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

Abstract

It is shown that the inclusive rate of the rare weak radiative decays $B \to X_s γ$ 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 $< {\overline B} | \bar b σ\cdot G b | B > / m_c^2$. 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.