The effect of the higher-order mesonic interactions is investigated on the chiral symmetry breaking in the presence of an external magnetic field. The effective of higher-order mesonic potential is employed and is numerically solved in the mean-field approximation. The chiral symmetry breaking increases with increasing magnetic field. Two sets of free parameterization are investigated on the magnetic catalysis. A comparison is discussed with the original sigma model and other studies. The obtained results are included that the higher-order mesonic interactions play an important role in the magnetic catalysis.
We consider the evolution of critical temperature both for the formation of a pion condensate as well as for the chiral transition, from the perspective of the linear sigma model, in the background of a magnetic field. We developed the discussion for the pion condensate in one loop approximation for the effective potential getting magnetic catalysis for high values of B, i.e. a raising of the critical temperature with the magnetic field. For the analysis of the chiral restoration, we go beyond this approximation, by taking one loop thermo-magnetic corrections to the couplings as well as plasma…
The chiral symmetry breaking in the presence of external magnetic field is studied in the framework of logarithmic quark-sigma model. The effective logarithmic mesonic potential is employed and is numerically solved in the mean-field approximation. We find that the chiral symmetry breaking enhances in comparison with the original sigma model. Two sets of parameterization are investigated in the present model. We find that increasing coupling constant enhances the breaking symmetry while increasing sigma mass inhibits enhancing chiral broken vacuum state. A comparison with the Numbu-Jona-Lasini…
We study the behavior of strongly interacting matter under an external constant magnetic field in the context of nonlocal chiral quark models within the mean field approximation. We find that at zero temperature the behavior of the quark condensates shows the expected magnetic catalysis effect, our predictions being in good quantitative agreement with lattice QCD results. On the other hand, in contrast to what happens in the standard local Nambu-Jona-Lasinio model, when the analysis is extended to the case of finite temperature our results show that nonlocal models naturally lead to the Invers…
Apart from Magnetic Catalysis at low temperatures, recent LQCD studies have shown the opposite effect at temperatures near the transition region: instead of enhancing, the magnetic field suppresses the quark condensates (Inverse Magnetic Catalysis). In this paper, two approaches are discussed within NJL-type models with Polyakov Loop that reproduce both effects.
We investigate the effects of strong magnetic fields on the QCD phase structure at vanishing density by solving the gluon and quark gap equations, and by studying the dynamics of the quark scattering with the four-fermi coupling. The chiral crossover temperature as well as the chiral condensate are computed. For asymptotically large magnetic fields we find magnetic catalysis, while we find inverse magnetic catalysis for intermediate magnetic fields. Moreover, for large magnetic fields the chiral phase transition for massless quarks turns into a crossover. The underlying mechanisms are then inv…
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
We explore the effect of magnetic field on chiral condensation in QCD via a simple bottom up holographic model which inputs QCD dynamics through the running of the anomalous dimension of the quark bilinear. Bottom up holography is a form of effective field theory and we use it to explore the dependence on the coefficients of the two lowest order terms linking the magnetic field and the quark condensate. In the massless theory, we identify a region of parameter space where magnetic catalysis occurs at zero temperature but inverse magnetic catalysis at temperatures of order the thermal phase tra…
Motivated by recent work on inverse magnetic catalysis at finite temperature, we study the quark-meson model using both dimensional regularization and a sharp cutoff. We calculate the critical temperature for the chiral transition as a function of the Yukawa coupling in the mean-field approximation varying the renormalization scale and the value of the ultraviolet cutoff. We show that the results depend sensitively on how one treats the fermionic vacuum fluctuations in the model and in particular on the regulator used. Finally, we explore a $B$-dependent transition temperature for the Polyakov…
In this paper we explore the chiral phase transition in QCD within the three-flavor Nambu-Jona-Lasinio (NJL) model with a negative coupling constant in the isoscalar axial-vector channel, which is associated with a polarized instanton--anti-instanton molecule background. The QCD phase diagram described in this scenario shows a new first order phase transition around the transition temperature $T_c$ toward a phase without chiral condensates, but with nontrivial dynamic chiral chemical potentials for the light quarks, spontaneously giving rise to local $\mathcal {CP}$ violation and local chirali…
