The two-loop electroweak bosonic corrections to sin2⁡θeffb

The prediction of the effective electroweak mixing angle sin2⁡θeffb in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the Zb¯b vertex. Numerical predictions are presented in the form of a fitting formula as function of MZ,MW,MH,mt and Δα, αs. For central input values, we obtain a relative correction of Δκb(α2,bos)=−0.9855×10−4, amounting to about a quarter of the fermionic corrections, and corresponding to sin2⁡θeffb=0.232704. The integration of the corresponding two-loop vertex Feynman integrals with up to three dimensionless parameters in Minkowskian kinematics has been performed with two approaches: (i) Sector decomposition, implemented in the packages FIESTA 3 and SecDec 3, and (ii) Mellin-Barnes representations, implemented in AMBRE 3/MB and the new package MBnumerics.