Analysis of the Photon Spectrum in Inclusive B → X s γ Decays

Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in B → Xs γ 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 byproduct, we obtain the bound λ1 < 0 for one of the parameters of the heavy quark effective theory. The integral over the B → Xs γ structure function is related to the shape function that governs the fall-off of the lepton spectrum close to the endpoint in B → Xu l ν̄ decays. A measurement of the photon spectrum in rare B-decays can therefore help to obtain a model-independent determination of Vub. (submitted to Physical Review D)