The heavy quark expansion for lifetimes: Towards the QCD corrections to power suppressed terms

We consider the Heavy Quark Expansion (HQE) for the nonleptonic decay rates of heavy hadrons, and compute the NLO QCD corrections to power terms up to order $1\mathrm{/}{m}_Q^2$. We neglect the masses of the final-state quarks, so the application of our result is mainly for charmed hadrons. Our result can be applied also to bottomed hadrons as they constitute the main effect to this order up to corrections of $\mathcal{O}(m_c\mathrm{/}{m}_b)$ and contributions due to penguin operators. We discuss the impact of our result for the lifetimes of heavy hadrons.