Dynamical Quark Mass Research Articles

Holographic Schwinger effect and chiral condensate in SYM theory

We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the $SU(N_c)$ SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for ${\cal N}=2$ SYM theory and the analysis is extended to the finite temperature deconfinement and the zero temperature confinement phases of the Yang-Mills (YM) theory. By comparing the obtained production rates with the one of the supersymmetric case, the dynamical quark mass is estimated and we find how it varies with the chiral condensate. Based on this analysis, we give a speculation on the extension of the Nambu-Jona-Lasinio model to the finite temperature YM theory, and four fermi coupling is evaluated in the confinement theory.

Dynamical chiral symmetry with an infrared finite gluon propagator

In this work we study dynamical quark mass generation using an infrared finite gluon propagator obtained from quenched lattice simulations. The quark gap equation is solved using a purely non-Abelian Ansatz for the quark-gluon vertex, which displays a dependence on the ghost dressing function and the scalar component of quark-ghost scattering kernel. For the former quantity we use quenched lattice results, while for the latter we derive its own integral equation at the one-loop-dressed approximation. This latter quantity is then coupled to the system of equations governing the two Dirac structures of the quark propagator. It turns out that when a current quark mass of 5 MeV is introduced, the constituent quark mass generated from the gap equation is of the order of 310 MeV. In addition, the pion decay constant computed from the resulting quark propagator is in good agreement with the physical value.

Subtractive Renormalization of the NJL model *

In this work, we apply a subtractive renormalization method to the SU(2) Nambu-Jona-Lasinio (NJL) model in Born approximation and compare the results obtained here with those achieved by the standard momentum cutoff regularization. We have computed the dynamical quark mass, the chiral condensate, the pion mass and the quark-antiquark T-matrix as a function of the cutoff Λ and the subtraction scale ξ. We have shown that both approaches give similar results and the dependence of the physical quantities on the subtraction point ξ is much weaker than the dependence on the cutoff Λ.

Magnetized quark matter with a magnetic-field dependent coupling

It was recently derived that the QCD running coupling is a function of the magnetic field strength under the strong magnetic field approximation. Inspired by this progress and based on the self-consistent solutions of gap equations, the properties of two-flavor and three-flavor quark matter are studied in the framework of the Nambu--Jona-Lasinio model with a magnetic-field-dependent running coupling. We find that the dynamical quark masses as functions of the magnetic field strength are not monotonous in the fully chirally broken phase. Furthermore, the stability of magnetized quark matter with the running coupling is enhanced by lowering the free energy per baryon, which is expected to be more stable than that of the conventional constant coupling case. It is concluded that the magnetized strange quark matter described by running coupling can be absolutely stable.

Quark propagator in a truncation scheme beyond the rainbow approximation

The quark propagator is studied under a truncation scheme beyond the rainbow approximation by dressing the quark-gluon vertex non-perturbatively. It is found that, in the chiral limit with dynamical symmetry breaking, the dynamical quark mass and the quark condensate are significantly enhanced due to the non-Abelian contribution arising from the three-gluon interaction compared to those under the rainbow approximation; and the critical strength of the dynamical chiral symmetry breaking is much lowered. The Abelian contribution is much smaller than the non-Abelian contribution. A technical issue on removing the ultraviolet divergences including the overlapping divergences is discussed.

On the role of dynamical quark mass generation in chiral symmetry breaking in QCD

The phenomenon of dynamical quark mass generation is studied in QCD within the framework of a gauge invariant formalism. An exact relationship is established between the equation satisfied by the scalar part of the two-point gauge invariant quark Green's function and the quark-antiquark bound state equation in the chiral limit. A possible nontrivial solution of the former yields a massless pseudoscalar solution of the bound state equation with vanishing total momentum. The result is also corroborated by the corresponding Ward-Takahashi identity. The problem is explicitly solved in two-dimensional QCD in the large-Nc limit.

Overlap quark propagator in coulomb gauge QCD and the interrelation of confinement and chiral symmetry breaking

The chirally symmetric overlap quark propagator is explored in Coulomb gauge for the first time. This gauge is especially well suited for studying the interrelation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergence of the vector dressing function of the inverse quark propagator. Using quenched gauge field configurations on a $20^4$ lattice, the dressing functions of the quark propagator as well as the dynamical quark mass function are evaluated, also in the chiral limit. Chiral symmetry is artificially restored by removing the low mode contribution from the quark propagator. After removing enough low-lying modes, the dynamical quark mass function approaches the current quark mass in the whole momentum region and goes to zero in the chiral limit. However, the vector dressing function is unaffected by the low-mode removal. It follows that the quark energy dispersion is still infrared divergent and quarks in such a chiral symmetry restored phase are still confined within a hadron.

