Dynamical Quark Mass Generation Research Articles

Shear viscosity coefficient of magnetized QCD medium near chiral phase transition

We study the properties of the shear viscosity coefficient of quark matter at finite temperature and chemical potential near chiral phase transition in a strong background magnetic field. A strong magnetic field induces anisotropic features, phase-space Landau-level quantization, and if the magnetic field is sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter transport characteristics. The modified Nambu-Jona-Lasinio (NJL) model with inverse magnetic catalysis effect by fitting the Lattice QCD (LQCD) results is used to calculate the changes of quasiparticle related thermodynamic quantities, and the shear viscosity of the system medium, which is analyzed under the relaxation time approximation. We quantify the influence of the order of chiral phase transition and the critical endpoint on dissipative phenomena in such a magnetized medium. When the magnetic field exists, the shear viscosity coefficient of the dissipative fluid system can be decomposed into five different components. In strong field limit, we make a detailed study of the dependencies of $\eta_{2}$ and $\eta_{4}$ on temperature and magnetic field for the first order phase transition and critical endpoint transition. respectively. It is found that $\eta_{2}$ and $\eta_{4}$ both decrease with magnetic field and increase with temperature, and the discontinuities of $\eta_{2}$ and $\eta_{4}$ occur at the first order phase transition point.

Numerical study of the twist-3 asymmetry ALT in single-inclusive electron-nucleon and proton-proton collisions

We provide the first rigorous numerical analysis of the longitudinal-transverse double-spin asymmetry ${A}_{LT}$ in electron-nucleon and proton-proton collisions for the case where only a single pion, jet, or photon is detected in the final state. Given recent extractions of certain, previously unknown, nonperturbative functions, we are able to compute contributions from all terms relevant for ${A}_{LT}$ and make realistic predictions for the observable at Jefferson Lab (JLab) 12 GeV, COMPASS, the future Electron-Ion Collider, and the Relativistic Heavy Ion Collider. We also compare our results to a JLab 6 GeV measurement, which are the only data available for this type of reaction. The twist-3 nature of ${A}_{LT}$ makes it a potentially fruitful avenue to probe quark-gluon-quark correlations in hadrons as well as provide insights into dynamical quark mass generation in QCD.

Anisotropic electrical conductivity of magnetized hot quark matter

We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A~magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these issues, we used a quasi-particle description of quark matter in which the electric charge carriers are constituent quarks with temperature- and magnetic-field-dependent masses predicted by a Nambu--Jona-Lasinio model. The model accurately describes recent lattice QCD results showing magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudo-critical temperature ($T_{\rm pc}$) of the QCD phase transition. We found that the magnetic field increases the conductivity component parallel to it and decreases the transverse component, in qualitative agreement with recent lattice QCD results. In addition, we found that: (1)~the space anisotropy of the conductivity increases with~$B$, (2)~the longitudinal conductivity increases due to phase-space Landau-level quantization, (3)~a lowest Landau level approximation behaves poorly for temperatures close to $T_{\rm pc}$, and (5)~inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\rm pc}$. Our study adds to the existing body of work on the hot quark matter electrical conductivity by incorporating nontrivial temperature and magnetic field effects on dynamical mass generation.

Dynamical quark mass generation in QCD3 within the Hamiltonian approach in Coulomb gauge

We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in d = 2 spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in d = 3, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in d = 3 to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in d = 2.

On the connection between quark propagation and hadronization

We investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and {widetilde{E}} twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.

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.

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.

Non-Perturbative Analysis of Various Mass Generation by Gluonic Dressing Effect with the Schwinger-Dyson Formalism in QCD

As a topic of "quantum color dynamics", we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size $R$ is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size $R$ is taken to be smaller than a hadron, $R\sim 1$ fm, and larger than a constituent quark, $R\sim 0.3$ fm. We find that the compact diquark with $R\simeq 0.3$ fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect.

