Analysis of the photon spectrum in inclusiveB→Xsγdecays

Abstract

Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\to X_s\gamma$ 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 ${\lambda }_1<0\mathrm{}$ for one of the parameters of the heavy quark effective theory. An integral over the $B\to X_s\gamma$ structure function is related to the shape function that governs the fall off of the lepton spectrum close to the end point in $B\to X_u\ell \overline{\nu }$ decays. A measurement of the photon spectrum in rare $B$ decays can therefore help to obtain a model-independent determination of $V_{\mathrm{ub}}$.