Cigar-shaped quarkonia under strong magnetic field

TL;DR

This paper investigates how strong magnetic fields deform heavy quarkonium states using a potential model with anisotropic wave functions, revealing significant structural changes and mass shifts relevant for experiments and lattice QCD.

Contribution

It introduces a cylindrical Gaussian expansion method to analyze anisotropic wave functions of heavy quarkonia under magnetic fields, providing new insights into their structural deformation and mass shifts.

Findings

Wave functions deform significantly under strong magnetic fields.

Masses of heavy quarkonia experience notable shifts.

Wave function structures change drastically at energy level crossings.

Abstract

Heavy quarkonia in a homogeneous magnetic field are analyzed by using a potential model with constituent quarks. To obtain anisotropic wave functions and corresponding eigenvalues, the cylindrical Gaussian expansion method is applied, where the anisotropic wave functions are expanded by a Gaussian basis in the cylindrical coordinates. Deformation of the wave functions and the mass shifts of the $S$-wave heavy quarkonia ($\eta_c$, $J/\psi$, $\eta_c(2S)$, $\psi(2S)$ and bottomonia) are examined for the wide range of external magnetic field. The spatial structure of the wave functions changes drastically as adjacent energy levels cross each other. Possible observables in heavy-ion collision experiments and future lattice QCD simulations are also discussed.