Two-Loop $\mathcal{O}(\alpha {\alpha }_s)$ Corrections to the On-Shell Fermion Propagator in the Standard Model

In this paper we consider mixed two-loop electroweak corrections to the top quark propagator in the Standard Model. In particular, we compute the on-shell renormalization constant for the mass and wave function, which constitute building blocks for many physical processes. The results are expressed in terms of master integrals. For the latter practical approximations are derived. In the case of the mass renormalization constant we find agreement with the results in the literature.