The QCD Scale in the Heavy Quark Expansion

Abstract

We argue that consistency of the combined heavy quark and chiral effective lagrangian requires the QCD scale which multiplies $1/M$ in the heavy quark expansion to be the chiral symmetry breaking scale, $\Lambda_{CSB}$, rather than the QCD scale, $\Lambda_{QCD}$. This means that either there is large uncertainty in the accuracy with which the heavy quark effective theory can be applied to $c$ quarks or the cutoff scale of the heavy quark chiral effective theory is lower than has been assumed.