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We consider our recently obtained general structure of two point (self-energyand propagator) functions of quarks and gluons in a nontrivial background likea heat bath and an external magnetic field. Based on this, here we havecomputed free energy and pressure of quarks and gluons for a magnetized hot anddense deconfined QCD matter in weak field approximation. For heat bath we haveused hard thermal loop perturbation theory (HTLpt) in presence of finitechemical potential. For weak field approximations we have obtained the pressureof QCD matter, both with and without the high temperature expansion. Theresults with high $T$ expansions are completely analytic and gauge independentbut depends on the renormalization scale in addition to the temperature,chemical potential and the external magnetic field. We also discuss themodification of QCD Debye mass of such matter for an arbitrary magnetic field.Analytic expressions for Debye mass are also obtained for both strong and weakfield approximation. It is found to exhibit some interesting features dependingupon the three different scales, i.e, the quark mass, temperature and thestrength of the magnetic field. The various divergences appearing in the quarkand gluon free energies are regulated through appropriate counter terms. Inweak field approximation, the low temperature behavior of the pressure is foundto strongly depend on the magnetic field than that at high temperature. We alsodiscuss the specific problem with one-loop HTLpt associated with theover-counting of certain orders in coupling.

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