Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can pla
narize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.
We report on the progress in constructing contracted one-loop tensors. Analytic results for rank R=4 tensors, cross-checked numerically, are presented for the first time.
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 w
ith 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.
