# Magnetized baryons and the QCD phase diagram: NJL model meets the lattice

## TL;DR

This study combines lattice QCD simulations and the PNJL model to analyze how strong magnetic fields affect baryon spectra and the QCD phase diagram, revealing inverse magnetic catalysis and mass reductions.

## Contribution

It provides the first lattice-based baryon spectrum in magnetic fields and refines the PNJL model to match lattice results for the QCD phase diagram under magnetic influence.

## Key findings

- Baryon masses decrease with increasing magnetic field.
- The refined PNJL model reproduces inverse magnetic catalysis.
- Transition temperature lowers as magnetic field strength increases.

## Abstract

We determine the baryon spectrum of 1 + 1 + 1-flavor QCD in the presence of strong background magnetic fields using lattice simulations at physical quark masses for the first time. Our results show a splitting within multiplets according to the electric charge of the baryons and reveal, in particular, a reduction of the nucleon masses for strong magnetic fields. This first-principles input is used to define constituent quark masses and is employed to set the free parameters of the Polyakov loop-extended Nambu-Jona-Lasinio (PNJL) model in a magnetic field-dependent manner. The so constructed model is shown to exhibit inverse magnetic catalysis at high temperatures and a reduction of the transition temperature as the magnetic field grows - in line with non-perturbative lattice results. This is contrary to the naive variant of this model, which gives incorrect results for this fundamental phase diagram. Our findings demonstrate that the magnetic field dependence of the PNJL model can be reconciled with the lattice findings in a systematic way, employing solely zero-temperature first-principles input.