Bhabha scattering at NNLO with next-to-soft stabilisation

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.

6 pages, 3 figures

References in corpus (7)

• Automation of next-to-leading order computations in QCD: the FKS subtraction
• Matching perturbative and Parton Shower corrections to Bhabha process at flavour factories
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Expansion by regions: revealing potential and Glauber regions automatically
• Two-loop QED corrections to Bhabha scattering
• QED at NNLO with McMule
• Two-Loop Fermionic Corrections to Massive Bhabha Scattering

Cited by in corpus (9)

• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section from threshold to 1.2 GeV with the CMD-3 detector
• Muon-electron scattering at NNLO
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• The LBK theorem to all orders
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• Multiple soft-photon emission at next-to-leading power to all orders
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Disperon QED
• Analytic results for two-loop planar master integrals for Bhabha scattering