| In this thesis we study a number of decay modes of the B meson. First we discuss the rare inclusive leptonic decay B¯ → Xsℓ+ℓ -, where Xs denotes any hadronic state containing an s-quark. This decay is interesting primarily because it is potentially sensitive to new physics at a higher energy scale. Previous theoretical studies of this decay have calculated the nonperturbative corrections up to O&parl0;L2QCD/ m2b&parr0; ; we calculate the O&parl0;L3QCD/ m3b&parr0; corrections to the lepton invariant mass spectrum, the forward-backward asymmetry, and the hadronic invariant mass spectrum. The values of the nonperturbative parameters entering at this order are unknown, resulting in uncertainties in the Standard Model prediction. We estimate the size of these uncertainties by varying the nonperturbative parameters in a range suggested by dimensional analysis. We study how the uncertainties depend on experimentally motivated phase space cuts.; We also discuss the rare inclusive semileptonic decay B¯ → Xuℓnu, where Xu is any hadronic final state resulting from the weak b → u transition. We study the hadronic invariant mass spectrum as a means of measuring the CKM parameter |Vub|. Experimental backgrounds restrict the accessible phase space to a region where the spectrum is very sensitive to nonperturbative physics, and the spectrum is written in terms of nonperturbative functions called shape functions. We calculate the subleading shape function contributions, and estimate the uncertainty they induce in a measurement of |Vub|. We reduce the uncertainty by relating the spectrum to the photon energy spectrum of the radiative decay B¯ → Xsgamma, and we compare the uncertainties to those found when using the lepton energy spectrum to extract |Vub|.; Finally, we study two-body exclusive nonleptonic decays of the form B¯ → D(*) L, where L is a light meson (L = pi, K, rho). We consider these decay modes in a theoretical framework, called 'QCD factorization', which has attracted much interest in recent years. This framework provides no systematic way to calculate nonperturbative corrections to decay amplitudes. We estimate the parametric size of a class of nonperturbative corrections to these decays by partially summing the amplitudes to all orders in perturbation theory. |
