Lifetimes and heavy quark expansion.

Abstract

Kolya Uraltsev was one of the inventors of the Heavy Quark Expansion (HQE), that describes inclusive weak decays of hadrons containing heavy quarks and in particular lifetimes. Besides giving a pedagogic introduction into the subject, we review the development and the current status of the HQE, which just recently passed several non-trivial experimental tests with an unprecedented precision. In view of many new experimental results for lifetimes of heavy hadrons, we also update several theory predictions: τ (B+)/τ (Bd) = 1.04+0.05 −0.01 ± 0.02 ± 0.01, τ (Bs)/τ (Bd) = 1.001 ± 0.002, τ (b)/τ (Bd) = 0.935 ± 0.054 and ¯τ (0b )/¯τ (+ b ) = 0.95 ± 0.06. The theoretical precision is currently strongly limited by the unknown size of the nonperturbative matrix elements of four-quark operators, which could be determined with lattice simulations.