Precise calculation of M W , sin 2 θ̂ W ( M Z ) , and sin 2 θ lepteff

The two-loopO(gM t /M 2 W ) corrections are incorporated in the theoretical calculation ofMW , sinθ̂W (MZ), and sin 2 θ eff , as functions of MH . The analysis is carried out in a previously proposed MS formulation and two novel on-shell resummation schemes. It is found that the inclusion of the new effects sharply decreases the scheme and residual scale dependence of the calculations. QCD corrections are incorporated in two different approaches. Comparison with the world average of sin θ eff leads toMH = 127 +143 −71 GeV andMW = 80.367±0.048GeV, with small variations among the six calculations. ∗ On leave from Dipartimento di Fisica, Università di Padova, Padua, Italy. The theoretical calculation of the W -boson mass MW , the MS parameter sin θ̂W (MZ), and the effective mixing parameter sin θ eff represents one of the most important applications of the Standard Model (SM) at the level of its quantum corrections. We recall that sin θ eff is determined from on-resonance observables at LEP and SLC, while sin θ̂W (MZ) is theoretically very important, particularly in the context of GUT studies. The aim of this paper is to present an accurate calculation of these parameters that, in the case of MW and sinθ̂W (MZ), includes the recently evaluated two-loop contributions of O(g M t /M 2 W ) [1]. The corresponding contributions for the evaluation of sin θ eff are provided in the present paper. Although nominally subleading relative to the two-loop terms of O(gM t /M 4 W ), these effects have been found to be of comparable magnitude [1]. Our strategy is to study the incorporation of the O(gM t /M 2 W ) contributions in different renormalization schemes, and to investigate the residual scale dependence. In fact, as it will be shown, the inclusion of the new results greatly decreases the scheme and residual scale dependence of important radiative corrections. QCD corrections are evaluated following two different approaches. We recall that, using the accurately known parameters α, Gμ, and MZ as inputs, MW can be calculated from the expression [2] sc = A/M Z (1−∆r), (1) where s = 1 − c is an abbreviation for sin θW ≡ 1 − M W/M Z (MW and MZ are the physical masses of the intermediate bosons), A = πα/ √ 2Gμ = (37.2802GeV) , and ∆r is the relevant radiative correction [2]. In order to incorporate the O(gM t /M 2 W ) effects, it is necessary to specify the renormalization scheme employed in the evaluation of the one-loop contributions. In Ref. [1] this was done in the MS framework of Ref. [3], where 1−∆r = [1−∆r̂W ] ŝ2/s, (2) ŝ2/s = 1 + (c/s)(ê/ŝ2) ∆ρ̂, (3) ∆ρ̂ = Re [ AW W (M 2 W )− ĉAZZ(M Z) ] MS /M W , (4) ∆r̂W = −(2δe/e)MS + (e /ŝ2)f̂ , (5) f̂ = [ (ReAWW (M 2 W )− AWW (0))/M W + VW +M WBW ]