Abstract:
We study nonperturbative corrections to the inclusive rare decay B -> X_s l^+ l^- by performing an operator product expansion (OPE) to O(1/m_b^3). The values of the matrix elements entering at this order are unknown and introduce uncertainties into physical quantities. We study uncertainties introduced into the partially integrated rate, moments of the hadronic spectrum, as well as the forward-backward asymmetry. We find that for large dilepton invariant mass q^2 > M_{\psi'}^2 these uncertainties are large. We also assess the possibility of extracting the HQET parameters \lambda_1 and \bar{\Lambda} using data from this process.

Abstract:
It is shown that the inclusive rate of the rare weak radiative decays $B \to X_s \gamma$ contains a series of nonperturbative corrections, whose `short distance' scale is set by $m_c^{-1}$, rather than by $m_b^{- 1}$. The first correction in this series is expressed through the chromomagnetic interaction of the $b$ quark inside the $B$ meson and the relative magnitude of the effect is determined by the ratio $< {\overline B} | \bar b \sigma \cdot G b | B > / m_c^2$. Though the magnitude of this first correction is suppressed by a numerical coefficient, the sensitivity of the decay rate to the distance scale $m_c^{-1}$ may significantly limit the accuracy of purely perturbative predictions for the rate.

Abstract:
We present an estimate of certain higher order corrections to the contribution of the charm triangle loop in the inclusive B -> X_s gamma decay rate, recently discussed by Voloshin. We find that these corrections are minute and hence the result found by Voloshin, although small, is quite robust.

Abstract:
We reconsider the calculation of ${\cal O}(\Lambda^2_{QCD}/m^2_b)$ nonperturbative corrections to $\bar B\to X_sl^+l^-$ decay. Our analysis confirms the results of Ali et al. for the dilepton invariant mass spectrum, which were in disagreement with an earlier publication, and for the lepton forward-backward asymmetry. We also give expressions for the ${\cal O}(\Lambda^2_{QCD}/m^2_b)$ corrections to the left-right asymmetry. In addition we discuss the breakdown of the heavy quark expansion near the point of maximal dilepton invariant mass $q^2$ and consider a model independent approach to this region using heavy hadron chiral perturbation theory. The modes $\bar B\to\bar Kl^+l^-$ and $\bar B\to\bar K\pi l^+l^-$, which determine the endpoint region of the inclusive decay, are analyzed within this framework. An interpolation is suggested between the region of moderately high $q^2$, where the heavy quark expansion is still valid, and the vicinity of the endpoint described by chiral perturbation theory. We also comment on further nonperturbative effects in $\bar B\to X_sl^+l^-$.

Abstract:
We calculate O(alpha_s) two-loop virtual corrections to the differential decay width dGamma(B --> X_s l^+ l^-)/ds, where s is the invariant mass squared of the lepton pair. We also include those contributions from gluon bremsstrahlung which are needed to cancel infrared and collinear singularities present in the virtual corrections. Our calculation is restricted to the range 0.05 < s/m_b^2 < 0.25 where the effects from resonances are small. The new contributions drastically reduce the renormalization scale dependence of existing results for dGamma(B --> X_s l^+ l^-)/ds. For the corresponding branching ratio (restricted to the above s-range) the renormalization scale uncertainty gets reduced from +/- 13% to +/- 6.5%.

Abstract:
We present the results of the O(alpha_s) two-loop virtual corrections to the differential decay width dGamma(B -> X_s l+ l-)/ds, where s is the invariant mass squared of the lepton pair. Those contributions from gluon bremsstrahlung which are needed to cancel infrared and collinear singularities are also included. Our calculation is restricted to the range 0.05 < s/mb^2 < 0.25 where the effects from resonances are small. The new contributions drastically reduce the renormalization scale dependence of existing results for dGamma(B->X_s l+ l-)/ds. The renormalization scale uncertainty of the corresponding branching ratio (restricted to range mentioned above) gets reduced from +/-13% to +/-6.5%.

Abstract:
We discuss nonperturbative contributions to the inclusive rare $B$ decays $B\to X_s\gamma$ and $B\to X_s\ell^+\ell^-$. We employ an operator product expansion and the heavy quark effective theory to compute the leading corrections to the decay rate found in the free quark decay model, which is exact in the limit $m_b\to\infty$. These corrections are of relative order $1/m_b^2$, and may be parameterised in terms of two low-energy parameters. We also discuss the corrections to other observables, such as the average photon energy in $B\to X_s\gamma$ and the lepton invariant mass spectrum in $B\to X_s\ell^+\ell^-$.

Abstract:
Uncertainties in the theoretical prediction for the inclusive $\bar B\to X_s\gamma$ decay rate are examined. Certain nonperturbative effects involving a virtual $c\bar c$ loop, which are calculable using the operator product expansion, are discussed.

Abstract:
Uncertainties in the theoretical prediction for the inclusive $B\to X_s\gamma$ decay rate are discussed. We emphasize that there is no operator product expansion for this process. Nonetheless, some nonperturbative effects involving a virtual $c\bar c$ loop are calculable using the operator product expansion. They give a contribution to the decay rate that involves the B meson matrix element of an infinite tower of operators. The higher dimension operators give effects that are only suppressed by powers of $m_b\Lambda_{QCD}/m_c^2 \sim 0.6$, but come with small coefficients.

Abstract:
A nonperturbative quantization procedure based on a nonassociative decomposition of quantum field operators on nonassociative constituents is considered. It is shown that such approach gives rise to quantum corrections by calculations of expectation values of nonlinear functions of field operators. The corrections can in principle be measured as a radius of a force, characteristic length of nonlocal objects, the failure of connection compatibility with metric, and so on. The system of gravity interacting with Maxwell electromagnetism is considered. It is shown that quantum corrections from gravitoelectric coupling of a certain form leads to vanishing singularities of a point charge, including infinite self-energy.