Mass shift effects in nonperturbative multiphoton pair production for   arbitrary polarized electric fields
  The mass shift effects in multiphoton pair production of a nonperturbative nature for arbitrary polarized electric fields are investigated numerically by employing the real-time Dirac-Heisenberg-Wigner formalism, and theoretically by proposing an effective energy concept. It is found that the theoretical results are agreement with the numerical ones very well. It is the first time to consider the roles of the momenta of created particles and the polarizations of external fields played in the mass shift effects. These results can deepen the understanding of pair production in the nonperturbative threshold regime. Moreover, the distinct mass shift effects are observable in the forthcoming experiments and can be used as a probe to distinguish the electron-positron pair production from other background events. 
Z. L. Li, D. Lu, B. F. Shen, L. B. Fu, J. Liu, and B. S. Xie
hep-ph quant-ph