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Register a new userThe two-loop electroweak bosonic corrections to $sin^2theta_{rm eff}^{rm b}$
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The prediction of the effective electroweak mixing angle $sin^2theta_{rm eff}^{rm b}$ 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 $Delta{alpha}$, ${alpha_{rm s}}$. For central input values, we obtain a relative correction of $Deltakappa_{rm b}^{(alpha^2,rm bos)} = -0.9855 times 10^{-4}$, amounting to about a quarter of the fermionic corrections, and corresponding to $sin^2theta_{rm eff}^{rm b} = 0.232704$. 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.
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We present the first calculation of the two-loop electroweak fermionic correction to the flavour-dependent effective weak-mixing angle for bottom quarks, sin^2 theta_{eff}^{b anti-b}. For the evaluation of the missing two-loop vertex diagrams, two methods are employed, one based on a semi-numerical Bernstein-Tkachov algorithm and the second on asymptotic expansions in the large top-quark mass. A third method based on dispersion relations is used for checking the basic loop integrals. We find that for small Higgs-boson mass values, M_H ~ 100 GeV, the correction is sizable, of order O(10^{-4}).
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This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where bosonic refers to diagrams without closed fermion loops. Together with the corresponding results for the $Z$-pole asymmetries $A_l, A_b$, which have been presented earlier, this completes the theoretical description of $Z$-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, $Gamma_{rm Z}$, partial decay widths $Gamma_{e,mu},Gamma_{tau},Gamma_{ u},Gamma_{u},Gamma_{c},Gamma_{d,s},Gamma_{b}$, branching ratios $R_l,R_c,R_b$ and the hadronic peak cross-section, $sigma_{rm had}^0$. Theoretical intrinsic uncertainties from missing higher orders are also discussed.
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