Relativistic BDNK MHD Evolution in a Boost-Invariant Medium and Its Impact on Dilepton Production

TL;DR

This paper develops a causal, first-order relativistic MHD model incorporating magnetic and thermal interactions in a boost-invariant medium, analyzing effects on dilepton production in heavy-ion collisions.

Contribution

It introduces a coupled evolution framework for temperature and magnetic fields in relativistic MHD, highlighting their mutual backreaction and impact on dilepton emission.

Findings

Magnetic field responds more strongly to temperature changes than vice versa.

Magnetic feedback causes a suppression of low-mass dilepton spectra.

Enhanced cooling due to magnetic-thermal coupling influences dilepton yields.

Abstract

In this work, we explore a Bemfica--Disconzi--Noronha--Kovtun (BDNK)-type formulation of relativistic magnetohydrodynamics, providing a causal and stable first-order description of dissipative fluids. We derive coupled evolution equations for the temperature and magnetic field in a boost-invariant Bjorken background, restricting to $(0+1)$D dynamics while retaining all relevant first-order gradients. By varying the transport coefficients, we disentangle the interplay and mutual backreaction between the thermal and electromagnetic sectors. We find that, for comparable transport coefficients, the magnetic field responds more strongly to changes in the temperature evolution, while its feedback on the temperature remains subleading. We further analyze the number density evolution, which is sensitive to both temperature gradients and magnetic-field dynamics. We also investigate implications for dilepton production, where the magnetic field modifies the emission rate via the relaxation time in a kinetic-theory framework. The coupled evolution leads to a suppression of the low-mass dilepton spectrum, primarily driven by enhanced cooling in the presence of positive coupling between temperature gradients and magnetic-field evolution, as compared to scenarios without such feedback.