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, here 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 we have obtained the pressure of QCD matter, both with and without the high temperature expansion. The results with high $T$ expansions 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. Analytic expressions for Debye mass are 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 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 behavior 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.
Highlights
Quark gluon plasma (QGP) is a thermalized color deconfined state of nuclear matter in the regime of quantum chromodynamics (QCD) under extreme conditions such as very high temperature and/or density
We note that for jeBj 1⁄4 0 one gets back usual one-loop hard-thermal-loop perturbation theory (HTLpt) pressure [69,70,71,72,73,74,75,76,77]. From both plots one can observe that the low T (
In this paper we presented a systematic framework based on the general structure of two-point functions of a fermion and a gauge boson to evaluate the QCD pressure in nontrivial backgrounds, viz., when both heat bath and magnetic field are considered together
Summary
Quark gluon plasma (QGP) is a thermalized color deconfined state of nuclear matter in the regime of quantum chromodynamics (QCD) under extreme conditions such as very high temperature and/or density. In this paper-II, for the first time, by considering the general two point function of a quark [47] and a gluon [45] in a hot but weakly magnetized deconfined QCD medium, we shall compute the pressure of quark-gluon plasma within HTL approximation. 1, Nc is the number of color in fundamental representation, and mD is the Debye screening mass in HTL approximation
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