Hot Quark Matter Research Articles

Analysis of charged hadrons’ transverse momentum distributions in p + Pb and Xe + Xe collisions at LHC energies

This paper is focused on comparative analysis of transverse momentum ( pT ) distributions across two different sets of experimental data from ALICE at the LHC, juxtaposing with the Monte-Carlo models EPOS-LHC and EPOS 1.99 simulations. The chosen collision sets have approximately same per nucleon energy. We analyze the transverse momentum spectra of hadrons ( π++π−, K++K− and p+p¯ ) in p+Pb collisions at sNN= 5.02 TeV, and Xe + Xe collisions at sNN= 5.44 TeV spanning a rapidity range of 0 < yCM < 0.5, centrality of 0 to 5% (the most central or head-on collisions). Analysis of the Hadrons yield is crucial for understanding the mechanism of underlying hadronization in the hot and dense quark matter produced in relativistic heavy ion collisions. The experimental results are compared with the predictions of hydrodynamic models EPOS-LHC and EPOS-1.99. It is notably found that the maximum yields of various particles occur at low pT. Furthermore, the comparison showed a slightly better agreement between experimental results and the predictions of the EPOS-LHC as opposed to that of EPOS-1.99. The EPOS-LHC model significantly shows an enhanced agreement with experimental results in the case of Xe+Xe collisions as compared to p+Pb collisions.

Causality violation and the speed of sound of hot and dense quark matter in the Nambu–Jona-Lasinio model

The Nambu--Jona-Lasinio model is widely used to study strong-interaction phenomena in vacuum and quark matter. Since the model is nonrenormalizable, one needs to work within a specific regularization scheme to obtain finite results. Here we show that a commonly used cutoff regularization scheme leads to unphysical results, such as superluminal speed of sound and wrong high-temperature behavior of the specific heat and other thermodynamical quantities. Such a troublesome feature of the cutoff regularization invalidates the model for temperature and baryon density values relevant to the phenomenology of heavy-ion collisions and compact stars. We show that the source of the problems stems from cutting off momentum modes in finite integrals depending on thermal distribution functions in the grand canonical potential. The problems go away when taking into account the full momentum range of those integrals. Explicit examples are worked out in the SU(2)-flavor version of the model.

Heavy quarkonia in a baryon asymmetric strongly magnetized hot quark matter

Recently there is a resurrection in the study of heavy quark bound states in a hot and baryonless matter with an ambient magnetic field but the matter produced at heavy-ion collider experiments is not perfectly baryonless, so we wish to explore the effect of small baryon asymmetry on the in-medium properties of the heavy quark bound states submerged in a strongly magnetized hot quark matter. Therefore, we have first given a revisit to the general covariant tensor structure of gluon self-energy in the above environment to compute the resummed propagator for gluons. This resummed propagator embodies the properties of medium, which gets translated into the (complex) potential between Q and Q¯ placed in the medium. We observe that the baryon asymmetry makes the real-part of potential slightly more attractive and weakens the imaginary-part. This opposing effects thus lead to the enhancement of binding energies and the reduction of thermal widths of QQ¯ ground states, respectively. Finally, the properties of quarkonia thus deciphered facilitate to compute the dissociation points of J/ψ and ϒ, which are found to have slightly larger values in the presence of baryon asymmetry. For example, J/ψ gets dissociated at 1.64Tc, 1.69Tc, and 1.75Tc, whereas ϒ is dissociated at 1.95Tc, 1.97Tc and 2.00Tc, for μ=0,60 and 100 MeV, respectively. This observation prevents early dissociation of quarkonia in the matter produced at ultrarelativistic heavy ion collisions with a small net baryon number, compared to the ideal baryonless matter.

