TTP08-26 Two-loop QED hadronic corrections to Bhabha scattering

heoretical predictions for Bhabha scattering at the two-loop level require the inclusion of hadronic vacuum polarization in the photon propagator. We present predictions for the contri butions from reducible amplitudes which are proportional to the vacuum polarization $\pi(q^2 )$ and from irreducible ones where the vacuum polarization appears in a loop representing ve rtex or box diagrams. The second case can be treated by using dispersion relations with a we ight function proportional to the $R$-ratio as measured in electron-positron annihilation in to hadrons and kernels that can be calculated perturbatively. We present simple analytical f orms for the kernels and, using two convenient parametrizations for the function $R(s)$, num erical results for the quantities of interest. As a cross check we evaluate the correspondin g corrections resulting from light and heavy lepton loops and we find perfect agreement with

previous calculations. For the hadronic correction our result are in good agreement with a

previous evaluation.