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 provide an exact calculation of next-to-next-to-leading order (NNLO) massive corrections to Bhabha scattering in QED, relevant for precision luminosity monitoring at meson factories. Using realistic reference event selections, exact numerical resu
lts for leptonic and hadronic corrections are given and compared with the corresponding approximate predictions of the event generator BabaYaga@NLO. It is shown that the NNLO massive corrections are necessary for luminosity measurements with per mille precision. At the same time they are found to be well accounted for in the generator at an accuracy level below the one per mille. An update of the total theoretical precision of BabaYaga@NLO is presented and possible directions for a further error reduction are sketched.
The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2eps dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach
and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in eps. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops.
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.
We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses
me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.
