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 corresponding matrix elements,\, we calculate the $D^{\pm ,o,s}$ and $B^{\pm ,o,s}$ meson lifetimes. The results for D mesons are in a reasonable agreement with the data,\, while it is predicted: $[Γ(B_d)-Γ(B^\pm)]/Γ_B\se 4\%\,$ (and the lifetime difference of the $B_d$ and $B_s$ mesons is even smaller);\, $[Γ(B_s^{short})-Γ(B_s^{long})]/{\ov Γ}(B_s)\se 8\%\,.$ The role of the weak annihilation and Pauli interference contributions to the lifetime differences is 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: $M_c\se 1.65\,GeV,\,\, M_b\se 5.04\,GeV\,,$ and the decay constants are: $f_D(M_c)\se 165\,MeV\,,\,\,f_B(M_b)\se 120\,MeV\,$. It is also shown that the nonfactorizable corrections to the $B-\bar{B}$ mixing are large,\, $B_B(M_b)\se (1-18\%)\,.$ 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): $|V_{cb}|\se 4.2\cdot 10^{-2}\,,\, |V_{td}|\se 1.3\cdot 10^{-2}\,,\, |V_{ub}/V_{cb}|\se 0.10\,,\, \{\,A\se 0.86\,,\,\,ρ\se -0.40\,,\,\, η\se 0.20\,\}.$

small improvements in the text and Table 2, Latex, 18 pages

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