Nuclear form factor, validity of the equivalent photon approximation and Coulomb corrections to muon pair production in photon-nucleus and nucleus-nucleus collisions

TL;DR

This paper investigates the effects of nuclear form factors, the validity of the equivalent photon approximation, and Coulomb corrections on muon pair production in photon-nucleus and nucleus-nucleus collisions, providing refined theoretical insights and cross section calculations.

Contribution

It demonstrates the necessity of realistic nuclear form factors, confirms the accuracy of the equivalent photon approximation, and calculates small Coulomb corrections for muon pair production.

Findings

Realistic form factors are essential for accurate predictions.

The equivalent photon approximation is highly accurate for these processes.

Coulomb corrections are small, justifying the use of the Born approximation.

Abstract

We study in detail the influence of the nuclear form factor both on the Born cross section and on the Coulomb corrections to the photo-production of muon pairs off heavy nuclei (gamma Z -> mu+ mu- Z$) and in heavy-ion collisions (ZZ -> ZZ mu+ mu-). Our findings indicate a number of issues which have not been sufficiently described as yet in the literature: (i) the use of a realistic form factor, based on the Fermi charge distribution for the nucleus, is absolutely indispensable for reliable theoretical predictions; (ii) we checked quantitatively that the equivalent photon approximation has a very good accuracy for the discussed processes; and (iii) we present a leading logarithmic calculation of the Coulomb corrections which correspond to multi-photon exchange of the produced mu+/- with the nuclei. These corrections are found to be small (on the percent level). Our result justifies using the Born approximation for numerical simulations of the discussed process at the RHIC and LHC colliders. Finally, we calculate the total cross section for muon pair production at RHIC and LHC.