Spin interactions in mesons in strong magnetic field

TL;DR

This paper develops a relativistic framework to analyze spin interactions in mesons under strong magnetic fields, revealing significant hyperfine shifts and active tensor forces that challenge perturbative approaches.

Contribution

It introduces a relativistic Hamiltonian formalism that separates spin-dependent interactions in mesons within magnetic fields, extending nonrelativistic models and highlighting nonperturbative effects.

Findings

Hyperfine shifts grow linearly with magnetic field strength

Tensor forces are active in all meson states at nonzero magnetic field

Perturbation theory becomes invalid at large magnetic fields

Abstract

Spin interactions in relativistic quark-antiquark system in magnetic field is considered in the framework of the relativistic Hamiltonian, derived from the QCD path integral. The formalism allows to separate spin-dependent terms from the basic spin-independent interaction, contained in the Wilson loop, and producing confining and gluon exchange interaction. As a result one obtains relativistic spin-spin interaction $V_{ss}$, generalizing its nonrelativistic analog. It is shown, that in large magnetic field $eB, V_{ss}$ modifies and produces hyperfine shifts which grow linearly with $eB$ and preclude the use of perturbation theory. We also show, that tensor forces for $eB \neq 0$ are active in all meson states, but do not grow with $eB$