  We study the lepton pair photoproduction in peripheral heavy-ion collisions
based on the formalism in our previous work [Phys. Rev. D 104, 056011 (2021)].
We present the numerical results for the distributions of the transverse
momentum, azimuthal angle and invariant mass for $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$ pairs as functions of the impact parameter and other kinematic
variables in Au+Au collisions. Our calculation incorporates the information on
the transverse momentum and polarization of photons which is essential to
describe the experimental data. We observe a broadening effect in the
transverse momentum for lepton pairs with and without smear effects. We also
observe a significant enhancement in the distribution of $\cos(2\varphi)$ for
$\mu^{+}\mu^{-}$ pairs. Our results provide a baseline for future studies of
other higher order corrections beyond Born approximation and medium effects in
the lepton pair production.
