Bhabha scattering at NNLO with next-to-soft stabilisation

TL;DR

This paper introduces a new method to stabilize NNLO calculations of Bhabha scattering by expanding soft photon energies, enabling fully differential results and improving numerical stability in QED computations.

Contribution

A novel stabilization technique for real-virtual matrix elements at NNLO in Bhabha scattering using next-to-soft expansion and the method of regions.

Findings

Achieved stable, fully differential NNLO results for Bhabha scattering.

Implemented the method within the McMule framework.

Enabled precise Monte Carlo simulations at NNLO accuracy.

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.