We compute the QCD corrections to the decay rate difference in the B s -B s system, ∆Γ Bs , in the next-to-leading logarithmic approximation using the heavy quark expansion approach. Going beyond leading order in QCD is essential to obtain a proper matching of the Wilson coefficients to the matrix elements of local operators from lattice gauge theory. The lifetime difference is reduced considerably at next-to-leading order. We find (∆Γ/Γ)063] in terms of the bag parameters B, B S in the NDR scheme. As a further application of our analysis we also derive the next-to-leading order result for the mixing-induced CP asymmetry in inclusive b → uūd decays, which measures sin 2α. [3,4]. In principle, a measured value for ∆Γ Bs could also give some information on the mass difference ∆M Bs [5], if the theoretical prediction for the ratio (∆Γ/∆M) Bs can be sufficiently well controlled [6]. Furthermore, as pointed out in [7], if non-standardmodel sources of CP violation are present in the B s system, ∆Γ Bs can be smaller (but not larger) than expected in the standard model. For this reason a lower bound on the standard model prediction is of special interest.The calculation of inclusive non-leptonic b-hadron decay observables, such as ∆Γ Bs , uses the heavy quark expansion (HQE). The decay width difference is expanded in powers of Λ QCD /m b , each term being multiplied by a series of radiative corrections in α s (m b ). In the case of (∆Γ/Γ) Bs , the leading contribution is parametrically of order 16πIn the framework of the HQE the main ingredients for a reliable prediction (less than 10% uncertainty) are a) subleading corrections in the 1/m b expansion, b) the non-perturbative matrix elements of local four-quark operators between B-meson states and c) O(α s ) radiative corrections to the Wilson coefficients of these operators. The first issue has been addressed in [6]. The hadronic matrix elements can be studied using numerical simulations in lattice QCD. In this letter, we present the next-to-leading order QCD radiative corrections to the Wilson coefficient functions for ∆Γ Bs . In addition to removing another item from the above list and reducing certain renormalization scale ambiguities of the leading order prediction, the inclusion of O(α s ) corrections is necessary for a satisfactory matching of the Wilson coefficients to the matrix elements to be obtained from lattice calculations.Our results provide the first calculation of perturbative QCD effects beyond the leading logarithmic approximation to spectator effects in the HQE for heavy hadron decays. The consideration of subleading QCD radiative effects has implications of conceptual interest for the construction of the HQE. Soft gluon emission from the spectator s quark in the B s meson leads to power-like IR singularities in individual contributions, which would apparently impede the HQE construction, because they cannot be absorbed into matrix elements of local operators. It has already been explained in [8], how these severe IR divergences cancel in the...

Combining our results for various O(alpha[s]) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B[over ]-->X[s]gamma)=(3.15+/-0.23) x 10(-4) for Egamma>1.6 GeV in the B[over ]-meson rest frame. The four types of uncertainties:nonperturbative (5%), parametric (3%), higher-order (3%), and m(c)-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.

In this article, we perform an extensive study of flavor observables in a two-Higgs-doublet model (2HDM) with generic Yukawa structure (of type III). This model is interesting not only because it is the decoupling limit of the Minimal Supersymmetric Standard Model (MSSM) but also because of its rich flavor phenomenology which also allows for sizable effects not only in FCNC processes but also in tauonic B decays. We examine the possible effects in flavor physics and constrain the model both from tree-level processes and from loop-observables. The free parameters of the model are the heavy Higgs mass, tan β (the ratio of vacuum expectation values) and the "non-holomorphic". In our analysis we constrain the elements ǫ f ij in various ways: In a first step we give order of magnitude constraints on ǫ f ij from 't Hooft's naturalness criterion, finding that all ǫ f ij must be rather small unless the third generation is involved. In a second step, we constrain the Yukawa structure of the type-III 2HDM from tree-level FCNC processesand µ − → e − e + e − ) and observe that all flavor off-diagonal elements of these couplings, except ǫ u 32,31 and ǫ u 23,13 must be very small in order to satisfy the current experimental bounds. In a third step, we consider Higgs mediated loop contributions to FCNC processes (b → s(d)γ, B s,d mixing, K − K mixing and µ → eγ) finding that also ǫ u 13 and ǫ u 23 must be very small, while the bounds on ǫ u 31 and ǫ u 32 are especially weak. Furthermore, considering the constraints from electric dipole moments (EDMs) we obtain constrains on some parameters ǫ u,ℓ ij . Taking into account the constraints from FCNC processes we study the size of possible effects in the tauonic B decaysand τ → K(π)ν which are all sensitive to tree-level charged Higgs exchange. Interestingly, the unconstrained ǫ u 32,31 are just the elements which directly enter the branching ratios for B → τ ν , B → Dτ ν and B → D * τ ν . We show that they can explain the deviations from the SM predictions in these processes without fine tuning. Furthermore, B → τ ν , B → Dτ ν and B → D * τ ν can even be explained simultaneously. Finally, we give upper limits on the branching ratios of the lepton flavor-violating neutral B meson decays (B s,d → µe, B s,d → τ e and B s,d → τ µ) and correlate the radiative lepton decays (τ → µγ, τ → eγ and µ → eγ) to the corresponding neutral current lepton decays (τ − → µ − µ + µ − , τ − → e − µ + µ − and µ − → e − e + e − ). A detailed appendix contains all relevant information for the considered processes for general scalar-fermion-fermion couplings.

We update the branching ratios for the inclusive decays B → X s + − and the exclusive decays B → (K, K * ) + − , with = e, µ, in the standard model by including the explicit O(α s ) and Λ QCD /m b corrections. This framework is used in conjunction with the current measurements of the branching ratios for B → X s γ and B → K + − decays and upper limits on the branching ratios for the decays B → (K * , X s ) + − to work out bounds on the Wilson coefficients C 7 , C 8 , C 9 and C 10 appearing in the effective Hamiltonian formalism. The resulting bounds are found to be consistent with the predictions of the standard model and some variants of supersymmetric theories. We illustrate the constraints on supersymmetric parameters that the current data on rare B decays implies in the context of minimal flavor violating model and in more general scenarios admitting additional flavor changing mechanisms. Precise measurements of the dilepton invariant mass distributions in the decays B → (X s , K * , K) + − , in particular in the lower dilepton mass region, and the forward-backward asymmetry in the decays B → (X s , K * ) + − , will greatly help in discriminating among the SM and various supersymmetric theories. *

The decay B →X s ␥ is studied at next to leading order in QCD in a class of models containing at least two Higgs doublets and with only one charged Higgs boson nondecoupled at low energy. The two-loop matching condition is calculated and it is found to agree with existing results. The complete dependence of the Wilson coefficients on the matching scale is given. The size of the next to leading order corrections is extensively discussed. Results for branching ratios, possible CP asymmetries, and lower bounds on the charged Higgs boson mass are presented when the convergence of the perturbative series appears fast enough to yield reliable predictions. Regions in the parameter space of these models where the next to leading order calculation is still not a good approximation of the final result for these observables are singled out.