Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma 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 m_b-2E_gamma = O(Lambda_QCD), 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 m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} 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/m_b) whenever the photon couples to light partons. In this work, these contributions will be 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 bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV 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 will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

Higher-order perturbative relativistic corrections to energies and properties

Relativistic effects need to be considered in quantum-chemical calculations on systems including heavy elements or when aiming at high accuracy for molecules containing only lighter elements. In the latter case, consideration of relativistic effects via perturbation theory is an attractive option. Among the available techniques, Direct Perturbation Theory (DPT) in its lowest order (DPT2) has become a standard tool for the calculation of relativistic corrections to energies and properties.In this work, the DPT treatment is extended to the next order (DPT4). It is demonstrated that the DPT4 correction can be obtained as a second derivative of the energy with respect to the relativistic perturbation parameter. Accordingly, differentiation of a suitable Lagrangian, thereby taking into account all constraints on the wave function, provides analytic expressions for the fourth-order energy corrections. The latter have been implemented at the Hartree-Fock level and within second-order Møller-Plesset perturbaton theory using standard analytic second-derivative techniques into the CFOUR program package. For closed-shell systems, the DPT4 corrections consist of higher-order scalar-relativistic effects as well as spin-orbit corrections with the latter appearing here for the first time in the DPT series.Relativistic corrections are reported for energies as well as for first-order electrical properties and compared to results from rigorous four-component benchmark calculations in order to judge the accuracy and convergence of the DPT expansion for both the scalar-relativistic as well as the spin-orbit contributions. Additionally, the importance of relativistic effects to the bromine and iodine quadrupole-coupling tensors is investigated in a joint experimental and theoretical study concerning the rotational spectra of CH2BrF, CHBrF2, and CH2FI.