Nonperturbative Corrections with Nonlocal Operators to Lifetime Ratios of Beauty Hadrons

Abstract

The motion of spectator quarks in decay of a beauty hadron is a nonperturbative effect which can usually be neglected. We find that the motion in some decay channels, which contribute total decay widths of beauty hadrons, can not be neglected.The contributions from these decay channels to decay widths are proportional to certain averages of the squared inverse of the momentum carried by a spectator quark. This fact results in that these contributions, suppressed by $1/m_b^3$ formally, are effectively suppressed by $1/m_b$. We find these contributions can be factorized into products of perturbative coefficients and nonperturbative parameters. We calculate these coefficients and define these nonperturbative parameters in terms of HQET matrix elements.Since these parameters are unknown, we are unable to give numerical predictions in detail. But with a simple model it can be shown that these contributions can be large.