Bethe-Heitler cross-section for very high photon energies and large muon scattering angles

TL;DR

This paper calculates the Bethe-Heitler cross-section for high-energy photons producing muon pairs at large angles, including new contributions from the muon pole, relevant for muon shielding in future colliders.

Contribution

It introduces a novel component due to the muon pole in the Bethe-Heitler process, extending previous models for high-energy photon interactions.

Findings

Derived practical formulas for muon production cross-sections.

Numerical examples illustrating the significance of the muon pole contribution.

Enhanced understanding of muon pair production at high energies.

Abstract

The cross-section for the process $\gamma + A \to \mu^+ + \mu^- + X$ is studied where the photon energy is of the order of several hundreds of GeV and where one of the leptons is scattered to large angles. This is of practical importance for muon shielding calculations at future linear electron colliders. In addition to the photon pole contribution which was previously considered especially by Y.S.Tsai, we identify another component due to the muon pole (equivalent photon and equivalent muon approximation). This is discussed following the usual Bethe-Heitler formula. Then we give practically useful formulae for inclusive lepton (muon) production along with some numerical examples.