Electroweak two-loop corrections to the effective weak mixing angle

TL;DR

The paper delivers a complete calculation of electroweak two-loop corrections to the effective weak mixing angle sin^2θ_eff, defined at NNLO using a pole scheme for Z-pole observables. It implements two independent methods for fermionic two-loop vertex diagrams and a combination of expansion and numerical techniques for bosonic diagrams, culminating in accurate parametrizations suitable for global SM fits. The work includes a rigorous error assessment, shows agreement and improvements over previous mt-expansion results, and provides practical formulas and Zfitter implementations to refine precision electroweak tests and Higgs-mass constraints. Overall, this advances the theoretical precision of electroweak observables to match upcoming experimental capabilities like GigaZ.

Abstract

Recently exact results for the complete electroweak two-loop contributions to the effective weak mixing angle were published. This paper illustrates the techniques used for this computation, in particular the methods for evaluating the loop diagrams and the proper definition of Z-pole observables at next-to-next-to-leading order. Numerical results are presented in terms of simple parametrization formulae and compared in detail with a previous result of an expansion up to next-to-leading order in the top-quark mass. Finally, an estimate of the remaining theoretical uncertainties from unknown higher-order corrections is given.

Figures (8)

• Figure 1: Genuine fermionic two-loop $Zl^+l^-$ vertex diagrams contributing to ^2θ^lept_eff$\sin^2\theta^{\hbox{\footnotesize lept}}_{\hbox{\footnotesize eff}}$.
• Figure 2: Examples of bosonic two-loop $Zl^+l^-$ vertex diagrams contributing to ^2θ^lept_eff$\sin^2\theta^{\hbox{\footnotesize lept}}_{\hbox{\footnotesize eff}}$.
• Figure 3: Example of a two-loop vertex diagram with a top-quark sub-loop.
• Figure 4: Example of scalar prototype integral. The thick line is massive with mass $m$, while the thin lines represent massless propagators.
• Figure 5: Scalar master integrals for diagrams with a light fermion loop. Thick lines indicate massive gauge boson propagators, while thin lines correspond to light fermions of photons, which are taken massless. The dot in the last diagram indicates that this propagator appears two times.