Dynamical Quark Mass Research Articles

Mass splitting and spin alignment for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field in NJL model

Based on the Nambu–Jona–Lasinio (NJL) model, we develop a framework for calculating the spin alignment of vector mesons and applied it to study ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field. We calculate mass spectra for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons and observe mass splitting between the longitudinally polarized state and transversely polarized states. The ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} meson in a thermal equilibrium system is preferred to occupy the state with spin λ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =0$$\\end{document} than those with spin λ=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =\\pm 1$$\\end{document}, because the former state has a smaller energy. As a consequence, we conclude that the spin alignment will be larger than 1/3 if one measures along the direction of the magnetic field, which is qualitatively consistent with the recent STAR data. Around the critical temperature TC=150MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{C}=150~\\hbox {MeV}$$\\end{document}, the positive deviation from 1/3 is proportional to the square of the magnetic field strength, which agrees with the result from the non-relativistic coalescence model. Including the anomalous magnetic moments for quarks will modify the dynamical masses of quarks and thus affect the mass spectra and spin alignment of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons. The discussion of spin alignment in the NJL model may help us better understand the formation of hadron’s spin structure during the chiral phase transition.

Convergence of Ginzburg–Landau Expansions: Superconductivity in the Bardeen–Cooper–Schrieffer Theory and Chiral Symmetry Breaking in the Nambu–Jona-Lasinio Model

Abstract We study the convergence of the Ginzburg–Landau (GL) expansion in the context of the Bardeen–Cooper–Schrieffer (BCS) theory for superconductivity and the Nambu–Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature T and chemical potential μ. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap Δ and dynamical quark mass M are given by Δconv = πT and $M_{\rm conv} = \sqrt{\mu ^2 + (\pi T)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.

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.

Parton Distribution Functions for Pseudoscalar Mesons in the Confining Effective Chiral Quark Theory

This review paper presents the gluon, sea, and valence quark distributions of the pseudoscalar (PS) mesons. The calculations of the parton structure of PS mesons are performed using the Bethe-Salpeter equation-Nambu--Jona-Lasinio (BSE-NJL) model, which offers a clear description of the dynamical chiral symmetry breaking (D$\chi$SB) of the low-energy nonperturbative quantum chromodynamics (QCD), with the help of the Schwinger proper-time regularization scheme that simulates the color QCD confinement. Our results for the dynamical quark mass -- which emerged from the spontaneous chiral symmetry breaking (S$\chi$SB) -- are generated via the chiral condensate in the chiral limit and beyond. Results for the valence parton distribution functions for the PS meson at the factorization scale $Q = 2$ GeV are in excellent agreement with experimental data and the gluon distribution for the pion fitted well with the lattice QCD and Jefferson Lab Angular Momentum (JAM) QCD global fit analysis.

Lattice QCD calculation of the Collins-Soper kernel from quasi-TMDPDFs

This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV $< q_T < 1.7$ GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass, $m_\pi=538(1)$ MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.

Diphoton production rate in relativistic nuclear collisions

In this study, we have made an effort to reveal some information about the space-time evolution of quark gluon plasma (QGP). We deal with one of the important signature of quark gluon plasma from the analysis of the experimental results on electromagnetic probes which are measured at relativistic heavy-ion collider (RHIC) and large hadron collider (LHC). Electromagnetic radiations as diphotons emitted from hot and dense matter are investigated using a phenomenological model with quasiparticle approach at temperatures above critical temperature. In this, we use thermodynamically consistent quasiparticle model composed of quarks and gluons. Due to interactions among the quarks, mass of these particles is generated in highly dense and hot matter of QGP. The mass of these particles is temperature dependent and it is found that the model works well at temperatures above the critical temperature. Thus, this work is carried out using a phenomenological model in heavy-ion collisions in the limit of high temperature and zero chemical potential. The rate of diphoton production is calculated by suitably fitted parametrization factors in quark mass. We found an appreciable enhancement using thermal quark mass as compared to dynamical quark mass in the current results of two photon production rate. The results are compared with earlier estimated diphoton production rates from QGP and hadronic matter. Our results are therefore enhanced in comparison to the other theoretical results. The estimation of diphoton emission anticipates useful insights in the relevant range of mass. So these insights on diphotons can be advantageous tool for spectroscopy and thermometry in high energy heavy-ion collisions at RHIC and LHC.

