Nonresonant e+e− pair annihilation to μ+μ− pair in the field of light wave

We present, for general relativistic case, a theoretical study of nonresonant annihilation of e^--e⁺ pair in mu^--mu⁺ pair. We analyze condition of appearance of resonance. Itpsilas derived the expressions for the nonresonant amplitude and cross-section of studied process. It is shown that in the case of the ultrarelativistic energies the partial differential cross-section is factorized as a product of the cross-section of annihilation of an electron-positron pair to a muon pair in the absence of the external field and the probability of emission (absorption) |l| - photons from the wave. After summation over all possible processes of emission and absorption of photons of the wave all the essential quantum terms cancel each other. As a result the cross-section coincides with the cross-section of annihilation of an electron-positron pair to a muon pair in the absence of the external field.