Analysis of the photon spectrum in inclusive B-->Xs gamma decays.

Abstract

Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decays. The shape of the spectrum is determined by a universal structure function, which describes the distribution of the light-cone momentum of the $b$ quark inside the $B$ meson. The moments of this function are proportional to forward matrix elements of higher-dimension operators. As a by-product, we obtain the bound ${\ensuremath{\lambda}}_{1}<0$ for one of the parameters of the heavy quark effective theory. An integral over the $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ structure function is related to the shape function that governs the fall off of the lepton spectrum close to the end point in $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays. A measurement of the photon spectrum in rare $B$ decays can therefore help to obtain a model-independent determination of ${V}_{\mathrm{ub}}$.