum rules withk=1,k=2 andk=3 for the ρ meson and conclude that, unlike to thek=1 case, thek=2 andk=3 sum rules do not yield a satisfactory scheme for the prediction of the resonance parameters unless many higher condensates are known. We show that, for practical applications with the present knowledge of condensates, the standard exponential QCD sum rules are the most suitable ones out of the class considered.