Lifetimes and HQE

Alexander Lenz

Published 2014-05-14, updated 2014-12-18Version 2

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 to 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: $\tau (B^+) / \tau (B_d) = 1.04^{+0.05}_{-0.01} \pm 0.02 \pm 0.01$, $\tau (B_s) / \tau (B_d) = 1.001 \pm 0.002$, $\tau (\Lambda_b)/ \tau (B_d) = 0.935 \pm 0.054$ and $\bar {\tau} (\Xi_b^0) / \bar{\tau} (\Xi_b^+) = 0.95 \pm 0.06$. The theoretical precision is currently strongly limited by the unknown size of the non-perturbative matrix elements of four-quark operators, which could be determined with lattice simulations.