The Heavy Quark Expansion for the Charm Quark

TL;DR

This paper reformulates the Heavy Quark Expansion for charm quarks, expressing it as an expansion in _{ m QCD}/m_c and lpha_s(m_c) with order-one coefficients, highlighting differences from bottom quark expansions.

Contribution

It introduces a new rearrangement of the Heavy Quark Expansion for charm quarks, incorporating additional terms in the leading order unlike the bottom quark case.

Findings

Expansion in _{ m QCD}/m_c and lpha_s(m_c) with order-one coefficients

Leading term includes free-quark decay and four-quark operator matrix elements

Provides a framework for more accurate charm decay calculations

Abstract

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 $\Lambda_{\rm QCD} / m_c$ and $\alpha_s (m_c)$ 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.