Abstract
A critical subject in fully differential QED calculations originates from numerical instabilities due to small fermion masses that act as regulators of collinear singularities. At next-to-next-to-leading order (NNLO) a major challenge is therefore to find a stable implementation of numerically delicate real-virtual matrix elements. In the case of Bhabha scattering this has so far prevented the development of a fixed-order Monte Carlo at NNLO accuracy. In this paper we present a new method for stabilising the real-virtual matrix element. It is based on the expansion for soft photon energies including the non-universal subleading term calculated with the method of regions. We have applied this method to Bhabha scattering to obtain a stable and efficient implementation within the McMule framework. We therefore present for the first time fully differential results for the photonic NNLO corrections to Bhabha scattering.
Highlights
Electron-positron or Bhabha scattering is one of the best studied processes in the Standard Model [1]
With this method it is possible to make reliable predictions for Bhabha scattering at the differential level including the full set of next-to-next-to-leading order (NNLO) quantum electrodynamics (QED) corrections
One of the main complications in the calculation of fully differential higher-order corrections in QED is the occurrence of numerical instabilities in real-emission contributions due to finite but small fermion masses acting as collinear regulators
Summary
Electron-positron or Bhabha scattering is one of the best studied processes in the Standard Model [1]. The main bottleneck in this regard has been the real-virtual contribution that suffers from numerical instabilities when integrated over the phase space of the emitted photon The source of these instabilities can be traced back to the disparate scales in the process introduced by the small electron mass that acts as a regulator of collinear divergences. To verify our method we have compared with approximate results from BABAYAGA at the cross section as well as at the differential level and found agreement within the expected 0.1% precision With this method it is possible to make reliable predictions for Bhabha scattering at the differential level including the full set of NNLO QED corrections.
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