The effective electroweak mixing angle $\sin^2\theta_{eff}$ with two-loop fermionic contributions

Abstract

We present the results from a calculation of the full electroweak two-loop fermionic contributions to the effective leptonic mixing angle of the $Z$ boson, $\sin^2\theta_{eff}$, in the Standard Model. On-shell renormalization and analytic calculations are performed for the three-point vertex functions at zero external momenta, whereas irreducible three-point integrals for non-vanishing external momenta are evaluated semi-analytically applying two different methods. Comparisons with a previous calculation show complete agreement.