Precise Prediction for the W-Boson Mass in the Standard Model

The presently most accurate prediction for the W-boson mass in the Standard Model is obtained by combining the complete two-loop result with the known higherorder QCD and electroweak corrections. The numerical impact of the different contributions is analysed in detail. A simple parametrisation of the full result is presented, which approximates the full result for MW to better than 0.5 MeV for 10 GeV ≤ MH ≤ 1 TeV if the other parameters are varied within their combined 2σ region around their experimental central values. The different sources of remaining theoretical uncertainties are investigated. Their effect on the prediction of MW is estimated to be about 4 MeV for MH ∼ 300 GeV. email: [email protected] email: [email protected] email: [email protected] email: [email protected] The relation between the W-boson mass,MW, the Z-boson mass,MZ, the fine structure constant, α, and the Fermi constant, Gμ, M W ( 1− M 2 W M Z ) = πα √ 2Gμ (1 + ∆r) , (1) is of central importance for precision tests of the electroweak theory. Accordingly, a lot of effort has been devoted over more than two decades to accurately predict the quantity ∆r, which summarises the radiative corrections, within the Standard Model (SM) and extensions of it. The one-loop result [1] can be written as ∆r = ∆α− c 2 W sW ∆ρ+∆rrem(MH), (2) where cW = M 2 W/M 2 Z, s 2 W = 1−cW. It involves large fermionic contributions from the shift in the fine structure constant due to light fermions, ∆α ∝ logmf , and from the leading contribution to the ρ parameter, ∆ρ. The latter is quadratically dependent on the topquark mass, mt, as a consequence of the large mass splitting in the isospin doublet [2]. The remainder part, ∆rrem, contains in particular the dependence on the Higgs-boson mass, MH. Higher-order QCD corrections to ∆r are known at O(ααs) [3] and O(αα s ) [4, 5]. Recently the full electroweak two-loop result for ∆r has been completed. It consists of the fermionic contribution [6,7,8], which involves diagrams with one or two closed fermion loops, and the purely bosonic two-loop contribution [9]. Beyond two-loop order the results for the pure fermion-loop corrections (i.e. contributions containing n fermion loops at n-loop order) are known up to four-loop order [10]. They contain in particular the leading contributions in ∆α and ∆ρ. Most recently results for the leading three-loop contributions of O(Gμmt ) and O(Gμαsmt ) have been obtained for arbitrary values of MH (by means of expansions around MH = mt and for MH ≫ mt) [11], generalising a previous result which was obtained in the limitMH = 0 [12]. Eq. (1) is usually employed for predicting the W-boson mass,