Delayed versus accelerated quarkonium formation in a magnetic field

TL;DR

This paper investigates how magnetic fields influence the formation times of heavy quarkonia, revealing delayed formation for some states and early formation for others due to spin mixing effects.

Contribution

It introduces a phenomenological approach to analyze quarkonium formation times in magnetic fields, including effects of time-dependent fields relevant to heavy-ion collisions.

Findings

Magnetic fields delay vector quarkonium formation.

Time-dependent magnetic fields cause early formation of pseudoscalar quarkonia.

Spin mixing modifies quarkonium properties in magnetic environments.

Abstract

Formation time of heavy quarkonia in a homogeneous magnetic field is analyzed by using a phenomenological ansatz of the vector current correlator. Because the existence of a magnetic field mixes vector quarkonia ($J/\psi$, $\psi^\prime$) and their pseudoscalar partners ($\eta_c$, $\eta_c^\prime$), the properties of the quarkonia can be modified through such a spin mixing. This means that the formation time of quarkonia is also changed by the magnetic field. We show the formation time of vector quarkonia is delayed by an idealized constant magnetic field, where the formation time of the excited state becomes longer than that of the ground state. As a more realistic situation in heavy-ion collisions, effects by a time-dependent magnetic field are also discussed, where delayed formation of $J/\psi$ and $\psi^\prime$ and very early formation of $\eta_c$ and $\eta_c^\prime$ are found.