Heavy meson spectroscopy under strong magnetic field

TL;DR

This paper investigates how strong magnetic fields affect the spectra and wave functions of various heavy mesons using a potential model and cylindrical Gaussian expansion, revealing energy level shifts and wave function deformations.

Contribution

It introduces a method to analyze anisotropic meson wave functions in magnetic fields and explores magnetic catalysis effects on heavy-light mesons.

Findings

Energy levels vary significantly with magnetic field strength.

Wave functions deform due to spin mixing and Landau levels.

Magnetic catalysis influences light quark masses in mesons.

Abstract

Spectra of the neutral heavy mesons, $\eta_c(1S,2S)$, $J/\psi$, $\psi(2S)$, $\eta_b(1S,2S,3S)$, $\Upsilon(1S,2S,3S)$, $D$, $D^\ast$, $B$, $B^\ast$, $B_s$ and $B_s^\ast$, in a homogeneous magnetic field are analyzed in a potential model of constituent quarks. To obtain anisotropic wave functions and the corresponding eigenvalues, the cylindrical Gaussian expansion method is applied, where the wave functions for transverse and longitudinal directions in the cylindrical coordinate are expanded by the Gaussian bases separately. Energy level structures in the wide range of magnetic fields are obtained and the deformation of the wave functions is shown, which reflects effects of the spin mixing, the Zeeman splitting and quark Landau levels. The contribution from the magnetic catalysis in heavy-light mesons is discussed as a change of the light constituent quark mass.