The $\rho$ and $A$ mesons in strong abelian magnetic field in SU(2) lattice gauge theory

TL;DR

This study investigates how strong external magnetic fields affect the masses of neutral rho and A mesons in SU(2) lattice gauge theory, revealing spin-dependent mass shifts.

Contribution

It provides the first lattice calculation of neutral meson mass dependence on magnetic fields in SU(2) gauge theory, including extrapolation and renormalization procedures.

Findings

Masses of neutral mesons with zero spin decrease with increasing magnetic field.

Masses of mesons with spin ±1 increase with magnetic field.

Performed lattice extrapolation and renormalization of meson masses.

Abstract

We calculated correlators of vector, axial and pseudoscalar currents in external strong abelian magnetic field according to SU(2) gluodynamics. The masses of neutral $\rho$ and $A$ mesons with various spin projections to the axis parallel to the external magnetic field B have been calculated. We found that the masses of neutral mesons with zero spin $s=0$ decrease in increasing magnetic field, while the masses of the $\rho$ and $A$ mesons with spin $s=\pm 1$ increase in the mentioned field. Also we performed extrapolation and renormalization of masses on the lattice.