Next-to-leading order QCD corrections to the lifetime difference of Bs mesons

Abstract

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...

Particle-antiparticle mixing,εK, ΔΓq, ASLq, ACP(Bd→ψKS), ACP(Bs→ψphi) and B→Xs,dγ in the Littlest Higgs model with T-parity

“…We note that the theoretical prediction for Re(Γ s 12 /M s 12 ) obtained in [63] and updated in (3.46) is smaller than the value found in [64]. This difference is mainly due to the contribution of O(1/m 4 b ) in the Heavy Quark Expansion (HQE), which in [64] is wholly estimated in the vacuum saturation approximation (VSA), while in [63] the matrix elements of two dimension-seven operators are expressed in terms of those calculated on the lattice.…”

“…This difference is mainly due to the contribution of O(1/m 4 b ) in the Heavy Quark Expansion (HQE), which in [64] is wholly estimated in the vacuum saturation approximation (VSA), while in [63] the matrix elements of two dimension-seven operators are expressed in terms of those calculated on the lattice. Being the O(1/m 4 b ) contribution important, it is interesting to estimate the size of the O(1/m 5 b ) terms.…”

Width difference in the Bs0-Bs0 system from lattice HQET

“…The B-parameters in table 1 are QCD scheme dependent, they all are in the NDR-MS scheme. In order to make contact with the NLO computation of [2], we have subtracted the evanescents operators in the renormalization of O and O S as in [2]. For B LR and B LR S we use the prescription of [17].…”

Studying ofBs0−B¯s0mixing andBs→KWang1, Xu2, Chang3 et al. 2011Phys. Rev. D383430View full textAdd to dashboardCite

“…where x c = m 2 c /m 2 b , G(x c ) = 0.030 and G 2 (x c ) = −0.937 at the m b scale [39], the 1/m b correctionsδ 1/m are given in Ref. [40], and 1/m 2 b corrections aren't considered since they are small [41] …”