Bound-free pair production in ultra-relativistic ion collisions at the LHC collider: Analytic approach to the total and differential cross sections

TL;DR

This paper develops an analytic approach to estimate total and differential cross sections for bound-free electron-positron pair production in ultra-relativistic ion collisions at the LHC, focusing on large-angle positron emission.

Contribution

It introduces simple analytic expressions for differential cross sections using the equivalent photon approximation and Sauter approach, validated against numerical calculations.

Findings

Analytic formulas agree well with numerical results.

Positron count rates depend strongly on detector acceptance.

Increasing detector acceptance can significantly enhance measurement feasibility.

Abstract

A theoretical investigation of the bound-free electron-positron pair production in relativistic heavy ion collisions is presented. Special attention is paid to the positrons emitted under large angles with respect to the beam direction. The measurement of these positrons in coincidence with the down--charged ions is in principle feasible by LHC experiments. In order to provide reliable estimates for such measurements, we employ the equivalent photon approximation together with the Sauter approach and derive simple analytic expressions for the differential pair--production cross section, which compare favorably to the results of available numerical calculations. Based on the analytic expressions, detailed calculations are performed for collisions of bare Pb$^{82+}$ ions, taking typical experimental conditions of the LHC experiments into account. We find that the expected count rate strongly depends on the experimental parameters and may be significantly enhanced by increasing the positron-detector acceptance cone.