Analysis of the Photon Spectrum in Inclusive $B\to X_s\gamma$ 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 $B\to X_s\gamma$ 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 ${\lambda }_1<0$ for one of the parameters of the heavy quark effective theory. The 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 endpoint in $B\to X_u\ell \bar{\nu }$ decays. A measurement of the photon spectrum in rare $B$-decays can therefore help to obtain a model-independent determination of $V_{ub}$.

(Sec. 5 has been modified, and a discussion of radiative corrections has been added to Sec. 6), 26 pages, CERN-TH.7113/93

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