Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states

In the presence of an electromagnetic background plane-wave field, electron, positron, and photon states are not stable, because electrons positrons emit photons decay into electron-positron pairs. This particle leads to exponential damping term in probabilities single nonlinear Compton scattering Breit-Wheeler pair production. this paper we investigate analytically numerically production including states' decay. For first compute spin- polarization-resolved expressions probabilities, provide some their asymptotic behaviors show that results total independent spin polarization bases. Then, present several plots differential for different pulse lengths quantum numbers. We observe it is crucial take account order stay always below unity factors also scale with intensity duration field. case probability behaves like a Poissonian distribution regime where recoil negligible. all considered cases, kinematic conditions such final particles momenta transverse propagation direction plane wave much smaller than longitudinal main spread momentum on along electric