QCD SUM-RULES AND NEUTRON-PROTON MASS DIFFERENCE

We use the method of QCD sum rules to investigate the neutron-proton mass difference. We include diagrams consistently up to dimension 9, assuming different up and down current-quark masses (m(u) not-equal m(d)), and distinguish between [0\:uuBAR:\0] and [0\:ddBAR:\0], the condensates of the up and down quarks. Using the typical current-quark masses mu = 5.1 MeV and Md = 8.9 MeV and the standard condensate values for average current-quark masses, we perform numerical analyses of the resultant QCD p and unity sum rules. In particular, numerical analyses of the difference equation from the p sum rules yield M(n) - M(p) = (1.35+/-0.24) MeV or (1.42+/-0.19) MeV, depending on the method of the analysis. Analogously, the difference equation from the unity sum rules yields M(n) - M(p) = (1.35+/-0.35) MeV or (0.95+/-0.25) MeV. These predictions are consistent among themselves and all are in reasonable agreement with the experimental value of 1.29 MeV.