We estimate the π+-π0 electromagnetic mass difference within the 1/N expansion approach to hadronic matrix elements. Perturbative QCD and a truncated meson theory describe the high- and low-photon-loop-momentum contributions, respectively. The matching between these complementary pictures for strong interactions is discussed.
Bardeen, W. A., Bijnens, J., & Gérard, J.-M. (1989). Hadronic Matrix Elements and the pi+ pi0 Mass Difference. Physical Review Letters, 62(12), 1343-1346. https://doi.org/10.1103/PhysRevLett.62.1343 (Original work published 1989)