Taming the bar BlongrightarrowXsγ spectrum by dressed gluon exponentiation

We show that the B \to X(s) gamma photon energy (E_gamma) spectrum can bereliably computed by resummed perturbation theory. Our calculation is based onDressed Gluon Exponentiation (DGE) incorporating Sudakov and renormalonresummation. It is shown that the resummed spectrum does not have theperturbative support properties: it smoothly extends to the non-perturbativeregion E_gamma > m/2, where m is the quark pole mass, and tends to zero nearthe physical endpoint. The calculation of the Sudakov factor, which determinesthe 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 Borelsummation. By using the same prescription in both, the cancellation of theleading renormalon ambiguity is respected. Furthermore, in computing theSudakov exponent we go beyond the formal next-to-next-to-leading logarithmicaccuracy using the large-order asymptotic behavior of the series, which isaccurately determined from the relation with the pole mass. Upon matching theresummed result with the next-to-leading order expression we compute thespectrum, obtain its moments as a function of a minimum photon energy cut,analyze sources of uncertainty and show that our predictions are in goodagreement with Belle data.Comment: Comments and references added; Error in overall normalization of differential spectra in Figs. 6 and 8-10 corrected; To appear in JHEP; 50 pages, 18 postscript figure