Perturbative QCD analysis of b-hadron lifetimes

Abstract

We develop perturbative QCD factorization theorems for inclusive b-hadron decays, in which radiative corrections characterized by the hadronic scale, the b-hadron mass, and the W boson mass are absorbed into a heavy hadron distribution function, a hard b quark decay amplitude, and a "harder" function, respectively. Double logarithmic corrections associated with a light energetic final-state quark, which appear at kinematic end points, are absorbed into a jet function. Various large logarithms contained in the above functions are summed to all orders, leading to the evolution factors among the three characteristic scales. The heavy hadron distribution function is identical to the one constructed in the framework of heavy quark effective theory. It is shown that hadron kinematics must be employed in factorization theorems, and that perturbative contributions, depending on hadron kinematics, distinguish the lifetimes of the b-hadrons $B_d, B_s$ and $Λ_b$. Assuming the same heavy-quark-effective-theory parametesr $λ_1$ for these hadrons, we predict the lifetimes $τ(B_d)=1.56$ ps, $τ(B_s)=1.46$ ps and $τ(Λ_b)=1.22$ ps. We also predict the $B_u$ meson lifetime $τ(B_u)=1.62$ ps by varying the B meson distribution function slightly. All the above results are consistent with experimental data.