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The Heavy Quark Expansion for the Charm Quark

We show that one can re-arrange the Heavy Quark Expansion for inclusive weak decays of charmed hadrons in such a way that the resulting expansion is an expansion in $Λ_{\rm QCD} / m_c$ and $α_s (m_c)$ with order-one coefficients. Unlike in the case of the bottom quark, the leading term includes not only the contribution of the free-quark decay, but also a tower of terms related to matrix elements of four quark operators.