Taming the B --> X(s) gamma spectrum by Dressed Gluon Exponentiation

Abstract

We show that the B \to X(s) gamma photon energy (E_gamma) spectrum can be reliably computed by resummed perturbation theory. Our calculation is based on Dressed Gluon Exponentiation (DGE) incorporating Sudakov and renormalon resummation. It is shown that the resummed spectrum does not have the perturbative support properties: it smoothly extends to the non-perturbative region E_gamma > m/2, where m is the quark pole mass, and tends to zero near the physical endpoint. The calculation of the Sudakov factor, which determines the shape of the spectrum in the peak region, as well as that of the pole mass, which sets the energy scale, are performed using Principal-Value Borel summation. By using the same prescription in both, the cancellation of the leading renormalon ambiguity is respected. Furthermore, in computing the Sudakov exponent we go beyond the formal next-to-next-to-leading logarithmic accuracy using the large-order asymptotic behavior of the series, which is accurately determined from the relation with the pole mass. Upon matching the resummed result with the next-to-leading order expression we compute the spectrum, obtain its moments as a function of a minimum photon energy cut, analyze sources of uncertainty and show that our predictions are in good agreement with Belle data.