Magnetic polarizabilities of light mesons in $SU(3)$ lattice gauge theory

TL;DR

This study explores how magnetic fields influence the masses and polarizabilities of light mesons in SU(3) lattice gauge theory, revealing specific energy shifts and calculating magnetic polarizabilities without evidence of tachyonic modes.

Contribution

It provides the first lattice calculation of magnetic polarizabilities for neutral pseudoscalar and vector mesons in SU(3) gauge theory under strong magnetic fields.

Findings

Energy of $ ho^0$ with $s_z=0$ decreases with magnetic field.

Energy of $ ho^0$ with $s_z= ext{-}1, +1$ increases with magnetic field.

Magnetic polarizabilities of mesons are computed and extrapolated to zero lattice spacing.

Abstract

We investigate the masses (ground state energies) of neutral pseudoscalar and vector meson in $SU(3)$ lattice gauge theory in strong abelian magnetic field. The energy of $\rho^0$ meson with zero spin projection $s_z=0$ on the axis of the external magnetic field decreases, while the energies with non-zero spins $s_z=-1$ and $+1$ increase with the field. The energy of $\pi^0$ meson decrease as a function of the magnetic field. We calculated the magnetic polarizabilities of pseudoscalar and vector mesons for lattice volume $18^4$. For $\rho^0$ with spin $|s_z|=1$ and $\pi^0$ meson the extrapolations to zero lattice spacing have been done. We do not observe any evidence in favour of tachyonic mode existence.