Calculation of the D and B Meson Lifetimes

Abstract

Using the expansions of the heavy meson decay widths in the heavy quark mass and QCD sum rules for estimates of corresponding matrix elements,\, we calculate the $D^{\pm,o,s}$ decay widths and the $B^{\pm,o,s}$ lifetime differences. The results for D mesons are in agreement with the data,\, while it is predicted that $[\Gamma (B^o)-\Gamma (B^-)]/\Gamma_B\se 4\%\,,$ and the lifetime difference of the $B^o$ and $B_s$ mesons is even smaller. 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 perturbative pole quark masses are: $M_c\se 1.65\,GeV,\,\, M_b\se 5.04\,GeV\,,$ and the decay constants are: $f_D(M_c)\se 165\,MeV\,,\,\,f_B(M_b)\se 113\,MeV\,$. It is also shown that the nonfactorizable corrections to the $B^o-{\bar B}^o$ mixing are large,\, $B_B\se (1-18\%)\,.$ 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 $\epsilon ^{\prime}/\epsilon$ which is too large): $\lambda\se 0.22\,,\,\, A\se 0.825\,,\,\,\rho \se -0.4\,,\,\, \eta \se 0.2\,.$