Heavy quark masses from QCD sum rules

I review recent determinations of the (on-shell) charmand beauty-quark masses in the framework of relativistic and non-relativistic ratios of Laplace transform QCD moment sum rules. The validity of the non-relativistic version of QCD sum rules in this particular application is discussed. Invited talk at the Mexican School of Particles and Fields, Villahermosa, Mexico, October 1994. John Simon Guggenheim Fellow 1994-1995. With the advent of the Heavy Quark Effective Theory (HQET) there has been a revived interest in applications of QCD sum rules to the heavy quark sector. The purpose being the update of old determinations, as well as the performance of new calculations to extract accurate values of various dynamical quantities entering the HQET. Chief of these quantities is the ubiquitous heavy-quark mass. I review here recent determinations of the (on-shell) charmand beauty-quark masses [1] performed by confronting very accurate experimental data on the charmonium and the upsilon systems [2] with ratios of relativistic and non-relativistic Laplace transform QCD moments. The latter theoretical framework, suggested by Bertlmann [3], offers several advantages, e.g. radiative and nonperturbative corrections are well under control, and the non-relativistic limit follows quite naturally from quantum mechanical analogues [4]. This version of QCD sum rules leads to an expansion in powers of the inverse of the heavy quark mass which allows one to test the range of validity of the non-relativistic limit, and more generally, to assess the role of mass corrections. This might be of interest for calculations based on the simplifying assumption ΛQCD/mQ ≪ 1. Also, a comparison of the results from the relativistic and the non-relativistic determinations provides an estimate of the systematic uncertainties affecting this technique. I begin by considering the two-point function