Improved effective action for light quarks beyond the chiral limit

We propose an improvement of the Diakonov–Petrov effective action on the basis of the Lee–Bardeen results for the quark determinant in the instanton field. This improved effective action provides a proper account of the current quark masses, which is particularly important for strange quarks. This action is successfully tested by calculations of the quark condensate, the masses of the pseudoscalar meson octet and axial-anomaly low-energy theorems. Received: 19 October 1998 / Revised version: 17 January 1999 / Published online: 20 May 1999     

Quark matter and meson properties in a Nonlocal SU(3) chiral quark model at finite temperature

We study the finite temperature behavior of light scalar and pseudoscalar meson properties in the context of a three-flavor nonlocal chiral quark model. The model includes mixing with active strangeness degrees of freedom, and takes care of the effect of gauge interactions by coupling the quarks with a background color field. We analyze the chiral restoration and deconfinement transitions, as well as the temperature dependence of meson masses, mixing angles, and decay constants.     

Nonlinear σ-model and nucleon structure

The nonlinear σ-model with the Wess-Zumino action describes the nucleon as a soliton and incorporates the non-abelian chiral anomalies. Several studies have shown that the model works well except for the nucleon mass, which comes out consistently too large. We investigate this question beginning with the more general framework of the linear σ-model, which has besides a pseudoscalar meson sector, a fermion or quark sector, a scalar field and an interaction between the fermions via the scalar field. Using a path integral formulation, we express the fermion measure of the model as the product of a Jacobian and an invariant measure. Identifying this Jacobian as exp[iΓ _wz] , we find that the model breaks up into two parts, when in the pseudoscalar meson sector the scalar field is replaced by its vacuum value. The pseudoscalar part of the model becomes the nonlinear σ-model with the Wess-Zumino actionΓ _wz. The other part involves chiral fermions, the scalar field and their interaction. We continue this part back to the Minkowski space to determine its ground state and energy levels. We find that for a scalar field that vanishes at smallr, but rises sharply to its vacuum value at someR, the ground state energy of the interacting quark-scalar-field system can be lower than the ground state energy of the non-interacting quark system. This means the interaction between quarks and the scalar field can lead to a condensed ground state or vacuum and can reduce the overall energy of the system (a phase transition as in superconductivity). It is, therfore, not surprising that the nonlinear σ-model predicts too large a nucleon mass, since it implicitly assumes a normal non-interacting vacuum in the quark sector. Quarks are now quasiparticles that appear as excitations of the condensed vacuum. The nucleon structure that emerges from this investigation agrees fully with the phenomenological nucleon structure found from analysis of high energy elasticpp and \(\bar p\) p scattering at CERN ISR and SPS Collider.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

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.     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x     

Application of the heat-kernel method to the constituent quark model at finite temperature

The heat-kernel method is applied to the constituent quark model. We calculate the effect of thermal quark fluctuations on the meson action and the resulting quark condensate and ππ-scattering amplitude at finite temperature. The quarks produce a chiral phase transition only by their effect on the mesonic coupling constants. The s-wave isospin zero ππ-scattering amplitude diverges near the phase transition showing the necessity for a more sophisticated treatment of meson fluctuations.     

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.     

The linear meson model and chiral perturbation theory

We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings – of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the agree with previous phenomenological estimates. Received: 21 April 1997 / Published online: 20 February 1998     

Mesons in the Quark Model of Superconductivity Type

On the basis of a quark model of superconductivity type, effective chiral Lagrangians are obtained for strong, electromagnetic and weak interactions of scalar, pseudoscalar, vector and axial vector meson nonets at low energies. The spontaneous breaking of chiral symmetry plays an important role. The form factors of strong and electromagnetic vertices, meson masses and different types of meson decaysare discussed.     

