Non-perturbative signatures of non-linear Compton scattering

Abstract

The probabilities of various elementary laser - photon - electron/positron interactions display in selected phase space and parameter regions typical non-perturbative dependencies such as $\propto \mathcal{P}\exp \{-a{E}_{crit}/E\}$, where $\mathcal{P}$ is a pre-exponential factor, $E_{crit}$ denotes the critical Sauter-Schwinger field strength, and $E$ characterizes the (laser) field strength. While the Schwinger process with $a=a_S\equiv \pi$ and the non-linear Breit-Wheeler process in the tunneling regime with $a=a_{n\ell BW}\equiv 4m/3{\omega }^{\prime }$ (with ${\omega }^{\prime }$ the probe photon energy and $m$ the electron/positron mass) are famous results, we point out here that also the non-linear Compton scattering exhibits a similar behavior when focusing on high harmonics. Using a suitable cut-off $c>0$, the factor $a$ becomes $a=a_{n\ell C}\equiv \frac{2}{3}cm/(p_0+\sqrt{p_0^2-m^2)}$. This opens the avenue towards a new signature of the boiling point of the vacuum even for field strengths $E$ below $E_{crit}$ by employing a high electron beam-energy $p_0$ to counter balance the large ratio $E_{crit}/E$ by a small factor $a$ to achieve $E/a\to E_{crit}$. In the weak-field regime, the cut-off facilitates a threshold leading to multi-photon signatures showing up in the total cross section at sub-threshold energies.

arXiv comment21 pages, 13 figures

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• Positron energy distribution in factorized trident process
• Strong-field QED in Furry-picture momentum-space formulation: Ward identities and Feynman diagrams