$\pi_0$ pole mass calculation in a strong magnetic field and lattice constraints

TL;DR

This study calculates the neutral pion mass in a strong magnetic field using a modified NJL model, aligning with lattice QCD results and revealing a decreasing pion mass with increasing magnetic field.

Contribution

It introduces a magnetic field dependent coupling in the NJL model and compares results with lattice QCD, providing new insights into meson behavior under strong magnetic fields.

Findings

Pion mass decreases with increasing magnetic field.

Magnetic field has minimal effect on scalar mass.

Results closely match recent lattice QCD predictions.

Abstract

The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the $\pi_0$ meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as $f_{{\pi}_0}$ and $g_{\pi_0 q q}$.