We compute the critical temperature for the chiral transition in the background of a magnetic field in the linear sigma model, including the quark contribution and the thermo-magnetic effects induced on the coupling constants at one loop level. We show that the critical temperature decreases as a function of the field strength. The effect of fermions on the critical temperature is small and the main effect on this observable comes from the charged pions. The findings support the idea that the anticatalysis phenomenon receives a contribution due only to quiral symmetry effects independent of th…
We evaluate the impact of an external magnetic field on the chiral symmetry and confinement-deconfinement transition temperatures by using a vector-vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature $T$ and magnetic field strength $eB$ ($e$ represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral ($T_c^χ$) and deconfinement ($T_c^c$) transitions from their inflection points…
The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions under magnetic fields is investigated in a Pauli-Villars regularized PNJL model. A linear-in-$B$ term for quark anomalous magnetic moment is introduced to the Lagrangian density of our model, and it plays the role of inverse catalysis to the phase transitions. With fixed magnetic field, the critical temperature decreases with quark AMM. When fixing quark AMM, the critical temperature increases with magnetic field for a small quark AMM, but decreases with magnetic field for a large quar…
The phenomenon of magnetic catalysis of chiral symmetry breaking in the quantum chromodynamic theory in the framework of logarithmic quark sigma model is studied. Thermodynamic properties are calculated in the mean-field approximation such as the pressure, the entropy density, the energy density, and measure interaction. The pressure, the entropy density, and the energy density increase with increasing temperature and an external magnetic field. The critical temperature increases with increasing an external magnetic field. In addition, the chiral phase transition is crossover in the presence o…
Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at $T=0$ is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalizatio…
The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(μ_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $μ_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $μ_B^c$ d…
We investigate the QCD phase diagram for nonzero background magnetic fields using first-principles lattice simulations. At the physical point (in terms of quark masses), the thermodynamics of this system is controlled by two opposing effects: magnetic catalysis (enhancement of the quark condensate) at low temperature and inverse magnetic catalysis (reduction of the condensate) in the transition region. While the former is known to be robust and independent of the details of the interactions, inverse catalysis arises as a result of a delicate competition, effective only for light quarks. By per…
The dependence of the QCD coupling constant with a strong magnetic field and the implications for the critical temperature of the chiral phase transition are investigated. It is found that the coupling constant becomes anisotropic in a strong magnetic field and that the quarks, confined by the field to the lowest Landau level where they pair with antiquarks, produce an antiscreening effect. These results lead to inverse magnetic catalysis, providing a natural explanation for the behavior of the critical temperature in the strong-field region.
In this work, we consider the effect of a constant anomalous magnetic moment (AMM) of quarks in the SU(2) Nambu--Jona-Lasinio model in the mean field approximation. To this end, we use the Schwinger {\it ansatz}, which represents a linear magnetic field term in the Lagrangian. A regularization method inspired in the vacuum magnetic regularization (VMR) is adopted to avoid ultraviolet divergences. Our results indicate a smooth decrease of the pseudocritical temperature and quark condensates for magnetic fields $B \leq 0.1$ GeV$^2$ when a sizable AMM is considered. We found only a small window f…
We investigate the magnetism of QCD matter and pion mass under magnetic field considering the contribution from the tensor-type spin polarization and the anomalous magnetic moment (AMM) of quarks. It is found that the tensor-type spin polarization (TSP) induces the magnetic catalysis of chiral condensate and diamagnetism (negative magnetic susceptibility) of quark matter at low temperature, both neutral and charged pion masses increase quickly with magnetic field in the case of TSP. The anomalous magnetic moment (AMM) of quarks induces magnetic inhibition and a magnetic dependent AMM causes in…
We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high …
We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli-Villars regularization scheme.
