The electroweak pi(+)-pi(0) mass difference and weak matrix elements in the 1/N-c expansion

The pi(+) - pi(0) mass difference generated by the electroweak interactions of the Standard Model is expressed, to lowest order in the chiral expansio n and to leading order in alpha, in terms of an integral involving the same correlation function Pi(LR)(Q(2)) which governs the well known electromagn etic pi(+) - pi(0) mass difference. We calculate this contribution within t he framework of QCD in the limit of a large number of colours N-c. We show how this calculation, which requires non-trivial contributions from next-to -leading terms in the 1/N-c expansion, provides an excellent theoretical la boratory for studying issues of long- and short-distance matching in calcul ations of weak matrix elements of four-quark operators. The electroweak pi( +) - pi(0) mass difference turns out to be a physical observable which is u nder good analytical control and which should, therefore, be an excellent t estground of numerical evaluations in lattice-QCD and of model calculations in general. (C) 1998 Elsevier Science B.V. All rights reserved.