Comparing B -> X_u l nu_l to B -> X_s gamma

Abstract

We suggest a method to determine V_ub / V_ts through a comparison of B -> X_u l nu_l and B -> X_s gamma. The relevant quantity is the spectrum of the light-cone component of the final state hadronic momentum, which in B -> X_s gamma is the photon energy while in B -> X_u l nu_l this requires a measurement of both hadronic energy and hadronic invariant mass. The non-perturbative contributions at tree level to these distributions are identical and may be cancelled by taking the ratio of the spectra. Radiative corrections to this comparison are discussed to order alpha_s and are combined with the non-perturbative contributions.

16 pages, 4 figures. One Paragraph added, Version published in Phys.Rev. D60

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