Survival probabilities of charmonia as a clue to measure transient magnetic fields

TL;DR

This paper studies how magnetic fields affect the survival of charmonium states in heavy-ion collisions, proposing a method to estimate magnetic field strength from survival probabilities.

Contribution

It introduces a model that accounts for spin mixing and state transitions, providing a new way to infer magnetic fields from charmonium survival data.

Findings

Survival probabilities are sensitive to short-lived magnetic fields.

Sum over spin states yields an observable independent of initial spin configurations.

Approximate relation between survival sum and magnetic field strength squared.

Abstract

We investigate time evolution of $S$-wave charmonium populations under a time-dependent homogeneous magnetic field and evaluate survival probabilities of the low-lying charmonia to the goal of estimating the magnetic field strength at heavy-ion collisions. Our approach implements mixing between different spin eigenstates and transitions to radially excited states. We show that the survival probabilities can change even by an extremely short magnetic field. Furthermore, we find that the survival probabilities depend on the initial spin states. We propose the sum of the survival probabilities over spin partners as an observable insensitive to the initial states. We also find that the sum can be approximately given as a function of $\sigma B_0^2$ with a duration time $\sigma$ and the maximum strength of the magnetic field $B_0$.