Fermionic NNLO contributions to Bhabha scattering

TL;DR

This paper calculates two-loop fermionic corrections to Bhabha scattering using dispersion relations, providing numerical results for various fermion masses and kinematic conditions relevant for high-energy physics experiments.

Contribution

It introduces a method to compute NNLO fermionic contributions to Bhabha scattering via dispersion relations and kernel functions, including heavy fermion effects.

Findings

Numerical results for muon, tau, and top quark contributions across energy ranges.

Method enables precise predictions for small electron mass and various fermion masses.

Applicable to small- and large-angle scattering scenarios.

Abstract

We derive the two-loop corrections to Bhabha scattering from heavy fermions using dispersion relations. The double-box contributions are expressed by three kernel functions. Convoluting the perturbative kernels with fermionic threshold functions or with hadronic data allows to determine numerical results for small electron mass m_e, combined with arbitrary values of the fermion mass m_f in the loop, $m_e^2<<s,t,m_f^2$, or with hadronic insertions. We present numerical results for m_f = m_{\mu}, m_{\tau}, m_{top} at typical small- and large-angle kinematics ranging from 1 GeV to 500 GeV.