The non-perturbative corrections to the $\bar B \to X_sγ$ photon spectrum in a parton-like model

Abstract

We derive a new parton-like formula, which establishes a simple connection between the electroweak decay rate $Γ(\bar B \to X_sγ$) and the rate of a free b-quark decay. The main features of our approach are the treatment of the b-quark as an on-mass-shell particle and the inclusion of the effects arising from the b-quark transverse motion in the $\bar B$-meson. Using various b-quark light-front (LF) distribution functions, both phenomenological one and the ones derived from current constituent quark models, and neglecting perturbative corrections we compute the photon energy spectra and the moments of the shape function. It is shown that the parton-like approach is fully consistent with the Heavy Quark Effective Theory (HQET) provided the b-quark constituent mass is redefined in the way similar to that used in HQET to define the pole mass of the b quark. In this way the correction to first order in $1/m_b$ can be eliminated from the total width in agreement with the general statement of HQET. We have also found that the photon energy spectra calculated in the LF approach agree well with the ones obtained in the ACM model, provided the same distribution function is used as input in both cases. In spite of the simplicity of the model our results show a fair good agreement both with the HQET predictions and available experimental data.