Magnetic field in relativistic heavy ion collisions: testing the classical approximation

TL;DR

This paper tests the validity of using a classical magnetic field approximation in relativistic heavy ion collisions by comparing it to a quantum photon-based approach, finding a 10% difference that supports the classical treatment.

Contribution

It introduces a method to evaluate the classical approximation's validity in heavy ion collision magnetic fields by comparing classical and quantum calculations of a specific nucleon resonance process.

Findings

Classical and quantum approaches yield similar results within 10%

The classical approximation is validated for the studied process

Supports using classical magnetic fields in heavy ion collision models

Abstract

It is believed that in non-central relativistic heavy ion collisions a very strong magnetic field is formed. There are several studies of the effects of this field, where $\vec{B}$ is calculated with the expressions of classical electrodynamics. A quantum field may be approximated by a classical one when the number of field quanta in each field mode is sufficiently high. This may happen if the field sources are intense enough. In heavy ion physics the validity of the classical treatment was not investigated. In this work we propose a test of the quality of the classical approximation. We calculate an observable quantity using the classical magnetic field and also using photons as input. If the results of both approaches coincide, this will be an indication that the classical approximation is valid. More precisely, we focus on the process in which a nucleon is converted into a delta resonance, which then decays into another nucleon and a pion, i.e., $ N \to \Delta \to N' \pi$. In ultra-peripheral relativistic heavy ion collisions this conversion can be induced by the classical magnetic field of one the ions acting on the other ion. Alternatively, we can replace the classical magnetic field by a flux of equivalent photons, which are absorbed by the target nucleons. We calculate the cross sections in these two independent ways and find that they differ from each other by $\simeq 10$ \% in the considered collision energy range. This suggests that the two formalisms are equivalent and that the classical approximation for the magnetic field is reasonable.