The gradient flow of the Dirac spectrum

We construct chiral perturbation theory for the gradient flow of the microscopic Dirac eigenvalues and compute the density of and correlations between the microscopic eigenvalues at zero and non-zero flow time. The results show that the repulsion of the microscopic Dirac eigenvalues from the dynamical quark mass decreases with increasing gradient flow time. Furthermore, the flow of the spectral resolvent is compared to the flow of the chiral condensate obtained from a fermionic gradient flow.

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-Nc limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.

Effect of transverse gluons on chiral restoration in excited mesons

The effect of transverse gluons on the chiral symmetry patterns of excited mesons is studied in a Coulomb gauge QCD model. The linear rising static quark-antiquark potential and the transverse gluon propagator known from lattice studies are input into the model. The non-perturbative quark propagator, which enters the meson bound state equations, is derived from the Dyson--Schwinger equations and a complete set of mesons for general spin quantum number is presented. From analyzing the bound state equations for large spins it is demonstrated, that chiral and axial symmetry are restored. In this limit a complete degeneracy of all multiplets with given spin is observed. The effect of the transverse gluon interaction is shown to vanish rapidly as the spin quantum number is increased. For vanishing dynamical quark mass the expected meson degeneracies are recovered.

Light quark mass reweighting

We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_\pi=620 MeV) and m_l=0.01 (m_\pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.

Dilepton Emission at Temperature Dependent Baryonic Quark-Gluon Plasma

Dilepton emission is calculated from quark-gluon plasma (QGP) with the consideration of temperature dependent chemical potential (TDCP). The model is considered to be quasi-model and hence take the dynamical quark mass as a finite value dependence on temperature. The temperature in quark mass enhances in the growth of dilepton emission rates. The emission rate of dilepton spectrum is shown in the intermediate mass region (IMR) of 1.0 - 4.0 GeV and its rate is observed to be a strong increasing function of the temperature dependent chemical potential for quark and anti-quark annihilation.

Stability of colour-flavour locked quark matter with three massive quark flavours

We investigate the role of the dynamical masses of up, down, and strange quarks on the stability of electrically and colour neutral Colour-Flavour Locked (CFL) quark matter in chemical equilibrium. We derive a condition for the stability of such matter in terms of the chemical potentials of quarks and electrons, the quark masses, as well as the pairing gap. The free energy density of CFL quark matter is analyzed for a broad range of dynamical quark masses. A comparison with ordinary (non-CFL) quark matter shows that low strange quark masses favor colour superconductivity. Stability of the CFL phase can also be achieved, however, for larger values of the quark chemical potential and larger values of the dynamical strange quark mass, provided the differences between the quark masses are not too big.

The quarkyonic phase and the [formula omitted] symmetry

We investigate the interplay between the ZNc symmetry and the emergence of the quarkyonic phase, adding the flavor-dependent complex chemical potentials μf=μ+iTθf with (θf)=(0,θ,−θ) to the Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model. When θ=0, the PNJL model with the μf agrees with the standard PNJL model with the real chemical potential μ. When θ=2π/3, meanwhile, the PNJL model with the μf has the ZNc symmetry exactly for any real μ, so that the quarkyonic phase exists at small T and large μ. Once θ varies from 2π/3, the quarkyonic phase exists only on a line of T=0 and μ larger than the dynamical quark mass, and the region at small T and large μ is dominated by the quarkyonic-like phase in which the Polyakov loop is small but finite.

Dilepton production in finite baryonic quark–gluon plasma

We study the evolution of hot plasma through a statistical model in the hadronic medium. Evolution of the plasma can be expressed by the free energy at finite temperature and quark chemical potential of the constituent particles in the system. In this study, the dynamical quark mass is dependent on momentum and temperature. The evolution is explained through thermodynamic variables like free energy and entropy curve. These variables show the behaviour of the system for the different chemical potentials, μ, at these transition temperatures T = 150–170 MeV. Moreover, the study of the dilepton production at these finite temperatures and quark chemical potentials from the fireball of quark–gluon plasma shows a specific structure of dilepton spectrum in the intermediate mass region of 1.0–4.0 GeV and its production rate is observed to be a strong increasing function of quark chemical potential for quark and antiquark annihilation. We further observe lepton spectra coming from the hadronic phase in the low mass M = 0–1.2 GeV region.

