Fermionic NNLO contributions to Bhabha scattering

Understand

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.