$O(m_c^{-2})$ nonperturbative corrections to the inclusive rate of the decay $B\to X_s\gamma$

Abstract

It is shown that the inclusive rate of the rare weak radiative decays $B\to X_s\gamma$ contains a series of nonperturbative corrections, whose `short distance' scale is set by $m_c^{-1}$, rather than by $m_b^{-1}$. The first correction in this series is expressed through the chromomagnetic interaction of the $b$ quark inside the $B$ meson and the relative magnitude of the effect is determined by the ratio $<\overline{B}|\bar{b}\sigma \cdot Gb|B>/m_c^2$. Though the magnitude of this first correction is suppressed by a numerical coefficient, the sensitivity of the decay rate to the distance scale $m_c^{-1}$ may significantly limit the accuracy of purely perturbative predictions for the rate.

Comments: 6 pages, LaTeX. Numerical error corrected. As a result the emphasis of the paper is modified