The electroweak pi^+ - pi^0 mass difference and weak matrix elements in the 1/Nc expansion

The pi^+ - pi^0 mass difference generated by the electroweak interactions of the Standard Model is expressed, to lowest order in the chiral expansion 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 electromagnetic pi^+ - pi^0 mass difference. We calculate this contribution within the 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/Nc expansion, provides an excellent theoretical laboratory for studying issues of long- and short-distance matching in calculations of weak matrix elements of four-quark operators. The electroweak pi^+ - pi^0 mass difference turns out to be a physical observable which is under good analytical control and which should, therefore, be an excellent testground of numerical evaluations in lattice-QCD and of model calculations in general.