  This paper investigates the electromagnetic production of lepton pairs with
low transverse momentum in relativistic heavy ion collisions. We estimate the
initial photons' transverse momentum contributions by employing models where
the average transverse momentum squared of the incoming photon can be
calculated in the equivalent photon approximation. We further derive an all
order QED resummation for the soft photon radiation, which gives an excellent
description of the ATLAS data in ultra-peripheral collisions at the LHC. For
peripheral and central collisions, additional $p_T$-broadening effects from
multiple interaction with the medium and the magnetic field contributions from
the quark-gluon plasma are also discussed.
