Determination of quark masses and the running of α

The precise knowledge of the hadronic production cross section constitutes an essential ingredient in the determination of standard model parameters like quark masses or the hadronic contribution to the running Δα of the fine structure constant. It is shown that a direct large mass expansion of the photonic vacuum polarization at order 0(αs3) up to the first moment is sufficient to determine the MS masses of the charm and bottom quarks with high precision. In contrast, the evaluation of Δα requires the reconstruction of the vacuum polarization at this order over a wide center of mass energy range. For this purpose differential equations have been used to calculate the large mass and large momentum expansions as well as a numerical approximation at orders 0(αs2) and 0(αs3nf2). The full result can be obtained once the IBP reduction of the integrals is completed. (orig.)