On The Expected Photon Spectrum in B -> X + gamma and Its Uses
Abstract
The recent analysis of the photon energy spectrum in B -> X_s+\gamma transitions by the CLEO collaboration suggests that only a small fraction of photons carries energies below 2 GeV. Their fit actually yields about 5% for this fraction. It is argued that this number would significantly underestimate the expected size of the spectrum below 2 GeV. The latter has great practical importance. Extracting |V_{ub}| from the invariant hadronic mass M_X in B -> X\ell\nu one has to impose a cut on M_X to suppress the b->c background; the fraction of b->u events satisfying such a cut can be related to the photon spectrum via universality relations for the heavy quark distribution function. It is shown that potentially significant uncertainties enter in theoretical evaluation of the integrated end-point lepton spectrum or the width with a too high value of the lower cut on q^2. It is argued that the cut on M_X is robust in this respect, and a method is proposed to incorporate 1/m_b effects into the corresponding universality relations.Keywords
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