Resummation of the α expansion for nonlinear pair production by an electron in a strong electromagnetic field

Abstract

We show how to resum the Furry-picture $\ensuremath{\alpha}$ 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, $\ensuremath{\alpha}={e}^{2}/4\ensuremath{\pi}$. The effective expansion parameter, $T$, is $\ensuremath{\alpha}$ times $eE/m\ensuremath{\omega}\ensuremath{\gg}1$, which makes higher orders in $\ensuremath{\alpha}$ important. We show that they can change the sign of the spin-dependent part already at $T<1$, which will be experimentally accessible. We also present a new resummation method that essentially does to a convergent series what Borel-Pad\'e resummation does to an asymptotic series.