Radiative B decay spectrum: DGE at NNLO

Abstract

We compute the differential B -> X_s gamma decay width in the Standard Model as a function of the photon energy using Dressed Gluon Exponentiation (DGE). The resummed spectrum is matched with the fixed-order expansion, making use of the next-to-next-to-leading order (NNLO) results for the matrix element of the magnetic dipole interaction O_7 and NLO ones for other operators in the effective Weak Hamiltonian. We develop a new technique to implement constraints on the analytic structure of the Sudakov factor in moment space. This improves the behavior of the resummed spectrum away from the Sudakov region. We also derive an analytic expression for the Borel transform of the perturbative series for the O_7 spectrum in the large-beta_0 limit. Using this example we demonstrate that exponentiation in moment space is necessary for the calculation of the spectrum for E_gamma > 2 GeV. Finally, we investigate numerically the relation between renormalons, power corrections and support properties. We present predictions for the branching fraction and the first few spectral moments as a function of a cut E_gamma>E_0 and estimate the theoretical uncertainty.