Collision-energy dependence of the Breit-Wheeler process in heavy-ion collisions and its application to nuclear charge radius measurements

Abstract

The collision energy dependence of the cross section and the transverse momentum distribution of dielectrons from the Breit-Wheeler process in heavy-ion collisions are computed in the lowest-order QED and found to be sensitive to the nuclear charge distribution and the infrared divergence of the ultra-Lorentz-boosted Coulomb field. Within a given experimental kinematic acceptance, the cross section is found to increase while the pair transverse momentum ($\sqrt{\ensuremath{\langle}{p}_{T}^{2}\ensuremath{\rangle}}$) decreases with increasing beam energy. We demonstrate that the transverse-momentum component of Weizs\"acker-Williams photons is due to the finite extent of the charge source and electric field component in the longitudinal direction. We further clarify the connection between the nuclear charge distribution and the kinematics of produced ${e}^{+}{e}^{\ensuremath{-}}$ from the Breit-Wheeler process, and propose a criterion for the validity of the Breit-Wheeler process in relativistic heavy-ion collisions. Following this approach we demonstrate that the experimental measurements of the Breit-Wheeler process in ultrarelativistic heavy-ion collisions can be used to quantitatively constrain the nuclear charge radius. The extracted parameters show sensitivity to the impact parameter dependence, and can be used to study the initial-state and final-state effects in hadronic interactions.