  We study the lepton pair production in the photodisintegration of the
deuteron process. The complete seven-fold differential cross section is
calculated via the Bethe-Heitler mechanism with final state interactions taken
into account. The deuteron bound state is described by a relativistic covariant
deuteron-nucleon vertex. With numerical results, we find that the differential
cross section has strong dependence on the lepton azimuthal angle in the small
polar angle region and sharp peaks appear in the dependence on the invariant
mass of the produced lepton pair or the two nucleons in the final state. We
demonstrate that such nearly singular feature originates from the collinearity
between the produced lepton or antilepton and the incident photon, and it is
physically regularized by the lepton mass in our calculation. The final state
interaction between the knocked-out nucleon and the recoil nucleon
redistributes the differential cross section over the missing momentum, with a
significant enhancement at large missing momentum and a suppression in the
intermediate region. With a further decomposition of the final state
interaction contribution, it is found that the on-shell term dominates the near
quasi-elastic region while the off-shell term dominates the other end. In
addition, we examine the contribution from the interference between the proton
amplitude and the neutron amplitude, which as expected is found negligible even
if the proton-neutron rescattering is included. The result in this work can
serve as an input for the analysis and background estimation of multiple
exclusive measurements at Jefferson Lab and future electron-ion colliders.
