Heavy Quark Expansion for Heavy Hadron Lifetimes: Completing the $1\mathrm{/}{m}_b^3$ Corrections

We complete the calculation of the contributions from the dimension six operators in the heavy quark expansion for the total lifetime of heavy hadrons. We give the expressions for the Wilson coefficients of the Darwin term ${\rho }_D$ and the spin-orbit term ${\rho }_{\mathrm{L}\mathrm{S}}$ at tree level.