Mass of the charm-quark from QCD sum rules

Relativistic and non-relativistic ratios of Laplace transform QCD moment sum rules for charmonium are used in order to determine the value of the on-shell charmquark mass. The validity of the non-relativistic version of QCD sum rules in this particular application is discussed. After using current values of the perturbative and non-perturbative QCD parameters, as well as experimental data on the J/ψ system, we obtain mc(Q 2 = m2c) = 1.46 ± 0.07 GeV. John Simon Guggenheim Fellow 1994-1995 Recently, the value of the (on-shell) beauty-quark mass has been determined [1] by confronting very accurate experimental data on the upsilon system [2] with ratios of nonrelativistic Laplace transform QCD moments. This theoretical framework, suggested by Bertlmann [3], offers several advantages, e.g. radiative and non-perturbative 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. Non-relativistic Laplace moments appear to have a sensitive dependence on the quark mass. In fact, in spite of the large uncertainties affecting the values of ΛQCD and the non-perturbative gluon condensate, mb can be extracted from the upsilon data with high precision. This extraction is performed by confronting the ratios of Laplace transform moments calculated from experiment with those from theory. The latter involve the QCD parameters mb, Λ, < αsG 2 >, etc.. These ratios are functions of the Laplace variable, which acts as a short distance expansion parameter, and one finds a reasonably wide region in this variable where there is a matching between experiment and theory for a specific value of the quark mass. As pointed out in [1], a straightforward extension of this technique to the charm-quark may not work, as radiative and mass corrections could exceed 100 % . This would be true if the window in the Laplace variable would be the same for beauty and for charm. However, there is no a-priori reason for this to be the case. In fact, as also suggested in [3], the matching between theory and experiment for the beauty and the charm quarks could take place at different ranges of the Laplace variable. If this range is such that radiative, non-perturbative, and mass corrections remain small, then it would become possible to extract the value of the charm quark from this framework.