One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

Abstract

Abstract:We have studied how the equation of state of thermal QCD with two light flavors is modified in a strong magnetic field. We calculate the thermodynamic observables of hot QCD matter up to one-loop, where the magnetic field affects mainly the quark contribution and the gluon part is largely unaffected except for the softening of the screening mass. We have first calculated the pressure of a thermal QCD medium in a strong magnetic field, where the pressure at fixed temperature increases with the magnetic field faster than the increase with the temperature at constant magnetic field. This can be understood from the dominant scale of thermal medium in the strong magnetic field, being the magnetic field, in the same way that the temperature dominates in a thermal medium in the absence of magnetic field. Thus although the presence of a strong magnetic field makes the pressure of hot QCD medium larger, the dependence of pressure on the temperature becomes less steep. Consistent with the above observations, the entropy density is found to decrease with the temperature in the presence of a strong magnetic field which is again consistent with the fact that the strong magnetic field restricts the dynamics of quarks to two dimensions, hence the phase space becomes squeezed resulting in the reduction of number of microstates. Moreover the energy density is seen to decrease and the speed of sound of thermal QCD medium increases in the presence of a strong magnetic field. These findings could have phenomenological implications in heavy ion collisions because the expansion dynamics of the medium produced in non-central ultra-relativistic heavy ion collisions is effectively controlled by both the energy density and the speed of sound.

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

“…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]…”

“…Also using HTL approximation, some thermodynamic quantities in lowest Landau level (LLL) within the strong field approximation has been numerically computed in Ref. [22]. However, for the gluonic case, this calculation assumes that the only effect of the magnetic field is to shift the Debye mass without any change in the general structure of two point functions at the finite temperature.…”

“…It has explicitly been shown [38][39][40][41] that the presence of an external magnetic field breaks the rotational symmetry and the situation is quite different from what has been assumed in Ref. [22]. This seeks an improvement of the general structure of two point functions used in Ref.…”

Viscosity vs. vorticity in the quark-gluon plasma

“…The underlying physics of this phenomenon can only be a matter of conjecture. We may note, however, that it has been argued [41] that strong magnetic fields in the QGP (at LHC rather than RHIC impact energies) constrict the relevant phase space in a specific manner, and so tend to reduce the entropy density of the plasma. It may well be that some analogous mechanism is at work here, since vorticity and magnetic fields often have similar effects 12 .…”

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

“…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.…”