Two-Loop Four-Fermion Scattering Amplitude in QED.

We present the first fully analytic evaluation of the transition amplitude for the scattering of a massless into a massive pair of fermions at the two-loop level in quantum electrodynamics. Our result is an essential ingredient for the determination of the electromagnetic coupling within scattering reactions, beyond the currently known accuracy, which has a crucial impact on the evaluation of the anomalous magnetic moment of the muon. It will allow, in particular, for a precise determination of the leading hadronic contribution to the (g-2)_{µ} in the MUonE experiment at CERN, and therefore can be used to shed light on the current discrepancy between the standard model prediction and the experimental measurement for this important physical observable.

Heavy-flavor contribution to Bhabha scattering.

We evaluate the last missing piece of the two-loop QED corrections to the high-energy electron-positron scattering cross section originating from the vacuum polarization by heavy fermions. The calculation is performed within a new approach applicable to a wide class of perturbative problems with mass hierarchy. The result is crucial for the high-precision physics program at existing and future e(+) e(-) colliders.

QCD corrections to static heavy-quark form factors.

Interactions of heavy quarks, in particular, of top quarks, with electroweak gauge bosons are expected to be very sensitive to new physics effects related to electroweak symmetry breaking. These interactions are described by the so-called static form factors, which include anomalous magnetic moments and the effective weak charges. We compute the second-order QCD corrections to these static form factors, which turn out to be sizable and need to be taken into account in searches for new anomalous coupling effects.