Dilepton production in the photodisintegration of the deuteron

TL;DR

This paper analyzes lepton pair production in deuteron photodisintegration, calculating the differential cross section with final state interactions, revealing angular dependencies, peaks, and the effects of collinearity and nucleon rescattering.

Contribution

It provides a comprehensive calculation of the differential cross section including final state interactions and collinearity effects, which enhances understanding of lepton pair production in deuteron disintegration.

Findings

Strong dependence of cross section on lepton azimuthal angle.

Sharp peaks in invariant mass distributions due to collinearity.

Final state interactions significantly alter the missing momentum distribution.

Abstract

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.