JASPER: a software for quantum chromodynamics Dyson-Schwinger equation numerical calculation

The JASPER program is the first part of the high-performance computing information system for estimate some elementary particle properties, developing at Petersburg Nuclear Physics Institute. The JASPER is an implementation of the Dyson-Schwinger equation numerical solution for simple dressed quark propagator calculation in rainbow approximation. The Dyson-Schwinger equation solution with the Marice-Tandy Ansatz is one of several phenomenological approaches to obtain quantitative results in quantum chromodynamics (QCD) within strong coupling regime. The JASPER program is programmed in the C++ language and uses the numerical algorithms from the GNU Scientific Library (GSL). The numerical results for dynamical quark mass in complex Euclidean space were obtained. This result will be employed to study the hadron spectrum with the Bethe-Salpeter equation approach.

Influence of magnetic fields on the stability and the phase transition of quark matter in the Nambu–Jona–Lasinio model

In the presence of the external magnetic fields, we investigate the stability of quark matter as well as the phase transition in the framework of two flavor Nambu–Jona–Lasinio model. The investigation focuses on the magnetic effects with the fixed coupling constant and the running coupling constant G(B, T) depending on both magnetic field and temperature. The dynamical quark mass can be increased by strong magnetic fields and be reduced by the running coupling constant G(B, T). The baryon number density is also increased by strong magnetic fields but is weakly influenced by the running coupling constant G(B, T). Importantly, the stability can be enhanced by the magnetic fields of a proper strength. While it will be reduced by the much weaker or much stronger magnetic fields. The magnetic-field-dependence in the running coupling constant has slight effect on the stability. Finally, the phase transition and the location of critical end point for both coupling cases are numerically shown.

Effect of the anomalous magnetic moment of quarks on magnetized QCD matter and meson spectra

We systematically investigate the effects made by the anomalous magnetic moment (AMM) of quark in the magnetized QCD matter, including the magnetic susceptibility, the inverse magnetic catalysis around the critical temperature and the modified neutral and or charged pion and rho meson's spectra. The dynamical AMM of quark, coupling with magnetic field, causes Zeeman splitting in the energy dispersion of quark and thus changes the magnetism properties and masses of magnetized mesons. Unfortunately, we found that the lattice results of the quark matter under magnetic fields cannot fully be explained via including the AMM interaction. It is observed that the AMM of quark reduces the dynamical quark mass and therefore induces the inverse magnetic catalysis around ${T}_{c}$. The neutral pion is very sensitive to the AMM term and its mass decreases with magnetic field quickly. On the contrary, the charged pion mass shows a nontrivial behavior, i.e., linearly increases with the weak and moderate magnetic fields and then saturates at strong region. For rho mesons, AMM coupling modifies the masses of neutral rho particles for all ${s}_{z}$ consistently, while it reduces the masses of charged rho mesons for ${s}_{z}=+1$, 0 but enhances the mass of ${s}_{z}=\ensuremath{-}1$ state. The magnetic susceptibility at low temperatures can be either positive or negative with different strengths of AMM interaction.

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.

Chirally Improved Quark Pauli Blocking in Nuclear Matter and Applications to Quark Deconfinement in Neutron Stars

The relativistic mean field (RMF) model of the nuclear matter equation of state was modified by including the effect of Pauli-blocking owing to quark exchange between the baryons. Different schemes of a chiral enhancement of the quark Pauli blocking was suggested according to the adopted density dependence of the dynamical quark mass. The resulting equations of state for the pressure are compared to the RMF model DD2 with excluded volume correction. On the basis of this comparison a density-dependent nucleon volume is extracted which parameterizes the quark Pauli blocking effect in the respective scheme of chiral enhancement. The dependence on the isospin asymmetry is investigated and the corresponding density dependent nuclear symmetry energy is obtained in fair accordance with phenomenological constraints. The deconfinement phase transition is obtained by a Maxwell construction with a quark matter phase described within a higher order NJL model. Solutions for rotating and nonrotating (hybrid) compact star sequences are obtained, which show the effect of high-mass twin compact star solutions for the rotating case.