Meson Lagrangians in a superconductor quark model

On the basis of a effective “superconductivity”-type four-quark interaction, phenomenological Lagrangians are obtained for interactions of scalar, pseudoscalar, vector, and axial vector meson nonets. The Lagrangians include mass terms breaking chiral and U(3) invariance and corresponding to the quark masses m_u ≠ m_d ≠ m_s. It is shown that upon introducing boson fields the masses of current quarks in the initial Lagrangian are replaced by the masses of constituent quarks in the phenomenological boson Lagrangians. Estimates of these masses are presented. Electromagnetic interactions are considered, and the vector dominance model is derived. The widths of various meson decays are calculated.     

Meson loops in the f0(980) and a0(980) radiative decays into ρ , ω

We calculate the radiative decay widths of the a ₀(980) and f ₀(980) scalar mesons into ργ and ωγ considering the dynamically generated nature of these scalar resonances within the realm of the chiral unitary approach. The main ingredient in the evaluation of the radiative width of the scalar mesons are the loops coming from the decay into their constituent pseudoscalar-pseudoscalar components and the subsequent radiation of the photon. The dominant diagrams with only pseudoscalar mesons in the loops are found to be convergent while the divergence of those with a vector meson in the loop are written in terms of the two-meson loop function easily regularizable. We provide results for all the possible charge channels and obtain results, with uncertainties, which differ significantly from quark loops models and some version of vector meson dominance.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

H-particle in a chiral quark model

In this paper we discuss the binding energy of the H-particle using a chiral quark model, where pion exchange plays an important role to reproduce the mass difference between the nucleon and Δ resonance. Since the main source for the bound H-particle is believed to be the color magnetic interaction, which gives the nucleon and Δ mass difference, it is very interesting to investigate whether the chiral quark model gives rise to the bound H-particle or not. We employ an extended resonating group method in order to take into account the possibility of a change of baryon wave functions when two baryons interact with each other. We found that a change of baryon size together with the Hamiltonian which consists of gluon, pseudoscalar meson and sigma meson exchange potentials gives rise to the bound H-particle. The binding energy is found to be about 25 MeV in a hybrid chiral quark model. Differences between the ordinary gluon dominant model and chiral quark models are also investigated. It is found that a pure chiral model has no bound state when the widely used sigma-quark coupling strength is employed.     

Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

Inspired by the construction of the Gribov–Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the ρ$\rho$ meson mass and decay constant.     

B-meson decay constant from unquenched lattice QCD

We present determinations of the -meson decay constant f(B) and f(B)(s)/f(B) using the MILC Collaboration unquenched gauge configurations, which include three flavors of light sea quarks. The mass of one of the sea quarks is kept around the strange quark mass, and we explore a range in masses for the two lighter sea quarks down to m(s)/8. The heavy quark is simulated using nonrelativistic QCD, and both the valence and sea light quarks are represented by the highly improved (AsqTad) staggered quark action. The good chiral properties of the latter action allow for a more accurate chiral extrapolation to physical up and down quarks than has been possible in the past. We find f(B)=216(9)(19)(4)(6) MeV and f(B)(s)/f(B)=1.20(3)(1).     

Chiral symmetry suppression of two-photon couplings to excited SU(3) pseudoscalar mesons

Recent results from the Crystal Ball spectrometer show no evidence for two-photon production of the pseudoscalar resonances π(1300), η(1275) or η(1440). We give a simple theoretical argument showing that the two-photon couplings to excited SU(3) pseudoscalars are naturally suppressed by chiral symmetry in QCD. Effects of the spontaneous chiral symmetry breaking nevertheless give a finite contribution to the two-photon coupling, even in the limit of zero quark mass. We construct an effective chiral meson lagrangian that incorporates these qualitative properties, and use it to estimate the two-photon couplings in the chiral limit. The results are well compatible with experiment.     

The quark‐level linear σ model

This review of the quark‐level linear σ model (QLLσM) is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2)× SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non‐strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low‐energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and <π |H_weak|K>. Links are made with the vector‐meson‐dominance model, the BCS theory of superconductivity, and chiral‐symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.