Resummation of the $α$ expansion for nonlinear pair production

We show how to resum the Furry-picture $α$ expansion in order to take quantum radiation reaction and spin transition into account in the nonlinear trident process in (pulsed) plane-wave background fields. The results are therefore nontrivial functions of both the background field strength, $eE$, and the coupling to the quantized photon field, $α=e^2/4π$. The effective expansion parameter, $T$, is $α$ times $eE/mω\gg1$, which makes higher orders important. We show that they can change the sign of the spin dependent part already at $T<1$, which will be experimentally accessible.

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