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• W1924890570 abstract "The current status of the theoretical predictions for the electroweak precision observables MW, sin θeff and mh within the MSSM is briefly reviewed. The impact of recent electroweak two-loop results to the quantity ∆ρ is analysed and the sensitivity of the electroweak precision observables to the top-quark Yukawa coupling is investigated. Furthermore the level of precision necessary to match the experimental accuracy at the next generation of colliders is discussed. ∗email: Sven.Heinemeyer@physik.uni-muenchen.de †email: Georg.Weiglein@durham.ac.uk 1128 Parallel Sessions 1 Electroweak precision observables in the MSSM Electroweak precision tests, i.e. the comparison of accurate measurements with predictions of the theory at the quantum level, allow to set indirect constraints on unknown parameters of the model under consideration. Within the Standard Model (SM) precision observables like the W-boson mass, MW, and the effective leptonic weak mixing angle, sin θeff , allow in particular to obtain constraints on the Higgs-boson mass of the SM. In the Minimal Supersymmetric extension of the SM (MSSM), on the other hand, the mass of the lightest CP-even Higgs boson, mh, can be predicted in terms of the mass of the CP-odd Higgs boson, MA, and tanβ, the ratio of the vacuum expectation values of the two Higgs doublets. Via radiative corrections it furthermore sensitively depends on the scalar top and bottom sector of the MSSM. Thus, within the MSSM a precise measurement of MW, sin 2 θeff and mh allows to obtain indirect information in particular on the parameters of the Higgs and scalar top and bottom sector. The status of the theoretical predictions for mh within the MSSM has recently been reviewed in Ref. [1]. The theoretical predictions, based on the complete one-loop and the dominant two-loop results, currently have an uncertainty from unknown higher-order corrections of about ±3 GeV, while the parametric uncertainty from the experimental error of the top-quark mass presently amounts to about ±5 GeV. For the electroweak precision observables within the SM very accurate results are available. This holds in particular for the prediction for MW, where meanwhile all ingredients of the complete two-loop result are known. The remaining theoretical uncertainties from unknown higher-order corrections within the SM are estimated to be [2–4] SM : δM th W ≈ ±6 MeV, δ sin θ eff ≈ ±7× 10−5. (1) They are smaller at present than the parametric uncertainties from the experimental errors of the input parameters mt and ∆αhad. The experimental errors of δmt = ±5.1 GeV [5] and δ(∆αhad) = 36× 10−5 [5] induce parametric theoretical uncertainties of δmt : δM para W ≈ ±31 MeV, δ sin θ eff ≈ ±16× 10−5, δ(∆αhad) : δM para W ≈ ±6.5 MeV, δ sin θ eff ≈ ±13× 10−5. (2) For comparison, the present experimental errors of MW and sin 2 θeff are [5] δM exp W ≈ ±34 MeV, δ sin θ eff ≈ ±17× 10−5. (3) At one-loop order, complete results for the electroweak precision observables MW and sin θeff are also known within the MSSM [6, 7]. At the two-loop level, the leading corrections in O(ααs) have been obtained [8], which enter via the quantity ∆ρ, ∆ρ = ΣZ(0) M Z − ΣW(0) M W . (4) It parameterises the leading universal corrections to the electroweak precision observables induced by the mass splitting between fields in an isospin doublet [9]. ΣZ,W(0) denote the transverse parts of the unrenormalised Zand W-boson self-energies at zero momentum 2+3: Low Energies, Flavors, and CP 1129 transfer, respectively. The induced shifts in MW and sin 2 θeff are in leading order given by (with 1− sW ≡ cW = M W/M Z) δMW ≈ MW 2 cW cW − sW ∆ρ, δ sin θeff ≈ − c 2 Ws 2 W cW − sW ∆ρ. (5) For the gluonic corrections, results in O(ααs) have also been obtained for the prediction of MW [10]. The comparison with the contributions entering via ∆ρ showed that in this case indeed the full result is well approximated by the ∆ρ contribution. Contrary to the SM case, the two-loop O(ααs) corrections turned out to increase the one-loop contributions, leading to an enhancement of up to 35% [8]. Recently the leading two-loop corrections to ∆ρ at O(α2 t ), O(αtαb), O(α2 b) have been obtained for the case of a large SUSY scale, MSUSY MZ [11, 12]. These contributions involve the top and bottom Yukawa couplings and contain in particular corrections proportional to mt and bottom loop corrections enhanced by tanβ. Since for a large SUSY scale the contributions from loops of SUSY particles decouple from physical observables, the leading contributions can be obtained in this case in the limit where besides the SM particles only the two Higgs doublets of the MSSM are active. In the following section these results are briefly summarised. Comparing the presently available results for the electroweak precision observables MW and sin 2 θeff in the MSSM with those in the SM, the uncertainties from unknown higher-order corrections within the MSSM can be estimated to be at least a factor of two larger than the ones in the SM as given in eq. (1). 2 Leading electroweak two-loop contributions to ∆ρ The leading contributions of O(α2 t ), O(αtαb) and O(α2 b) to ∆ρ in the limit of a large SUSY scale arise from two-loop diagrams containing a quark loop and the scalar particles of the two Higgs doublets of the MSSM, see Ref. [12]. They can be obtained by extracting the contributions proportional to y t , ytyb and y 2 b, where yt = √ 2mt v sin β , yb = √ 2mb v cos β . (6) The coefficients of these terms can then be evaluated in the gauge-less limit, i.e. for MW,MZ → 0 (keeping cW = MW/MZ fixed). In this limit the tree-level masses of the charged Higgs boson H± and the unphysical scalars G, G± are given by mH± = M 2 A, m 2 G = m 2 G± = 0. (7) Applying the corresponding limit also in the neutral CP-even Higgs sector would yield for the lightest CP-even Higgs-boson mass mh = 0 and furthermore mH = M A, sinα = − cos β, cosα = sin β, where α is the mixing angle of the neutral CP-even states. However, in the SM the limit M H → 0 turned out to be only a poor approximation of the result for arbitrary M H , and the same feature was found for the limit mh → 0 within the 1130 Parallel Sessions MSSM [11, 12]. Furthermore, the neutral CP-even Higgs sector is known to receive very large radiative corrections. Thus, using the tree-level masses in the gauge-less limit turns out to be a very crude approximation. It therefore is useful to keep the parameters of the neutral CP-even Higgs sector arbitrary as far as possible (ensuring a complete cancellation of the UV-divergences), although the contributions going beyond the gauge-less limit of the tree-level masses are formally of higher order. In particular, keeping α arbitrary is necessary in order to incorporate non SM-like couplings of the lightest CP-even Higgs boson to fermions and gauge bosons. We first discuss the results for the O(α2 t ) corrections, which are by far the dominant subset within the SM, i.e. the O(αtαb) and O(α2 b) corrections can safely be neglected within the SM. The same is true within the MSSM for not too large values of tan β. In this case no further relations in the neutral CP-even Higgs sector are necessary, i.e. the parameters mh, mH and α can be kept arbitrary in the evaluation of the O(α2 t ) corrections. For these contributions also the top Yukawa coupling yt can be treated as a free parameter, i.e. it is not necessary to use eq. (6). This allows to study the sensitivity of the electroweak precision observables to variations in the top Yukawa coupling. 50" @default.
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• W1924890570 title "Precision Observables in the MSSM : Status and Perspectives" @default.
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