The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$

Abstract

The prediction of the effective electroweak mixing angle ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$ in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the $Z\bar{b}b$ vertex. Numerical predictions are presented in the form of a fitting formula as function of $M_Z,M_W,M_H,m_t$ and $\Delta \alpha$, ${\alpha }_{\mathrm{s}}$. For central input values, we obtain a relative correction of $\Delta {\kappa }_{\mathrm{b}}^{({\alpha }^2,\mathrm{bos})}=-0.9855\times 10^{-4}$, amounting to about a quarter of the fermionic corrections, and corresponding to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}=0.232704$. 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.

Comments: 14 pp; v2: some explanations and Tab.2 added, version published in PLB