Properties of light mesons in quark model

Abstract The properties of some mesons, such as π , ρ , have been investigated in the quasi-relativistic quark model. In particularly, their masses which are related to the dynamical masses of the constituent quarks, radii, and structures are studied. Interesting results are found, which can be explained in analogy with a hydrogen-like atom.

Gluons, Heavy and Light Quarks in the QCD Vacuum

We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size ~ 0:3 fm: We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size ρ ≈ 0:3 fm and average inter-instanton distance R ≈ 1 fm, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass M ~ (packing f raction)1/2 ρ-1 ≈ 360 MeV, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass Mg ≈ M. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by ΔmQ ~ packing fraction ρ-1 ≈ 70 MeV: Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass Mg. Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.

Effects of the temperature and magnetic-field dependent coupling on the properties of QCD matter

To reflect the asymptotic freedom in the thermal direction, a temperature-dependent coupling was proposed in the literature. We investigate its effect on QCD matter with and without strong magnetic fields. Compared with the fixed coupling constant, the running coupling leads to a drastic change in the dynamical quark mass, entropy density, sound velocity, and specific heat. The crossover transition of QCD matter at finite temperature is characterized by the pseudocritical temperature $T_\mathrm{pc}$, which is generally determined by the peak of the derivative of the quark condensate with respect to the temperature $d\phi/dT$, or equivalently, by the derivative of the quark dynamical mass $d M/dT$. In a strong magnetic field, the temperature- and magnetic-field-dependent coupling $G(eB,T)$ was recently introduced to account for inverse magnetic catalysis. We propose an analytical relation between the two criteria $d\phi/dT$ and $dM/dT$ and show a discrepancy between them in finding the pseudocritical temperature. The magnitude of the discrepancy depends on the behavior of $dG/dT$.

Heavy-heavy and heavy-light quarks interactions generated by QCD vacuum

The QCD vacuum is populated by instantons that correspond to the tunneling processes in the vacuum. This mechanism creates the strong vacuum gluon fields. As result, the QCD vacuum instantons induce very strong interactions between light quarks, initially almost massless. Such a strong interactions bring a large dynamical mass M of the light quarks and bound them to produce almost massless pions in accordance with the spontaneous breaking of the chiral symmetry (SBCS). On the other hand, the QCD vacuum instantons also interact with heavy quarks and responsible for the generation of the heavy-heavy and heavy-light quarks interactions, with a traces of the SBCS. If we take the average instanton size \rho=0.33 fm, and the average inter-instanton distance R=1 fm we obtain the dynamical light quark mass to be M = 365 MeV and the instanton media contribution to the heavy quark mass \Delta M=70 MeV. These factors define the coupling between heavy-light and heavy-heavy quarks induced by the QCD vacuum instantons. We consider first the instanton effects on the heavy-heavy quarks potential, including its spin-dependent part. We also discuss those effects on the masses of the charmonia and their hyperfine mass splittings. At the second part we discuss the interaction between a heavy and light quarks generated by instantons and it's effects.

Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k).

Effect of temperature and magnetic field on two-flavor superconducting quark matter

We investigate the effect of turning on temperature for the charge neutral phase of two-flavor color superconducting (2SC) dense quark matter in presence of constant external magnetic field. Within the Nambu-Jona-Lasinio model, by tuning the diquark coupling strength, we study the interdependent evolution of the quark Bardeen-Cooper-Schrieffer gap and dynamical mass as functions of temperature and magnetic field. We find that magnetic field $B \gtrsim 0.02$ GeV$^2$ ($10^{18}$ G) leads to anomalous temperature behavior of the gap in the gapless 2SC phase (moderately strong coupling), reminiscent of previous results in the literature found in the limit of weak coupling without magnetic field. The 2SC gap in the strong coupling regime is abruptly quenched at ultrahigh magnetic field due to the mismatched Fermi surfaces of up and down quarks imposed by charge neutrality and oscillation of the gap due to Landau level quantization. The dynamical quark mass also displays strong oscillation and magnetic catalysis at high magnetic field, although the latter effect is tempered by nonzero temperature. We discuss the implications for newly born compact stars with superconducting quark cores.