Treating the Lifetimes of Charm and Beauty Hadrons with QCD Plus a Bit More!

Abstract

The heavy quark expansion implemented through an operator product expansion provides us with a treatment of inclusive decays of beauty and charm hadrons that is genuinely derived from QCD,though it requires one additional assumption, namely that of 'local' quark-hadron duality. Subtleties in the application of factorization to hadronic expectation values are pointed out. The observed pattern in the charm lifetime ratios is reproduced in a semi-quantitative manner. The ratio $\tau (\Lambda _b)/\tau (B_d)$ cannot be pushed significantly below 0.9 -- unless one invokes a new hitherto unknown paradigm for evaluating baryonic matrix elements. One confidently predicts $\tau (B^-)$ to exceed $\tau (B_d)$ by several percent only. Failure of those predictions would force us to pay a hefty theoretical price, namely ultimately to abandon local duality as a practical concept.