Semileptonic Decays of Heavy Flavors in QCD

Abstract

A model independent approach based on a generalization of the operator product expansion is used to describe semileptonic decays of heavy flavors. In the first part of the dissertation we calculate differential distributions in the inclusive semileptonic weak decays of heavy flavors in QCD. In particular, the double distribution in electron energy and invariant mass of the lepton pair is calculated. The distributions are calculated as series in $m_Q^{-1}$ where $m_Q$ is the heavy quark mass. All effects up to $m_Q^{-2}$ are included. Also calculated are the energy distribution and semileptonic decay width for the case of a heavy lepton in the final state. Based on the results of the first part of the work, we calculate the full up to order $1/m_Q^2$ set of the OPE sum rules for the heavy flavor transitions and radiative corrections to them up to order $\alpha_s\Lambda_{QCD}/m_Q$. In the second part of this work a new model is proposed for the inclusive semileptonic decays of the $B$ mesons $B\rightarrow l\bar{\nu}X_c$, which is {\em defined} by the requirement that it should satisfy the QCD consistency conditions. These conditions are imposed in the form of the OPE sum rules. It is shown that under some natural assumptions the OPE sum rules provide sufficient number of constraints to fully determine exclusive contributions of a number of resonances in the final state of the decay. The theoretical results for the model are presented in the form suitable for comparison with experimental data. The proposed model can be used for experimental measurements of the heavy meson matrix element $\mu _\pi ^2$ which describes the kinetic energy of the heavy quark inside the hadron, as well as for extraction of the value of $|V_{cb}|$ from experimental data and other applications.