Bethe-Heitler lepton pair production in the deuteron breakup reaction

We study the lepton pair production via the Bethe-Heitler mechanism in the deuteron breakup reaction. The complete seven-fold differential cross section is calculated with final state interactions taken into account. The deuteron bound state is described by a relativistic covariant deuteron-nucleon vertex. The numerical results indicate that the differential cross section is highly dependent on the lepton's azimuthal angle in regions of small polar angles and exhibits sharp peaks in the distribution over the invariant mass of the generated lepton pair or the two nucleons in the final state. We demonstrate that such a 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 recoil nucleon redistributes the differential cross section over the missing momentum, with a significant enhancement at a 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. Additionally, we examine the contribution from the interference between the proton amplitude and neutron amplitude, which, as expected, is found negligible even if the proton-neutron rescattering is included. The results of this study can serve as inputs for the analysis and background estimation of multiple exclusive measurements at Jefferson Lab and future electron-ion colliders.