The B+−Bd0 lifetime difference beyond leading logarithms

Abstract

We compute perturbative QCD corrections to the lifetime splitting between the charged and neutral B meson in the framework of the heavy quark expansion. These next-to-leading logarithmic corrections are necessary for a meaningful use of hadronic matrix elements of local operators from lattice gauge theory. We find the uncertainties associated with the choices of renormalization scale and scheme significantly reduced compared to the leading-order result. We include the full dependence on the charm-quark mass m c without any approximations. Using hadronic matrix elements estimated in the literature with lattice QCD we obtain τ (B + )/τ (B 0 d ) = 1.053 ± 0.016 ± 0.017, where the effects of unquenching and 1/m b corrections are not yet included. The lifetime difference of heavy baryons Ξ 0 b and Ξ − b is also briefly discussed. PACS numbers: 12.38.Bx, 13.25.Hw, 14.40.Nd 2 The B + -B 0 d Lifetime Difference Beyond Leading Logarithms d b d b u c WA u b u b d c PI Figure 1: Weak annihilation (WA) and Pauli interference (PI) diagrams in the leading order of QCD. They contribute to Γ(B 0 d ) and Γ(B + ), respectively. The crosses represent |∆B| = 1 operators, which are generated by the exchange of W bosons. CKM-suppressed contributions are not shown.

Towards next-to-next-to-leading-log accuracy for the width difference in the $$ {B}_s-{\overline{B}}_s $$ system: fermionic contributions to order (m c /m b )0 and (m c /m b )1

“…This feature has been studied in refs. [10,28]. The NLO result for ∆Γ JHEP10(2017)191 expressed throughz is numerically very well reproduced ifz is set to zero in the NLO correction.…”

“…(18) of ref. [28]. Since we have set z = 0 in the charm lines attached to weak vertices, no NNLO corrections to the transformation occur.…”

Fluctuating annihilation cross sections and the generation of density perturbations

“…The result in [9] was the first complete calculation of perturbative QCD effects beyond the leading logarithmic approximation to spectator effects in the HQE for heavy hadron decays. Currently NLO-QCD corrections to spectator effects are known for the lifetime ratios of heavy hadrons [18,19,20] and for ∆Γ B d and the semileptonic CP-asymmetries [21,10].…”

CP violation in the Bs0 system

“…In these papers the full expressions for G s,xy and G s,xy S are given; they also include contributions from the QCD penguin operators Q 1 -Q 6 and the chromo-magnetic penguin operator Q 8 . (Beneke et al, 2002) found that the use ofm c (m b ) (charm mass at the bottom mass scale) instead ofm c (m c ), sums up large logs of the form m 2 c /m 2 b ln m 2 c /m 2 b to all orders; we will thus use the parameterz in our numerical analysis, given byz …”