Properties of neutral mesons in a hot and magnetized quark matter: Size-dependent effects

In this work we investigate the combined finite-size and thermomagnetic effects on the properties of neutral mesons in a hot medium, in the context of the Nambu--Jona-Lasinio model. In particular, by using the mean-field approximation and the Schwinger proper time method in a toroidal topology with periodic and antiperiodic conditions, we evaluate the chiral phase transition, the critical coupling, the constituent quark mass and meson observables like the ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\sigma}$ meson masses and pion decay constant under the change of the size, temperature and strength of external magnetic field. The results indicate that the observables are strongly affected by the conjoint effects of relevant variables and also by the periodicity of the boundary conditions chosen, and the net result will depend on the balance of these competing phenomena.

Properties of Hot Quark Matter with Neutrino Confinement in the NJL Model

The thermodynamic characteristics of hot $\beta$-equilibrium three-flavor quark matter with neutrino confinement are studied in terms of the local SU(3) Nambu-Jona-Lasinio (NJL) model, which also accounts for the 't Hooft interaction which leads to mixing of quark flavors. For different temperatures $T \in [20 \div 100]$ MeV and baryon number densities $n_B \in [0 \div 1.8]$ fm$^{-3}$ the constituent quark masses, quark condensates, and relative contributions of individual types of particles to the pressure and chemical potentials of the constituent particles are determined. In order to determine the role of neutrinos in the hot quark matter, the pressures and energies in states with and without neutrinos are compared. Keywords: hot quark matter: neutrino confinement: NJL model: equation of state.

Impacts of inverse magnetic catalysis on screening masses of neutral pions and sigma mesons in hot and magnetized quark matter

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 a 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., ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\sigma}$ mesons, as well as the screening mass differences between them. Particularly, it is found that the $eB$ dependences of two alternative (pseudo)critical temperatures for the chiral transition defined by $\ensuremath{\sigma}\ensuremath{-}{\ensuremath{\pi}}^{0}$ meson screening mass differences are consistent with that defined by the quark condensate.

The axion potential in quark matter

We study the QCD axion potential in hot and dense quark matter, within an NJL-like model that includes the coupling of the axion to quarks. Firstly we compute the effect of the chiral QCD crossover on the axion mass and self-coupling. Then, we compute the axion potential and study the domain walls. We find that the energy barrier between two adjacent vacuum states decreases in the chirally restored phase: this results in a lower surface tension of the walls. Finally we comment on the possibility of abundant production of walls in hot and dense quark matter.

Thermoelectric transport coefficients of quark matter

A thermal gradient and/or a chemical potential gradient in a conducting medium can lead to an electric field, an effect known as thermoelectric effect or Seebeck effect. In the context of heavy-ion collisions, we estimate the thermoelectric transport coefficients for quark matter within the ambit of the Nambu–Jona Lasinio (NJL) model. We estimate the thermal conductivity, electrical conductivity, and the Seebeck coefficient of hot and dense quark matter. These coefficients are calculated using the relativistic Boltzmann transport equation within relaxation time approximation. The relaxation times for the quarks are estimated from the quark–quark and quark–antiquark scattering through meson exchange within the NJL model. As a comparison to the NJL model estimation of the Seebeck coefficient, we also estimate the Seebeck coefficient within a quasiparticle approach.

Inverse magnetorotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

We study the properties of a hot and magnetized quark matter in a rotating cylinder in the presence of a constant magnetic field. To do this, we solve the corresponding Dirac equation using the Ritus eigenfunction method. This leads to the energy dispersion relation, Ritus eigenfunctions, and the quantization relation for magnetized fermions. To avoid causality-violating effects, we impose a certain global boundary condition, and study its effect, in particular, on the energy eigenmodes and the quantization relations of fermions. Using the fermion propagator arising from this method, we then solve the gap equation at zero and nonzero temperatures. At zero temperature, the dynamical mass $\bar{m}$ does not depend on the angular frequency, as expected. We thus study its dependence on the distance $r$ relative to the axis of rotation and the magnetic field $B$, and explore the corresponding finite size effect for various couplings $G$. We then consider the finite temperature case. The dependence of $\bar{m}$ on the temperature $T$, magnetic field $B$, angular frequency $\Omega$, and distance $r$ for various $G$ is studied. We show that $\bar{m}$ decreases, in general, with $B$ and $\Omega$. This is the ''inverse magneto-rotational catalysis (IMRC)'' or the ''rotational magnetic inhibition'', previously discussed in the literature. To explore the evidence of this effect in the phase diagrams of our model, we examine the phase portraits of the critical temperature $T_c$ as well as the critical angular frequency $\Omega_c$ with respect to $G, B,\Omega$, and $r$ as well as $G, B, T$, and $r$, respectively. We show that $T_{c}$ and $\Omega_c$ decrease, in particular, with $B$. This is interpreted as clear evidence for IMRC.