We study the behavior of strongly interacting matter under a strong external magnetic field in the context of chiral quark models that include nonlocal interactions. In particular, we analyze the influence of a constant magnetic field on the chiral quark condensates at zero and finite temperature, studying the deconfinement and chiral restoration critical temperatures and discussing the observed "magnetic catalysis" and "inverse magnetic catalysis" effects. In addition, we analyze in this framework the behavior of the $π^0$ mass and decay constant. The predictions of nonlocal chiral quark mode…
We study the in-medium masses of the heavy quarkonium (charmonium and bottomonium) states in isospin asymmetric nuclear matter in presence of an external magnetic field. The mass modifications of the heavy quarkonia are obtained from the medium modifications of a scalar dilaton field, $χ$, calculated within a chiral effective model. The dilaton field is introduced in the model through a scale invariance breaking logarithmic potential, and, simulates the gluon condensates of QCD. Within the chiral effective model, the values of the dilaton field along with the scalar (isoscalar, $σ(\sim \langle…
The effect of anomalous magnetic moment of quarks on thermodynamic properties of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio model at finite temperature $T$, chemical potential $μ$, and in the presence of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$ ansatz for the quark anomalous magnetic moment in term of the nonperturbative Bohr magneton is considered. In a two-dimensional flavor space, it leads to the correction $\hat{T}_{Sch}=\hatκ\hat{Q} eB$ in the energy dispersion relation of quarks. Here, $\hat{Q}$ is the quark charge matri…
In the chiral symmetric phase, the polarized instanton--anti-instanton molecule pairing induces a nontrivial repulsive interaction in the iso-scalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration phase, there is a first order phase transition for the spontaneous generation of local CP violation and chiral imbalance. Furthermore, it is found that external magnetic fields will lower the critical temperature for the local CP-odd phase transition and catalyze the chiral imbalance, which destroys the chiral condensate with pairing quarks betw…
We find that the inverse magnetic catalysis for $U(1)$ axial symmetry (AIMC: axial inverse magnetic catalysis) can emerge around the chiral crossover regime in the thermomagnetic QCD with 2 + 1 flavors at physical point. This phenomenon can be correlated with the IMC for the chiral $SU(2)_L \times SU(2)_R$ symmetry (CIMC: chiral IMC). We explicitly observe the AIMC based on a Nambu-Jona-Lasinio model with 2 + 1 quark flavors, where introduced anomalous magnetic moments of the quarks play the essential role to drive both the CIMC and AIMC. Our finding is shortly testable on lattices. Possible p…
Some of the advances made in the literature to understand the phase transitions of quark matter in the presence of strong magnetic field and finite temperature (zero quark chemical potential) are reviewed. We start by discussing the physics behind the Magnetic catalysis (MC) at zero/finite temperature and then focus on the lattice predictions for inverse magnetic catalysis (IMC) at high temperature and strong magnetic fields. Possible explanations for the IMC are covered as well. Finally, we discuss recent efforts to modify QCD (quantum chromodynamics) effective models in order to reproduce th…
We compute the vacuum one-loop quark-gluon vertex correction at zero temperature in the presence of a magnetic field. From the vertex function we extract the effective quark-gluon coupling and show that it grows with increasing magnetic field strength. The effect is due to a subtle competition between the color charge associated to gluons and the color charge associated to quarks, the former being larger than the latter. In contrast, at high temperature the effective thermo-magnetic coupling results exclusively from the contribution of the color charge associated to quarks. This produces a dec…
We study the impact of steady, homogeneous, and external parallel electric and magnetic field strength ($eE\parallel eB$), on the chiral symmetry breaking-restoration and confinement-deconfinement phase transitions. We also sketch the phase diagram of quantum chromodynamics (QCD) at finite temperature $T$ and in the presence of background fields. Our unified formalism for this study is based on the Schwinger-Dyson equations, symmetry preserving vector-vector contact interaction model of quarks, and the proper time regularization scheme. At $T=0$, in the purely magnetic case ($eE\rightarrow 0$)…
The kurtosis and skewness of net baryon-number fluctuations are studied for the magnetized phase diagram of three-flavor quark matter within the Polyakov extended Nambu$-$Jona-Lasinio model. Two models with magnetic catalysis and inverse magnetic catalysis are considered. Special attention is given to their behavior in the neighborhood of the light and strange critical end points (CEPs). Several isentropic trajectories that come close the CEPs are studied in order to analyze possible signatures of a CEP in the presence of external magnetic fields. The effect of the magnetic field on the veloci…
The chiral symmetry breaking in the presence of an external magnetic field is studied in the framework of logarithmic quark-sigma model with three flavors (u,d,s). The effective logarithmic mesonic potential is extended to strange quark and is numerically solved in the mean-field approximation. The present results show that the chiral symmetry breaking is sensitive for the strange quark flavour in the presence an external magnetic field. In addition, the effect of the free parameters is studied. A comparison with original sigma model is discussed.
Scalar sigma meson at finite temperature in nonlocal quark model
在基于夸克Dyson-Schwinger方程和介子Bethe-Salpeter方程的具有可分离相互作用核的非定域模型框架下，研究了π和σ束缚态的性质和温度行为. M_pi（T）、f_pi（T）、M_sigma（T）和Gamma_{sigma -> pi pi}（T）被认为是在解封闭和手性恢复跃迁之上和之下。
Sigma-term physics in the perturbative chiral quark model
本文应用微扰手征夸克模型（PCQM）分析了介子-重子σ项。这些量的解析表达式得到的基本参数的低能π介子核子物理（弱π衰变常数，轴向核子耦合，强π介子核子形状因子）和只有一个模型参数（半径的核子三夸克核心）。我们的结果为约45 MeV的π N σ项是在良好的协议与Gasser，Leutwyler和Sainio使用色散关系技术和利用手征对称性约束推导出的值。
