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Initial transverse-momentum broadening of Breit-Wheeler process in relativistic heavy-ion collisions

We calculate the cross section and transverse-momentum ($P_{\bot}$) distribution of the Breit-Wheeler process in relativistic heavy-ion collisions and their dependence on collision impact parameter ($b$). To accomplish this, the Equivalent Photon Approximation (EPA) was generalized in a more differential way compared to the approach traditionally used for inclusive collisions. In addition, a lowest-order QED calculation with straightline assumption was performed as a standard baseline for comparison. The cross section as a function of $b$ is consistent with previous calculations using the equivalent one-photon distribution function. Most importantly, the $P_{\bot}$ shape from this model is strongly dependent on impact parameter and can quantitatively explain the $P_{\bot}$ broadening observed recently by RHIC and LHC experiments. This broadening effect from the initial QED field strength should be considered in studying possible trapped magnetic field and multiple scattering in a Quark-Gluon Plasma (QGP). The impact-parameter sensitive observable also provides a controllable tool for studying extreme electromagnetic fields.