Dilepton photoproduction measures the fluctuations of initial electromagnetic fields in nuclear collisions

Dilepton production from two photon interactions $\gamma\gamma\rightarrow l^+l^-$ are studied in semi-central and peripheral nuclear collisions. Based on Weizs\"acker-Williams approach, it is shown that the dilepton photoproduction is proportional to the electromagnetic (EM) fields $\sim E^2B^2$ and therefore sensitive to the magnitude and lifetime of initial EM fields which last only for a short time and are hard to be measured in experiments directly. We propose dilepton photoproduction as a probe for the nuclear charge fluctuations, which are crucial for the electric/magnetic field induced chiral and charge particle evolutions. We calculate the relative standard deviation of dilepton mass spectrum with event-by-event fluctuating nuclear charge distributions (and EM fields).