Electromagnetic corrections to ππ scattering lengths: some lessons for the implementation of meson exchange models

The leading (in chiral order) electromagnetic corrections to s-wave ππ scattering lengths are computed using chiral perturbation theory (ChPT). Contributions associated, not with one-photon exchange, but rather with contact terms in the effective electromagnetic Lagrangian, are shown to dominate previously computed radiative corrections, and to bring experimental values into closer agreement with strong ChPT to one-loop order. It is also shown that omitting such electromagnetic contact terms (as in typical meson-exchange model treatments) would, when combined with experimental input, lead to the erroneous conclusion that ππ → ππ exhibited very large strong isospin breaking. Implications for standard “electromagnetic subtraction” procedures, and for the construction of meson-exchange models in general, are also discussed.