Inclusive rare B decays using effective field theories

grantor: University of TorontoIn this thesis we will discuss several properties of rare decays of ' B' mesons. First we discuss properties of the inclusive radiative decay 'B¢' [right arrow] 'Xs'ã, where 'Xs' stands for any hadronic state containing an 's' quark. We extend previous studies of this decay, which included perturbative corrections to order Ã's' and nonperturbative contributions up to order ([Lambda]QCD/' mb')2 and calculate the O ([Lambda]QCD/'mb')3 contributions to this decay. The values of the nonperturbative parameters entering at this order are unknown, leading to uncertainties in the standard model prediction of this decay. We estimate the size of these nonperturbative uncertainties by varying these parameters in the range suggested by dimensional analysis. We also estimate uncertainties arising from a cut on the photon energy which is required experimentally. Another decay mode investigated is 'B¢' [right arrow] ' Xs'¾+¾-. We study the O ([Lambda]QCD/'mb')3 contributions to the leptonic invariant mass spectrum, the forward-backward asymmetry and hadronic invariant mass moments and estimate the resulting uncertainties. We calculate how the size of these uncertainties depend on the value of an experimental cut that has to be applied to eliminate the large background from other 'B' decays. A model independent way to determinate the CKM matrix element @' Vub'@ from the dilepton invariant mass spectrum of the inclusive decay B&d1;[right arrow]Xu¾+ n&d1; is presented next. We show that cuts required to eliminate the charm background still allow for a theoretically clean way to determine the CKM matrix element @'Vub'@. We also discuss the utility of the 'B¢' [right arrow] 'Xs'¾ +¾- decay rate above the y (2'S') resonance to reduce the resulting uncertainties. Finally, we introduce a novel effective theory valid for highly energetic particles. In decays where the phase space is sufficiently restricted such that final state particles have very high energies compared to their mass, the perturbative as well as nonperturbative series diverge. The effective theory presented allows to sum perturbative Sudakov logarithms in a framework that also incorporates the nonperturbative physics in such limits of phase space.Ph.D