Pressure of a weakly magnetized hot and dense deconfined QCD matter in one-loop hard-thermal-loop perturbation theory

Abstract

We consider our recently obtained general structure of two point (self-energy and propagator) functions of quarks and gluons in a nontrivial background like a heat bath and an external magnetic field. Based on this we have computed free energy and pressure of quarks and gluons for a magnetized hot and dense deconfined QCD matter in weak field approximation. For heat bath we have used hard thermal loop perturbation theory (HTLpt) in presence of finite chemical potential. For weak field approximations, the results are completely analytic and gauge independent but depends on the renormalization scale in addition to the temperature, chemical potential and the external magnetic field. We also discuss the modification of QCD Debye mass of such matter for an arbitrary magnetic field. An analytic expression for Debye mass is also obtained for both strong and weak field approximation. It is found to exhibit some interesting features depending upon the three different scales, i.e, the thermal quark mass, temperature and the strength of the magnetic field. The various divergences appearing in the quark and gluon free energies are regulated through appropriate counter terms. In weak field approximation, the low temperature behaviour of the pressure is found to strongly depend on the magnetic field than that at high temperature. We also discuss the specific problem with one-loop HTLpt associated with the over-counting of certain orders in coupling.

Anisotropic pressure of deconfined QCD matter in presence of strong magnetic field within one-loop approximation

“…N ξ = 1/(2πξ) D/2 is the normalization that originates from the introduction of a Gaussian integral at each location of position while averaging over the gauge condition function with a width ξ, the gauge fixing parameter. Gluon free energy can now be written [21] as…”

“…In recent years numerous activities have been in progress such as magnetic catalysis [1][2][3], inverse magnetic catalysis [4][5][6][7][8][9][10][11][12] and chiral magnetic effect [13][14][15] at finite temperature, and the chiral-and color-symmetry broken/restoration phase [16][17][18][19][20]. Also in progress is the study related to the equation of state (EoS) in thermal perturbative QCD (pQCD) models [21,22], holographic models [23,24] and various thermodynamic properties [19,20,25,26], refractive indices and decay constant of hadrons [27][28][29][30][31][32][33][34]; soft photon production from conformal anomaly [35,36] in HIC; modification of dispersion properties in a magnetized hot QED [37,38] and QCD [38][39][40][41] medium; and various transport coefficients [42]…”

“…[68] that is limited to the temperature range (100-300)MeV. Recently we have computed [21] the thermomagnetic EoS for the hot magnetized QCD medium within the weak magnetic field and HTL approximation. Also using HTL approximation, some thermodynamic quantities in lowest Landau level (LLL) within the strong field approximation has been numerically computed in Ref.…”

Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium

“…In weak magnetic field approximation α does not contribute upto O[(eB)] 2 , one gets simple form of the above dispersive modes [19] P 2 − σ = 0,…”

“…Recently, several studies have found the effect of magnetic catalysis [8][9][10], i.e., the enhancement of phase transition temperature of QCD matter in presence of external magnetic field, whereas, some results of inverse magnetic catalysis [11][12][13][14][15][16][17][18] have been reported. Various properties of QCD matter at weak coupling in presence of magnetic field is being studied including the equation of state [19][20][21], transport properties [22][23][24]. Modification of QCD Debye mass and the two point correlation functions of quarks [25] and gluons [26][27][28] i.e., partons have been analyzed recently.…”