Pattern of Lifetimes of Beauty Hadrons and Quark-Hadron Duality in Heavy   Quark Expansion
  We discuss (i) the evaluation of the expectation values of four-quark operators assuming that the heavy quark expansion for $b$ sector converges at the third order in $1/m_Q$, and (ii) the estimation of the duality breaking short distance nonperturbative corrections to the parton decay rate. We finally point out the implications of the result obtained for the assumption of quark-hadron duality in heavy quark expansion. 
S. Arunagiri (U. Madras)