QCD Phase Diagram and the Constant Mass Approximation

Dynamical generation of quark masses in the infrared region of QCD plays an important role to understand the peculiar nature of the physics of hadrons. As it is known, the solution of QCD gap equation for the quark mass function is flat for low momentum, but smoothly evolves to the perturbative behavior at high momentum. In this work, we use an effective truncation of QCD gap equation valid up to 1 GeV, and implement it at finite temperature and chemical potential to understand the QCD phase diagram for chiral symmetry breaking-chiral symmetry restoration, and confinement-deconfinement phase transitions from the Schwinger-Dysin equations point of view. Our effective kernel contains a gluon dressing function with two light quark flavors Nf = 2, with current quark mass 0.0035 GeV. An effective coupling, adjusted to reproduce the behavior of the chiral condensate at finite T complements our truncation. We find the critical end point of the phase diagram located at the temperature TE = 0.1245 GeV and the baryonic chemical potential μEB = 0.211 GeV.

Soft breaking of BRST invariance for introducing non-perturbative infrared effects in a local and renormalizable way

The possibility of introducing non-perturbative infrared effects leading to a modification of the long distance behavior of gauge theories through a soft breaking of the BRST invariance is investigated. The method reproduces the Gribov–Zwanziger action describing the restriction of the domain of integration in the Feynman path integral to the Gribov region and a model for the dynamical quark mass generation is presented. The soft symmetry breaking relies on the introduction of BRST doublets and massive physical parameters, which allow one to distinguish the infrared region from the ultraviolet one, within the same theory.

Effective potential evaluations in a modified PQCD

A procedure discussed in a previous work for properly defining the Feynman diagrams at any number of loops in a modified version of PQCD, is employed here to evaluate some zero- and one-loop corrections to the effective potential, as functions of the gluon and quark condensate parameters. The calculated terms indicate an instability of massless QCD under the development of quark condensates even in the absence of the gluon one. Therefore, a mechanism is suggested for the dynamical generation of quark masses and condensates. The absence of indications coming from lattice calculations to this possibility could be determined by the current limitations in treating fermion determinants.

Kugo-Ojima confinement and QCD Green's functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relations to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, α(0) = 8.915 N c . Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.

Baryons as non-topological chiral solitons

The present review gives a survey of recent developments and applications of the Nambu-Jona-Lasinio model with N f = 2 and N f = 3 quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N f) L ⊗SU(N f) R ⊗U(1) V approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu-Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.

Multi-Mass Callan-Symanzik Equation. II

The Callan-Symanzik equation is generalized so as to include several independent fermion masses. The resulting equation is applied to exploration of the possibility of dynamical generation of quark masses in the absence of Higgs fields. l ),2) describes the response of Green's func­ tions against infinitesimal changes of the bare fermion mass. In reality, however, there are many independent fermion masses, and it is desirable to generalize it to multi-mass cases. For that purpose we have to know the mechanism of how the fermion masses as well as other masses are generated. In the standard gauge theory it is a conventional wisdom to assume that they are generated by spontaneous symmetry-breaking through the Higgs fields, but there is an alternative possibility that they are generated dynamically without recourse to the Higgs fields. In the present article we shall look for the latter possibility by formulating the CS equation in the multi-mass case .. In such an approach we assume that the masses of other particles can be expressed in terms of quark masses,3) at least in principle. In § 2 we briefly review the derivation of the CS equation in the single mass case in such a way that it facilitates the generalization to multi-mass cases. In § 3 we immediately generalize the CS equation to the multi-mass case provided that scalar densities relevant to mass-insertion are multiplicatively renormalized. Quantum chromodynamics (QCD) belongs to this category. The multi-mass CS equation is inhomogeneous because of the presence of the mass-insertion term, so that we shall transform it into a homogeneous form by introducing Green's functions with exponentiated mass-insertion. This subject has already been discussed elsewhere,3) but we shall recapitulate it in § 4 for compl€teness. The physical mass and coupling constant are shifted as a result of mass-insertion, and we shall study in § 5 how these relevant quantities are determined from the CS equation in the single mass case. At this stage we shall ask if it is possible to obtain a finite physical mass starting from a massless theory. This problem is generalized to the multi-mass case and it is investigated how this approach is related to the idea of spontaneous chiral-symmetry-breaking in § 6. Finally in § 7 the CS equation is derived when scalar densities are mixed under renormalization.

