Analysis of KL → π+π−γ in chiral perturbation theory

Abstract

We study the long-distance dominated K L → π + π − γ decay at O(p 6) in chiral perturbation theory. The complete calculation of the O(p 6) loop magnetic amplitude is carried out. At this chiral order the model-dependent part of the vector meson exchange contribution to the magnetic amplitude is evaluated in the two models: FM (Factorization Model) and FMV (Factorization Model in the Vector couplings). We predict, in an almost model-independent way, a slope of K L → π + π − γ in the range c ∼- −1.6, −1.8, consistently with the experimental value. We find that the experimental result for the width of K L → π + π − γ is compatible with a bigger breaking of the nonet symmetry in the weak vertices than previously stated. Thus we conclude that our analysis does not exclude an opposite sign to the one given by the dominance of the pion pole in the poorly known K L → γγ amplitude. A complete analysis of the O(p 3) weak vector-pseudoscalar-pseudoscalar ( VPP) vertex is also performed.