Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks with an instanton liquid is considered at nonzero density of quark/baryon matter in a phase where the diquark condensate is nonzero. It is shown that the inclusion of the relevant perturbation of the instanton liquid leads to an increase in the quark chemical potential μ_c. This in turn induces a considerable growth of the threshold quark-matter density at which one expects the emergence of color superconductivity.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

2γ decays of scalar mesons (σ(600), f0(980), and a0(980)) in the Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980), and a ₀(980) are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c approximation, where N _c is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f ₀ decay the K-loop contribution turns out to play the dominant role. The results are in satisfactory agreement with modern experimental data.     

Radiative decays of scalar mesons σ(600), f 0(980) and a 0(980) in the local Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980) and a ₀(980) as well a ₀ → ju(ω)γ and f ₀ → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c -approximation where N _c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f ₀ decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a ₀ → ju(ω)γ and f ₀ → ju(ω)γ widths are given.     

Screening of instantons in the quark gas

The grand partition function of quark matter is developed about an arbitrary classical gauge field configuration in a systematic weak coupling expansion. In the presence of a finite density massless quark gas the instanton induced effective quark interaction is modified by a factor exp[?2N_F(ω?)²], i.e. the baryon number chemical potential μ acts as an intrinsic infrared cutoff on the instanton scale size ?. The equation of state of the quark matter is also briefly discussed.     

Hadronization of quark systems

Hadronization in simple models of quark systems is discussed with emphasis on the combinatorial aspects. The numberN of quarks and the numberN _c of colours are the relevant variables. In onedimension and in the meson and baryon sector the problem is completely soluble. When multiquark hadrons are included an iterative procedure still allows a complete solution. Higher dimensions are difficult to treat but global hadronization, without dimensionality constraints, is again soluble. As a general result the baryon/meson ratio is, for large quark densities, rather large, ?1/3 and may grow without limit asN→∞.     

Study of semileptonic and nonleptonic decays of the B<Subscript>c</Subscript><Superscript>-</Superscript> meson

We evaluate semileptonic and two-meson nonleptonic decays of the B _c ^- meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one-body current operators at the quark level. Our model reproduces the constraints of heavy-quark spin symmetry obtained in the limit of infinite heavy-quark mass. For the two-meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches.     

Instanton liquid at a finite density of quark matter

For the case of finite quark and baryon densities, the interaction of light quarks with an instanton liquid is considered in a phase that involves a nonvanishing chiral condensate. The generating functional is considered in the tadpole approximation, and the behavior of the dynamical quark mass and the behavior of the chiral condensate, as well as the behavior of the instanton-liquid (gluon-condensate) density, which grows slightly with the quark chemical potential, are explored. Arguments are presented in favor of the statement that the quark-density threshold for the emergence of a diquark condensate grows sizably owing to interaction with the instanton liquid.     

Instantons: Dynamical mass generation,chiral Ward identities and the topological charge correlation function

When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the η′ to the topological charge correlation function, a relationship is derived in which m_η′²f_η′² is proportional to the vacuum energy density.     

Glueball spectrum from N_f=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using N_f = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67)GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter(around 1 GeV) and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.     

Large Nc in nonperturbative QCD

We comment on large N_c within the context of nonperturbative QCD. In particular, we consider the QCD-based bag model, the instanton gas approximation, and the η′ mass.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

Algebraic quantization of the SU(3) skyrmion

The algebraic quantization of the SU(3) skyrmion is presented. We discuss the role of the number of colors (N_c) in QCD and the Wess-Zumino term in the quantization. Two distinct dynamical group chains are shown to correspond to different methods of semiclassical quantization. We obtain most of the SU(6) quark model predictions for the skyrmion quantized with N_c=3.     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.     

Couplings of heavy hadrons with soft pions from QCD sum rules

We estimate the couplings in the Heavy Hadron Chiral Theory (HHCT) lagrangian from the QCD sum rules in an external axial field. We take into account the perturbative correction to the meson correlator in the infinite mass limit. With the perturbative correction and three successive power corrections, the meson correlator in an axial field becomes one of the best known correlators. In spite of this, the corresponding sum rule is not very stable. It yields the result , where is the central value of the heavy meson decay constant with the perturbative correction [14]. This result is surprisingly low as compared with the constituent quark model estimate . The sum rules for following from nondiagonal and diagonal baryon correlators in an external axial field suggest , while diagonal and nondiagonal baryon sum rules have too large uncertainties. Received: 19 June 1997 / Published online: 20 February 1998     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

ΔS = 0 effective weak chiral Lagrangianfrom the instanton vacuum

We investigate the ΔS = 0 effective chiral Lagrangian from the instanton vacuum. Based on the ΔS = 0 effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order and the next-to-leading order in the 1/N_c expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the 1/N_c expansion for the ΔS = 0 effective weak chiral Lagrangian, while they are in the leading order terms in the ΔS = 1 case. Three different types of form factors are employed and we find that the dependence on the different choices of the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed in the chiral limit. Arrival of the final proofs: 2 December 2005 PACS: 12.40.-y, 14.20.Dh     

Heavy Pseudoscalar Mesons in a Schwinger-Dyson–Bethe-Salpeter Approach

The mass spectrum of heavy pseudoscalar mesons, as quark–antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum-dependent masses of the constituents. This dependence is prior found by solving the Schwinger-Dyson equation for quark propagators in rainbow-ladder approximation. Such approximation is known to provide fast convergence of numerical methods and accurate results for lightest mesons. However, as the meson mass increases, the method becomes less stable and special attention must be devoted to details of means of solving the corresponding equations. We focus on the pseudoscalar sector and show that our numerical scheme describes fairly accurately the π, K, D, D _s and η _c ground states. The excited states are considered as well. Our calculations are directly related to future physics at FAIR.