Rare radiative B-meson decays - Pullin, Ben (The University of Edinburgh, 2021)
This thesis explores various aspects of radiative B-meson decays. Such processes are phenomenologically interesting since the inclusion of the photon exposes the process to a wider array of effective operators than in the purely leptonic mode. There has been recent interest, for example, in the decay Bs → γµ+µ − as a means of probing persisting anomalies in current flavour data. In the charged modes the presence of the photon acts to lift the helicity suppression leading to greater accessibility to experiment than the leptonic mode. Such a property has led to the decay Bu → γl−νl receiving a great deal of attention as a toy model for QCD factorisation and soft-collinear effective theories. By employing the framework of QCD sum rules on the light-cone this thesis extends the knowledge of B → γ transitions by computing the vector, tensor, and derivative form factors to twist-4 accuracy, including contributions from the 3- particle distribution amplitudes. Furthermore, the O(αs) corrections to both the perturbative and twist-2 contributions are computed. In the perturbative sector this requires the off-shell evaluation of 2-loop triangle diagrams with one internal mass, constituting 4 separate scales. Together this provides a more complete picture of the form factors than has been previously seen. Utilising results obtained in the calculation of the form factors we provide a determination of the effective couplings gHHxγ, where H refers to the heavy B-or D-meson and Hx represents the associated J P = 1± state. The couplings are accessible to experiment via the decay width Γ (Hx → Hγ) for which we provide a prediction and compare to experimental values where known. The evaluation of the couplings requires knowledge of a number of decay constants which we compute via the local operator product expansion. The evaluations comprise of both new results and improvements to existing work in which an ambiguity in the various scales involved has been removed. This thesis aims to present a pedagogical review of methods for computations of hadronic quantities, including applications of multi-loop techniques.
Keywords: sum rules; light-cone sum rules; local sum rules; B mesons; decay constants; form factors; D mesons; flavour physics; 2-loop calculations; radiative decays