Meson masses in electromagnetic fields with Wilson fermions

TL;DR

This study uses quenched Wilson fermions to analyze how background magnetic fields affect the light meson spectrum in QCD, revealing a decrease in neutral pion mass and stable vector meson mass, with implications for $ ho$-meson condensation.

Contribution

Introduces a novel magnetic field-dependent improvement term for Wilson fermions, enabling accurate continuum extrapolation of meson masses in magnetic fields.

Findings

Neutral pion mass decreases monotonically with magnetic field.

Vector meson mass remains nonzero at strong magnetic fields.

Lattice artifacts can mimic unphysical mass behavior without the new improvement term.

Abstract

We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured $\rho$-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field-induced mixing between $\rho$-mesons and pions. We also derive Ward-Takashi identities for QCD+QED both in the continuum formulation and for (order $a$-improved) Wilson fermions.