Analytical solution of magneto-hydrodynamics with acceleration effects of Bjorken expansion in heavy-ion collisions

In this article, we aim to study, in an analytical manner, the 1 + 1 longitudinal acceleration expansion of hot and dense quark matter as a conducting relativistic fluid with the electric conductivity \(\sigma \). To this end, the plasma is inserted in the presence of electric and magnetic fields, which are perpendicular together in the transverse plane. To be more realistic, we generalize the Bjorken solution, which includes the acceleration effects on the fluid expansion. We then apply a perturbation fashion in the initial condition to solve the relativistic magneto-hydrodynamics equations. This procedure leads us to achieve the exact algebraic expressions for both electric and magnetic fields. In the process, we also find the effects of the electromagnetic fields on the fluid’s acceleration and the energy density correction obtained from the magneto-hydrodynamics solutions.

Hot Quark Matter with Neutrino Confinement in Terms of the Local Nambu - Jona-Lasinio SU(3) Model

The thermodynamic characteristics of hot β-equilibrium, electrically neutral, three-flavor quark matter with neutrino confinement are studied. This kind of quark-lepton system is described thermodynamically using a local SU(3) Nambu - Jona-Lasinio (NJL) model that includes the ‘t Hooft interaction, leading to a mixing effect for the quark flavors. The energy density e and pressure P of the quark matter are determined numerically for baryon number densities in the range of nB ϵ [0.02 ÷ 1.8] fm-3 and temperatures of T ϵ [0 ÷ 100]MeV. These results are compared with the results for cold quark matter calculated in the same model framework but under the assumption that all neutrinos have already left the system. The dependence of the contribution of the individual quark flavors to the baryonic charge of the system for different temperatures is discussed. The isothermal and adiabatic speeds of sound in hot quark matter are both calculated as functions of the baryonic number density.

Renormalization group improved pressure for hot and dense quark matter

We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.

Dilepton production from magnetized quark matter with an anomalous magnetic moment of the quarks using a three-flavor PNJL model

Dilepton production from hot, dense and magnetized quark matter is studied using the three-flavor Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model in which the anomalous magnetic moment (AMM) of the quarks is also taken into consideration. This is done by first evaluating the thermo-magnetic spectral function of the vector current correlator employing the real time formalism of finite temperature field theory and the Schwinger proper time formalism. The constituent quark mass which goes as an input in the expression of the dilepton production rate (DPR), has been calculated using the three-flavor PNJL model employing Pauli-Villiars (PV) regularization. The obtained constituent quark mass being strongly dependent on the temperature, density, magnetic field and AMM of the quarks, captures the effect of `strong' interactions specifically around the (pseudo) chiral and confinement-deconfinement phase transition regions. The analytic structure of the spectral function in the complex energy plane has been analyzed in detail and a non-trivial Landau cut is found in the physical kinematic domains resulting from the scattering of the Landau quantized quark/antiquark with the photon which is purely a finite magnetic field effect. Due to the emergence of the Landau cut along with the usual unitary cut, the DPR is found to be largely enhanced in the low invariant mass region. Owing to the magnetic field and AMM dependence of the thresholds of these cuts, we find that the kinematically forbidden gap between the Unitary and Landau cuts vanishes at sufficiently high temperature, density and magnetic field leading to the generation of a continuous spectrum of dilepton emission over the whole invariant mass region. In order to see the effects of strangeness and confinement-deconfinement, the rates are compared with the three-flavor NJL and the two-flavor NJL and PNJL models.

