Speaker
Description
We study the QCD corrections to the spectator effects in the lifetimes of weakly decaying heavy hadrons containing a bottom quark in the framework of the Heavy Quark Expansion (HQE). These effects come from the contribution of dimension-6 four-quark effective operators which, despite being ${1\over m_b^3}$ suppressed, receive a phase-space enhancement. In our work, we neglect the light-quark masses and keep only the charm-quark mass, together with the bottom quark mass. The resulting masters integrals are then expressed in terms of an expansion in $x={m_c\over m_b}$. We present the state-of-the-art of our calculation of the Next-to-Next-to-Leading-Order Wilson coefficients that are obtained by matching the weak Hamiltonian with $\Delta B=1$ operators onto an effective $\Delta B=0$ Hamiltonian.
