Functional renormalization group study of neutral and charged pion under magnetic fields in the quark-meson model

TL;DR

This study uses the functional renormalization group within the quark-meson model to analyze how magnetic fields affect neutral and charged pion masses and decay constants at zero temperature, aligning with lattice QCD results.

Contribution

It provides a detailed FRG-based analysis of pion properties under magnetic fields, incorporating Landau level effects and weak-field expansion, which advances understanding beyond previous models.

Findings

Neutral pion mass decreases with magnetic field.

Charged pion mass increases with magnetic field.

Pion decay constant exhibits magnetic catalysis.

Abstract

We calculated the masses of neutral and charged pion and pion decay constants under an extra magnetic field at zero temperature. The quantum fluctuations are integrated through the functional renormalization group. We consider the quark and meson propagators in the Landau level representation and weak-field expansion, respectively. The neutral pion mass monotonically decreases with the magnetic field, while the charged pion mass monotonically increases with the magnetic field. The pion decay constant and the quark mass show the magnetic catalysis behavior at vanishing temperature. The neutral pion mass and pion decay constant are quantitatively in agreement with the lattice QCD results in the region of $eB < 1.2 {\rm GeV}^2$, and no non-monotonic mass behavior for charged pion has been observed in this framework.