  The present work deals with $e^+$-$e^-$ pair production in the four-nucleon
system. We first analyze the process as a purely electromagnetic one in the
context of a state-of-the-art approach to nuclear strong-interaction dynamics
and nuclear electromagnetic currents, derived from chiral effective field
theory ($\chi$EFT). Next, we examine how the exchange of a hypothetical
low-mass boson would impact the cross section for such a process. We consider
several possibilities, that this boson is either a scalar, pseudoscalar,
vector, or axial particle. The ab initio calculations use exact
hyperspherical-harmonics methods to describe the bound state and low-energy
spectrum of the $A\,$=$\,4$ continuum, and fully account for initial state
interaction effects in the $3+1$ clusters. While electromagnetic interactions
are treated to high orders in the chiral expansion, the interactions of the
hypothetical boson with nucleons are modeled in leading-order $\chi$EFT
(albeit, in some instances, selected subleading contributions are also
accounted for). We also provide an overview of possible future experiments
probing pair production in the $A\,$=$\,4$ system at a number of candidate
facilities.facilities.
