Analysis of the Photon Spectrum in Inclusive $B\to X_s\,γ$ Decays

Details Analysis of the Photon Spectrum in Inclusive $B\to X_s\,γ$ Decays Analysis of the Photon Spectrum in Inclusive $B\to X_s\,γ$ Decays

1993-12-20

arxiv.org/abs/hep-ph/9312311v2

Phys.Rev.D49:4623-4633,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.49.4623

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 $V_{ub}$.

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