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Bhabha scattering at NNLO with next-to-soft stabilisation
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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.
Forward citations
Cited by 2 Pith papers
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Towards testing $(g-2)_\tau$ in $e^+e^-\to\tau^+\tau^-$: radiative corrections and projections for Belle II
A complete one-loop QED calculation for polarized e+e- to tau+tau- is implemented in the McMule Monte-Carlo code, showing that Belle II with a polarized beam could test the tau anomalous magnetic moment at the 10^-5 level.
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On the extraction of $\alpha_\textit{em}(m_Z^2)$ at Tera-$Z$
Forward-region Bhabha ratios at Tera-Z could extract alpha_em(m_Z^2) with a projected statistical sensitivity of about 6e-6, below the current bottleneck.
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