One-Loop Calculations and the Mass of the Top Quark

Abstract

The top quark pole mass is affected by perturbative divergences known as renormalons, therefore this mass parameter possesses a theoretical ambiguity of order Λ_{QCD}, the infrared scale of divergence. We subtract a part of the static t\overline{t} potential and obtain the potential-subtracted mass which is renormalon-free and thus measurable with bigger precision. We demonstrate the presence of the renormalon ambiguity in the top quark pole mass and in the static t\overline{t} potential and with this the cancellation of the renormalon ambiguity in the potential-subtracted mass. Before we discuss renormalons, we review how one computes one-loop quantum corrections in QED and the SM, starting from the gauge-principles that underlie these theories. We focus on renormalisation and its non-perturbative implications, we discuss how the conservation of Noether current affects the counter terms in QED and verify the optical theorem explicitly for top quark decay.