The Nambu—Jona-Lasinio model of quantum chromodynamics

The Nambu---Jona-Lasinio model is reviewed in its flavor SU(2) and SU(3) versions applied to quarks. The dynamical generation of quark masses is demonstrated as a feature of chiral symmetry breaking. One finds that the associated meson spectra, as well as the meson static properties, can be well described. Current-algebra results, which arise as a consequence of symmetry considerations, automatically hold for this model and are explicitly demonstrated to do so. These include the Goldberger-Treiman and Gell-Mann-Oakes-Renner relations. Effects of finite temperature, finite chemical potential, and strong Maxwell and chromoelectromagnetic fields on the dynamically generated quark mass and the meson spectra are discussed. The alternative procedure of bosonization to obtain an effective Lagrange density in mesonic degrees of freedom, using the derivative expansion, is also presented. The current status in relating the results of this model to that of chiral perturbation theory is critically examined.

Quark Mass Generation and Renormalization Group

The possibility of dynamical generation of quark masses in quantum chromodynamics has been studied by means of renormalization group equations. Although we confine ourselves to QCD the quark-gluon system must be prepared to accommodate electroweak interactions in the next stage by satisfying a certain set of conservation laws defining chiral symmetry. In the absence of Higgs fields the requirement of chiral symmetry leads to a set of constraints to determine the quark mass ratios as well as the gauge coupling constant with the help of renormalization group

Quark Mass Generation and Renormalization Group

The possibility of dynamical generation of quark masses in quantum chromodynamics has been studied by means of renormalization group equations. Although we confine ourselves to QCD the quark-gluon system must be prepared to accommodate electroweak interactions in the next stage by satisfying a certain set of conservation laws defining chiral symmetry. In the absence of Higgs fields the requirement of chiral symmetry leads to a set of constraints to determine the quark mass ratios as well as the gauge coupling constant with the help of renormalization group.

The Nambu and Jona-Lasinio model: Its implications for Hadrons and Nuclei

We review recent developments and applications of the Nambu and Jona-Lasinio model with three quark flavours, based on the SU(3) L ⊗ SU(3) R ⊗ U(1) V symmetry of QCD. The model describes dynamical quark mass generation and spontaneous chiral symmetry breaking and includes effects of the axial U(1) anomaly. Mesons emerge as quark-antiquark modes; their spectra and properties are discussed. Properties of constituent quarks as quasi-particles, dressed by their strong interactions, are summarized. The quark-diquark structure of baryons is developed, and a brief summary is given on baryonic solitons as they result from the NJL model. Finally, selected implications for nuclear physics are described, such as the change of hadron structure in a dense and hot nuclear medium.

Erratum: Gauge-invariant, nonperturbative approach to quark confinement and chiral-symmetry breaking in QCD

A gauge-invariant, nonperturbative approach to quark confinement and chiral-symmetry breaking in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identities is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singularity like {ital q}{sup {minus}4} at small momenta, we obtain a nonperturbative, gauge-invariant, infrared-finite quark propagator, which has no pole (confinement-type solution) and implies chiral-symmetry breaking (dynamical quark mass generation), so that we establish a close connection between these nonperturbative phenomena. We discover that the ghost degrees of freedom play an essential role in the dynamics of chiral-symmetry breaking, but nevertheless the quark propagator we got was free of ghost complications. In addition to the infrared-finite solution, we find also two infrared-vanishing (after the removal of the infrared regulation parameter) solutions for the quark propagator. For the dynamical (nonperturbative) quark mass we derive the expression which exhibits an essential singularity in the coupling constant in accordance with renormalization-group solutions in the infrared region.

Gauge-invariant, nonperturbative approach to quark confinement and chiral-symmetry breaking in QCD.

A gauge-invariant, nonperturbative approach to quark confinement and chiral-symmetry breaking in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identities is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singularity like ${q}^{\ensuremath{-}4}$ at small momenta, we obtain a nonperturbative, gauge-invariant, infrared-finite quark propagator, which has no pole (confinement-type solution) and implies chiral-symmetry breaking (dynamical quark mass generation), so that we establish a close connection between these nonperturbative phenomena. We discover that the ghost degrees of freedom play an essential role in the dynamics of chiral-symmetry breaking, but nevertheless the quark propagator we got was free of ghost complications. In addition to the infrared-finite solution, we find also two infrared-vanishing (after the removal of the infrared regulation parameter) solutions for the quark propagator. For the dynamical (nonperturbative) quark mass we derive the expression which exhibits an essential singularity in the coupling constant in accordance with renormalization-group solutions in the infrared region.