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

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.

9 pages, 13 figures

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