Quarkonium radiative decays from the hadronic Paschen-Back effect

TL;DR

This paper investigates how strong magnetic fields deform P-wave quarkonium wave functions, affecting their radiative decay patterns, with analytic formulas derived for decay widths in the nonrelativistic limit.

Contribution

It introduces a polarized wave function basis to analyze the Hadronic Paschen-Back effect on P-wave quarkonia in strong magnetic fields, revealing anisotropic decay behaviors.

Findings

Wave functions are significantly deformed by the Hadronic Paschen-Back effect.

Decay widths become anisotropic due to wave function deformation.

Analytic formulas for decay widths are provided in the nonrelativistic limit.

Abstract

We study the radiative (E1 and M1) decays of P-wave quarkonia in a strong magnetic field based on the Lagrangian of potential nonrelativistic QCD. To investigate their properties, we implement a polarized wave function basis justified in the Paschen-Back limit. In a magnetic field stronger than the spin-orbit coupling, the wave functions of the P-wave quarkonia are drastically deformed by the Hadronic Paschen-Back effect. Such deformation leads to the anisotropy of the direction of decays from the P-wave quarkonia. The analytic formulas for the radiative decay widths in the nonrelativistic limit are shown, and the qualitative decay properties are discussed.