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Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED

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arxiv 2307.03098 v3 pith:BDW3TFB5 submitted 2023-07-06 hep-ph hep-th

Simon Badger , Jakub Kryś , Ryan Moodie , Simone Zoia This is my paper · ORCID
classification hep-phhep-th
keywords scatteringamplitudesmasslessoff-shellanalyticgammaloopsnumerical
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We compute the two-loop QED helicity amplitudes for the scattering of a lepton pair with an off-shell and an on-shell photon, $0\to\ell\bar\ell\gamma\gamma^*$, using the approximation of massless leptons. We express all master integrals relevant for the scattering of four massless particles with a single external off-shell leg up to two loops in a basis of algebraically independent multiple polylogarithms, which guarantees an efficient numerical evaluation and compact analytic representations of the amplitudes. Analytic forms of the amplitudes are reconstructed from numerical evaluations over finite fields. Our results complete the amplitude-level ingredients contributing to the N$^3$LO predictions of electron-muon scattering $e\mu\to e\mu$, which are required to meet the precision goal of the future MUonE experiment.

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Cited by 5 Pith papers

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