Calculation of the D- and B-meson lifetimes and the unitarity triangle parameters

Abstract

Using the expansions of the heavy-meson decay widths in the heavy quark mass and QCD sum rules for estimates of the corresponding matrix elements, we calculate the D ±,0, s decay widths and the B ±,0, s lifetime differences and branching ratios. The results for D-mesons are in reasonable agreement with the data, while it is predicted that [ г (B d) - г (B −) ]/ гB ≅ 4%, and the lifetime difference of the B d and B s mesons is even smaller. The lifetime difference of the long- and short-lived B s mesons is predicted to be: [г (B short s) - г (B long s)]/ г(B s ≅ 8% , the mass difference ratio of the short- and long-lived B s and B d mesons is: Δm s / Δm d ≅ 14, etc. The role of the weak annihilation and Pauli interference contributions to the lifetime differences are described in detail. In the course of self-consistent calculations the values of many parameters crucial for calculations with charmed and beauty mesons are found. In particular, the quark pole masses are: M c ≅ 1.65 GeV, M b ~- 5.04 GeV, and the decay constants are: ƒ D (M c) ≅ 165 MeV , ƒ B(M b) ≅ 120 MeV It is also shown that the nonfactorizable corrections to the B 0 - B⊂ mixing are large and, in particular, the B d meson “bag factor” is: B B ( M b ) ≅ (1–18%). The values of the unitarity triangle parameters are found, which are consistent with these results and the data available (except for the NA31 result for the ϵ′/ϵ which is too large): λ ≅ 0.221, A ≅ 0.86. ρ≅−0.36, η≅0.19.