Inverse magnetic catalysis: how much do we know about?

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 the IMC observed on the lattice simulations. We emphasize the fact that applying thermo-magnetic effects on the coupling constant of the NJL model significantly improve the effectiveness of the NJL model to obtain a reasonable physical description of hot and magnetized quark matter being in agreement with lattice results.

Modified MIT Bag Models—part II: QCD phase diagram and hot quark stars

In the present work we use the modified versions of the MIT bag model, on which both a vector field and a self-interacting term are introduced, to obtain hot quark matter and to investigate the QCD phase diagram. We first analyze two-flavored quark matter constrained to both the freeze-out and the liquid-gas phase transition at the hadronic phase. Later, three-flavored quark matter subject to β equilibrium and charge neutrality is used to compute quark star macroscopic properties, which are confronted with recent observational massive and canonical star radius results. Finally, a comparison with QCD phase diagrams obtained from the Nambu-Jona-Lasinio model is performed.

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.

Magnetized hot and dense quark matter in the Polyakov Nambu–Jona–Lasinio model

In a strong magnetic field, the hot dense quark matter is investigated in the Polyakov Nambu–Jona–Lasinio model. The value of a traced Polyakov loop is found as a nonmonotonous function of the chemical potential at lower magnetic fields and as a monotonous increasing function at high magnetic fields. The decreasing pseudocritical temperatures for the chiral restoration and the deconfinement crossover are reproduced by a temperature-and-magnetic-field-dependent coupling constant to reflect the inverse magnetic catalysis. Furthermore, the deconfined but chiral broken phase can be observed in the split region of the Tχ and Tϕ.

Effects of quark anomalous magnetic moment on the thermodynamical properties and mesonic excitations of magnetized hot and dense matter in PNJL model

Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the $ 2 $-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement transition temperatures in contrast to an enhancement in the chiral transition temperature in its absence. Using standard techniques of finite temperature field theory, the two point thermo-magnetic mesonic correlation functions in the scalar ($\sigma$) and neutral pseudoscalar ($\pi^0$) channels are evaluated to calculate the masses of $\sigma $ and $ \pi^0 $ considering the AMM of the quarks.

Effects of the anomalous magnetic moment of quarks on the dilepton production from hot and dense magnetized quark matter using the NJL model

Dilepton production rate (DPR) from hot and dense quark matter is studied in the presence of an arbitrary external magnetic field using the 2-flavour Nambu--Jona-Lasinio (NJL) model. The anomalous magnetic moment (AMM) of the quarks is taken into consideration while calculating the constituent quark mass as well as the DPR from the thermo-magnetic medium. An infinite number of quark Landau levels is incorporated so that no approximations are made on the strength of the background magnetic field. The analytic structure of the two point vector current correlation function in the complex energy plane reveals that, in addition to the usual Unitary cut, a non-trival Landau cut appears in the physical kinematic domains solely due to the external magnetic field. Moreover, these kinematic domains of the Unitary and Landau cuts are found to be significantly modified due to the AMM of the quarks. With finite AMM of the quarks, for certain values of the external magnetic field, the kinematically forbidden gap between the Unitary and Landau cuts are shown to vanish leading to the generation of a continuous spectrum of dilepton emission over the whole invariant mass region not observed earlier.

Characteristics of Hot Quark Matter with Neutrino Confinement

The MIT quark bag model is used to determine the thermodynamic characteristics of hot strange quark matter that is opaque to neutrinos. Three different variants of the lepton content of hot quark matter are considered. The numerical calculations are done for different temperatures and lepton charge densities. It is shown that in hot (kT~100 MeV) quark matter there are roughly as many neutrinos as massive leptons, the total energy of the leptons is 4-20 percent of the energy of the quarks, and during cooling an energy on the order of 30-40 percent of the total energy is released.