Abstract:
The one-loop supersymmetric QCD corrections to the top quark semileptonic decays $t\to b \bar{l} {\nu_l}$ are considered. The corrections are found to reduce the decay width. In the still acceptable parameter space the corrections to the percentage change in top quark semileptonic decay width can reach the level of -0.7%.

Abstract:
Recently, Neubert has suggested that a certain class of nonperturbative corrections dominates the shape of the electron spectrum in the endpoint region of semileptonic $B$ decay. Perturbative QCD corrections are important in the endpoint region. We study the effects of these corrections on Neubert's proposal. The connection between the endpoint of the electron spectrum in semileptonic $B$ decay and the photon spectrum in $b\rightarrow s\gamma$ is outlined.

Abstract:
We present a complete $O(\alpha_s^2)$ correction to the differential width of the inclusive semileptonic decay $b\to cl\nu_l$ at the kinematical point of vanishing invariant mass of the leptons, $q^2=0$. Together with the recently computed $O(\alpha_s^2)$ correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the $O(\alpha_s^2)$ effect in the total inclusive semileptonic decay width $b\to cl\nu_l$. We argue that the non-BLM part of the $O(\alpha_s^2)$ correction gives at most 1% correction to the inclusive semileptonic decay width $b\to cl\nu_l$. This significantly improves the credibility of extracting $|V_{cb}|$ from the inclusive semileptonic decays of the b-hadrons.

Abstract:
We present complete O(alpha_s^2) corrections to the decay b-->c+l+nu at the point where the invariant mass of the leptons sqrt{q^2} equals the c quark mass. We use this result, together with previously obtained corrections at the ends of the q^2 spectrum, to estimate the total width of the semileptonic b-->c decay with O(alpha_s^2) accuracy, essential for the |V_{cb}| determination.

Abstract:
In this paper, we review recent progress in the field of semileptonic decays of charm mesons, including topics on the relative branching ratio and the form factors. The comparison between the experimental form factor measurements and the Lattice QCD calculations is emphasized.

Abstract:
Perturbative corrections of the order of $\alpha_s$ to inclusive double differential lepton distribution from $b$ quark decay are considered. A perturbative correction to the charged lepton energy spectrum has been calculated for an arbitrary charged lepton mass. The perturbative contribution suppresses the partial rate but almost does not change the shape of energy distribution. Applications of our result to semileptonic B meson decays are briefly discussed.

Abstract:
We calculate the leading power corrections to the decay rates, distributions and hadronic spectral moments in rare inclusive \bxsll decays in the standard model, using heavy quark expansion (HQE) in $(1/m_b)$ and a phenomenological model implementing the Fermi motion effects of the b-quark bound in the B-hadron. We include next-to-leading order perturbative QCD corrections and work out the dependences of the spectra, decay rates and hadronic moments on the model parameters in either HQE and the Fermi motion model. In the latter, we take into account long-distance effects via $B \to X_s +(J/\psi, \psi^\prime,...) \to X_s \ell^+ \ell^- $ with a vector meson dominance ansatz and study the influence of kinematical cuts in the dilepton and hadronic invariant masses on branching ratios, hadron spectra and hadronic moments. We present leading logarithmic QCD corrections to the $b \to s \gamma\gamma$ amplitude. The QCD perturbative improved $B_{s}\to\gamma\gamma$ branching ratio is given in the standard model including our estimate of long-distance effects via $B_s \to \phi \gamma \to \gamma \gamma$ and $B_s \to \phi \psi \to \phi \gamma \to \gamma \gamma$ decays. The uncertainties due to the renormalization scale and the parameters of the HQE inspired bound state model are worked out.

Abstract:
We argue that a Tau-Charm factory (TCF) could improve our knowledge of CKM matrix elements since it is an incomparable tool to check the models and methods applied to extract $V_{bu}$ from $B$ decay partial widths. We report on some recent proposals to improve on parton model. Turning to exclusive decays, we compare the predictions from quark models, QCD sum rules, effective Lagrangians and lattice QCD. Quark models have anticipated on heavy quark symmetry. Their difficutly to account for the $q^2$ dependence might be partly cured by relativistic corrections. QCD sum rules and lattice seem to disagree on the $q^2$ dependence of axial form factors. We discuss the extrapolation from $D$ to $B$. Present uncertainties do not allow to predict reliably the $B\ra\pi,\rho l \nu$ matrix elements. We argue that QCD sum rules are in a good position to study $q^2$ dependence down to $q^2=0$. Lattice QCD is able to check the heavy quark scaling laws for the heavy to light semileptonic decays. It seems to confirm the increase of $A_2/A_1$ from $D$ to $B$ meson predicted by the scaling laws. Finally semileptonic decays in a TCF would give incomparable informations on $K\pi$ phase shifts, and on $K^{**}$ resonances.

Abstract:
I report on recent developments in the heavy-quark effective theory and its application to $B$ meson decays. The parameters of the effective theory, the spin-flavor symmetry limit, and the leading symmetry-breaking corrections to it are discussed. The results of a QCD sum rule analysis of the universal Isgur-Wise functions that appear at leading and subleading order in the $1/m_Q$ expansion are presented. I illustrate the phenomenological applications of this formalism by focusing on two specific examples: the determination of $V_{cb}$ from the endpoint spectrum in semileptonic decays, and the study of spin-symmetry violating effects in ratios of form factors. I also briefly comment on nonleptonic decays.

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.