Abstract:
We present a QCD-based approach to the endpoint region of the lepton spectrum in $\bar B\to X_u\,\ell\,\bar\nu$ decays. We introduce a genuinely nonperturbative form factor, the shape function, which describes the fall-off of the spectrum close to the endpoint. The moments of this function are related to forward scattering matrix elements of local, higher-dimension operators. We find that nonperturbative effects are dominant over a finite region in the lepton energy spectrum, the width of which is related to the kinetic energy of the $b$-quark inside the $B$ meson. Applications of our method to the extraction of fundamental standard model parameters, among them $V_{ub}$, are discussed in detail.

Abstract:
We apply the operator product expansion to resum the leading nonperturbative corrections to the endpoint region of the lepton spectrum in inclusive semileptonic $B\to X_q\,\ell\,\bar\nu$ decays, taking into account a finite quark mass $m_q$ in the final state. We show that both for $b\to c$ and $b\to u$ transitions, it is consistent to describe these effects by a convolution of the parton model spectrum with a fundamental light-cone structure function. The moments of this function are proportional to forward matrix elements of higher-dimension operators. The prospects for an extraction of the structure function from a measurement of the lepton spectrum are discussed.

Abstract:
Charmless semileptonic decays, ${\bar{B}} \to X_u \ell \bar{\nu}$, are studied in a sample of 232 million $B\bar{B}$ decays recorded with the BaBar detector, in events where the decay of the second $B$ meson is fully reconstructed. Inclusive charmless decays are selected in kinematic regions where the dominant background from semileptonic B decays to charm is reduced by requirements on the hadronic mass $M_X$ and the momentum transfer $q^2$. The partial branching fraction for ${\bar{B}} \to X_u \ell \bar{\nu}$ decays for $M_X<1.7$ GeV/c^2 and $q^2>8$ Gev^2/c^4 is measured to be $\Delta{\cal{B}}({\bar{B}} \to X_u \ell \bar{\nu}) = (0.87 \pm 0.09_{\rm stat}\pm 0.09_{\rm sys}\pm 0.01_{\rm th})\times 10^{-3}$. The CKM matrix element $|V_{ub}|$ is determined by using theoretical calculations of phase space acceptances. Theoretical uncertainties in this extrapolation are reduced by using the inclusive $b \to s \gamma$ photon spectrum and moments of the $b \to c \ell \bar{\nu}$ lepton energy and hadronic invariant mass.

Abstract:
Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\to X_s\,\gamma$ decays. The shape of the spectrum is determined by a universal structure function, which describes the distribution of the light-cone momentum of the $b$-quark inside the $B$-meson. The moments of this function are proportional to forward matrix elements of higher-dimension operators. As a by-product, we obtain the bound $\lambda_1<0$ for one of the parameters of the heavy quark effective theory. The integral over the $B\to X_s\,\gamma$ structure function is related to the shape function that governs the fall-off of the lepton spectrum close to the endpoint in $B\to X_u\,\ell\,\bar\nu$ decays. A measurement of the photon spectrum in rare $B$-decays can therefore help to obtain a model-independent determination of $V_{ub}$.

Abstract:
The invariant mass spectrum of the lepton pair in inclusive semileptonic $\bar B\to X_u \ell\bar\nu$ decay yields a model independent determination of $|V_{ub}|$. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when $d\Gamma / dq^2$ is integrated over $q^2 > (m_B-m_D)^2$, which is required to eliminate the $\bar B\to X_c \ell\bar\nu$ background. We discuss these backgrounds for $q^2$ slightly below $(m_B-m_D)^2$, and point out that instead of $q^2 > (m_B-m_D)^2 = 11.6 GeV^2$, the cut can be lowered to $q^2 \gtrsim 10.5 GeV^2$. This is important experimentally, particularly when effects of a finite neutrino reconstruction resolution are included.

Abstract:
We present $O(\alpha_s^2)$ QCD corrections to the fully-differential decay rate of a $b$-quark into inclusive semileptonic charmless final states. Our calculation provides genuine two-loop QCD corrections, beyond the Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic observable that can be probed in $b \to X_u e \bar \nu$ decays. Kinematic cuts that closely match those used in experiments can be fully accounted for. To illustrate these points, we compute the non-BLM corrections to moments of the hadronic invariant mass and the hadronic energy with cuts on the lepton energy and the hadronic invariant mass. Our results remove one of the sources of theoretical uncertainty that affect the extraction of the CKM matrix element $|V_{ub}|$ from charmless inclusive B-decays.

Abstract:
We develop the perturbative QCD formalism for inclusive semileptonic $B$ meson decays, which includes Sudakov suppression from the resummation of large radiative corrections near the high end of charged lepton energy. Transverse degrees of freedom of partons are introduced to facilitate the factorization of $B$ meson decays. Ambiguities appearing in the quark-level analysis are then avoided. A universal distribution function, arising from the nonperturbative Fermi motion of the $b$ quark, is constructed according to the heavy quark effective field theory based operator product expansion, through which the mean and the width of the distribution function are related to hadronic matrix elements of local operators. Charged lepton spectra of the $B\to X_u\ell\nu$ decay are presented. We find 50\% suppression near the end point of the spectrum. The overall suppression on the total decay rate is 8\% for the free quark model, and is less than 7\% for the use of smooth distribution functions. With our predictions, it is then possible to extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ from experimental data. We also discuss possible implications of our analysis when confronted with the rather small observed semileptonic branching ratio in $B$ meson decays.

Abstract:
We present partial branching fractions for inclusive charmless semileptonic B decays Bbar --> X_u ell nubar, and the determination of the CKM matrix element |V_{ub}|. The analysis is based on a sample of 383 million Y(4S) decays into B Bbar pairs collected with the BaBar detector at the PEP-II e+ e- storage rings. We select events using either the invariant mass M_X of the hadronic system, the invariant mass squared, q^2, of the lepton and neutrino pair, the kinematic variable P_+ or one of their combinations. We then determine partial branching fractions in limited regions of phase space: Delta B = (1.18 +- 0.09_{stat.} +- 0.07_{syst.} +- 0.01_{theo.}) x 10^{-3} (M_X < 1.55 GeV/c^2), Delta B = (0.95 +- 0.10_{stat.} +- 0.08_{syst.} +- 0.01_{theo.}) x 10^{-3} (P_+ < 0.66 GeV/c), and Delta B = (0.81 +- 0.08_{stat.} +- 0.07_{syst.} +- 0.02_{theo.}) x 10^{-3} (M_X < 1.7 GeV/c^2, q^2 > 8 GeV^2/c^4). Corresponding values of |V_{ub}| are extracted using several theoretical calculations.

Abstract:
Recent results on inclusive charmless semileptonic decays of B mesons are reviewed. Emphasis is given to measurements on the recoil of fully reconstructed B mesons, which allow to exploit several regions of phase space. Preliminary averages of the CKM matrix element $|V_{ub}|$ from the Heavy Flavour Working Group are shown, using four different theoretical calculations.

Abstract:
I report here recent measurements of observables from the inclusive decays $B\to X_s\gamma$ and $B\to X_s\ell^+\ell^-$. Included are measurements of the branching fractions and CP asymmetries for both channels, as well as the forward-backward lepton asymmetry in inclusive $B\to X_s\ell^+\ell^-$ decays, which is the first measurement of this quantity.