Factorization and non-local 1/mb corrections in the decay anti B → Xsγ

In this thesis, a systematic analysis of the anti B → Xsγ photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy mb-2Eγ=O(ΛQCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass mb, the hadronic energy scale ΛQCD and an intermediate scale √(ΛQCDmb) associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/mb) whenever the photon couples to light partons. In this work, these contributions are explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the anti B → Xsγ branching fraction, defined with a cut Eγ > 1.6GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5%. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry are considered. It is shown that these effects are dominant in the Standard Model and that a range of -0.6 < ASMCP < 2.8% is possible for the asymmetry, if resolved photon contributions are taken into account. (orig.)