The effect of dynamical quark mass on the calculation of a strange quark star's structure

We discuss the dynamical behavior of strange quark matter components, in particular the effects of density dependent quark mass on the equation of state of strange quark matter. The dynamical masses of quarks are computed within the Nambu-Jona-Lasinio model, then we perform strange quark matter calculations employing the MIT bag model with these dynamical masses. For the sake of comparing dynamical mass interaction with QCD quark-quark interaction, we consider the one-gluon-exchange term as the effective interaction between quarks for the MIT bag model. Our dynamical approach illustrates an improvement in the obtained equation of state values. We also investigate the structure of the strange quark star using Tolman-Oppenheimer-Volkoff equations for all applied models. Our results show that dynamical mass interaction leads to lower values for gravitational mass.

Pseudoscalar meson transition form factors in nonperturbative QCD approach

In this communication we discuss a few topics related to modern experimental data on physics of light pseudoscalar mesons. It includes the contribution of the pseudoscalar mesons to the muon anomalous magnetic moment (AMM), g − 2 , rare decays of light pseudoscalar mesons to a lepton pair, transition form factors of pseudoscalar mesons at large momentum transfer, the pion transversity form factor. Measuring the muon anomalous magnetic moment g − 2 and rare decays of light pseudoscalar mesons into a lepton pair P → l + l − serve as important test of the standard model. To reduce the theoretical uncertainty in the standard model predictions, the data on the transition form factors of light pseudoscalar mesons play significant role. Recently new data on behavior of these form factors at large momentum transfer was supplied by the BABAR collaboration. Within the nonlocal chiral quark model it is shown how to describe these data and how the meson distribution amplitude evolves as a function of the dynamical quark masses and meson masses.

Hadron-quark phase transition in dense matter

The two-Equation of State (EoS) model is used to describe the hadron-quark phase transition in asymmetric matter formed at high density in heavy-ion collisions. For the quark phase, the three-flavor Nambu–Jona-Lasinio (NJL) effective theory is used to investigate the influence of dynamical quark mass effects on the phase transition. At variance to the MIT-Bag results, with fixed current quark masses, the main important effect of the chiral dynamics is the appearance of an end point for the coexistence zone. We show that a first order hadron-quark phase transition may take place in the region T = (50 – 80) MeV and ρB = (2 – 4)ρ0, which is possible to be probed in the new planned facilities, such as FAIR at GSI-Darmstadt and NICA at JINR-Dubna. From isospin properties of the mixed phase some possible signals are suggested. The importance of chiral symmetry and dynamical quark mass on the hadron-quark phase transition is stressed.

Chiral density waves in theNJL2model with quark number and isospin chemical potentials

We investigate the phase portrait of the ($1+1$)-dimensional massless two-flavored ${\mathrm{NJL}}_{2}$ model containing a quark number chemical potential $\ensuremath{\mu}$ and an isospin chemical potential ${\ensuremath{\mu}}_{I}$ in the limit of a large number of colors ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$. Particular attention is paid to the question of to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that, at zero temperature and comparatively small values of $\ensuremath{\mu}$, i.e. at $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}\ensuremath{\approx}0.68{M}_{0}$ (${M}_{0}$ is the dynamical quark mass in the vacuum), only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of ${\ensuremath{\mu}}_{I}$. Contrary to this, for large values of $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$, two CDW phases appear in the $({\ensuremath{\mu}}_{I},\ensuremath{\mu})$-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals, and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.

Hadron-quark phase transition in asymmetric matter with dynamical quark masses

The two-Equation of State (EoS) model is used to describe the hadron-quark phase transition in asymmetric matter formed at high density in heavy-ion collisions. For the quark phase, the three-flavor Nambu--Jona-Lasinio (NJL) effective theory is used to investigate the influence of dynamical quark mass effects on the phase transition. At variance to the MIT-Bag results, with fixed current quark masses, the main important effect of the chiral dynamics is the appearance of an End-Point for the coexistence zone. We show that a first order hadron-quark phase transition may take place in the region T=(50-80)MeV and \rho_B=(2-4)\rho_0, which is possible to be probed in the new planned facilities, such as FAIR at GSI-Darmstadt and NICA at JINR-Dubna. From isospin properties of the mixed phase somepossible signals are suggested. The importance of chiral symmetry and dynamical quark mass on the hadron-quark phase transition is stressed. The difficulty of an exact location of Critical-End-Point comes from its appearance in a region of competition between chiral symmetry breaking and confinement, where our knowledge of effective QCD theories is still rather uncertain.