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

## TL;DR

This paper calculates the anisotropic pressure and magnetization of hot, dense QCD matter under strong magnetic fields using one-loop approximation, providing analytic expressions relevant for heavy-ion collision studies.

## Contribution

It presents a novel analytic calculation of anisotropic pressure and magnetization of deconfined QCD matter in strong magnetic fields within the one-loop approximation.

## Key findings

- QCD matter exhibits paramagnetic behavior under strong magnetic fields.
- Pressure differs along and perpendicular to the magnetic field direction.
- Analytic expressions for pressure and magnetization are derived.

## Abstract

Considering the general structure of the two point functions of quarks and gluons, we compute the free energy and pressure of a strongly magnetized hot and dense QCD matter created in heavy-ion collisions. In presence of strong magnetic field we found that the deconfined QCD matter exhibits a paramagnetic nature. One gets different pressure in a direction parallel and perpendicular to magnetic field due to the magnetization acquired by the system. We obtain both longitudinal and transverse pressure, and magnetization of a hot deconfined QCD matter in presence of magnetic field. We have used hard thermal loop approximation (HTL) for heat bath. We obtained completely analytic expression for pressure and magnetization under certain approximation. Various divergences appearing in free energy are regulated using appropriate counter terms. The obtained anisotropic pressure may be useful for magnetohydrodynamics description of a hot and dense deconfined QCD matter produced in heavy-ion collisions.