  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.
