P3H-25-019: QCD Corrections for Subleading Powers in $1/m_b$ for the nonleptonic $b\rightarrow c\b

induced by the operators $b \to c \bar c q$ ($q = s,d$). This calculation adds the last missing piece of the full NLO terms at $1/m_b^2$ in the heavy quark expansion of $B$-hadron lifetimes. We consider the current-current operator contributions to the decay modes $b\rightarrow c\bar c s$ and $b\rightarrow c \bar c d$, disregarding here the contributions from penguin operators and the weak chromomagnetic operator due to the smallness of their Wilson coefficients. However, using the technology set up here, all four quark-operator contributions can be calculated. We obtain analytical results with full dependence on the final-state charm quark mass, which we provide in the supplemental file “coefbccs.m”. |