Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities

The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in $1/N_c$. We organize the calculation in an $1/N_c$-expansion and separate long- and short-distance physics contributions by introducing an Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full Chiral Perturbation Theory calculation to order $e^2$ $p^2$ for the masses and $p^6$ for the polarizabilities. For the electromagnetic corrections to the masses, we confirm a large violation of Dashen's theorem getting a more precise value for this violation. We make comparison with earlier related work. Some phenomenological consequences are discussed too.