High precision prediction of the photon-energy spectrum in B → Xsγ

The rare decay $b \to s \gamma$ is an important process for testing the Standard Model (SM) of particle physics and for searching possible effects of new physics beyond it. Because this transition occurs only through quantum loops in the SM, it is particularly sensitive to hypothetical new heavy degrees of freedom appearing in the loops as virtual particles. Experimental measurements focus on the peak region at the photon-energy spectrum end-point, which provides crucial information on the overall decay rate of the inclusive process $B \to X_s \gamma$. In addition, the shape of the photon-energy spectrum contains direct information on the internal motion of the b quark inside the B meson. This nonperturbative effect is described by the so-called shape function, which plays a key role in precision studies of inclusive $B$-meson decays. In this thesis, we study the photon-energy spectrum in $B \to X_s \gamma$ decays within the framework of the $\Delta B = \Delta S = 1$ effective Hamiltonian. The analysis will incorporate, for the first time, recent results for the hard function and the fixed-order spectrum at next-to-next-to-next-to-leading order in perturbative QCD [1,2]. A further goal of the work is to compare different short-distance schemes used to define the bottom-quark mass and to assess their impact on theoretical predictions.