Inverse magnetic catalysis and regularization in the quark-meson model

TL;DR

This paper investigates inverse magnetic catalysis in the quark-meson model, analyzing how different regularization methods and the treatment of vacuum fluctuations influence the critical temperature for chiral symmetry restoration.

Contribution

It compares dimensional regularization and cutoff schemes in the quark-meson model and examines the impact of vacuum fluctuation treatment on inverse magnetic catalysis.

Findings

Results depend on the regularization scheme and vacuum fluctuation treatment.

The transition temperature T_0(B) cannot decrease with increasing magnetic field B.

Findings align with previous mean-field studies on inverse magnetic catalysis.

Abstract

Motivated by recent work on inverse magnetic catalysis at finite temperature, we study the quark-meson model using both dimensional regularization and a sharp cutoff. We calculate the critical temperature for the chiral transition as a function of the Yukawa coupling in the mean-field approximation varying the renormalization scale and the value of the ultraviolet cutoff. We show that the results depend sensitively on how one treats the fermionic vacuum fluctuations in the model and in particular on the regulator used. Finally, we explore a $B$-dependent transition temperature for the Polyakov loop potential $T_0(B)$ using the functional renormalization group. These results show that even arbitrary freedom in the function $T_0(B)$ does not allow for a decreasing chiral transition temperature as a function of $B$. This is in agreement with previous mean-field calculations.