# Magnetic catalysis and inverse catalysis for heavy pions

## TL;DR

This study uses lattice QCD simulations to explore how magnetic fields influence the QCD phase transition, revealing a critical pion mass above which inverse catalysis disappears and showing that magnetic fields generally lower the transition temperature.

## Contribution

The paper identifies the pion mass threshold for inverse catalysis and demonstrates that magnetic fields tend to decrease the QCD transition temperature across different quark masses.

## Key findings

- Inverse catalysis occurs only for light quarks below a certain pion mass.
- Magnetic fields reduce the QCD transition temperature.
- Heavy pions exhibit magnetic catalysis without inverse effects.

## Abstract

We investigate the QCD phase diagram for nonzero background magnetic fields using first-principles lattice simulations. At the physical point (in terms of quark masses), the thermodynamics of this system is controlled by two opposing effects: magnetic catalysis (enhancement of the quark condensate) at low temperature and inverse magnetic catalysis (reduction of the condensate) in the transition region. While the former is known to be robust and independent of the details of the interactions, inverse catalysis arises as a result of a delicate competition, effective only for light quarks. By performing simulations at different quark masses, we determine the pion mass above which inverse catalysis does not take place in the transition region anymore. Even for pions heavier than this limiting value - where the quark condensate undergoes magnetic catalysis - our results are consistent with the notion that the transition temperature is reduced by the magnetic field. These findings will be useful to guide low-energy models and effective theories of QCD.