ANALYSIS OF K-L-]PI(-)GAMMA IN CHIRAL PERTURBATION-THEORY()PI()

We study the long-distance dominated K-L --> pi(+)pi(-)gamma decay at O(p(6)) in chiral perturbation theory. The complete calculation of the O(p6) loop magnetic amplitude is carried out. At this chiral order th e model-dependent part of the vector meson exchange contribution to th e magnetic amplitude is evaluated in the two models: FM (Factorization Model) and FMV (Factorization Model in the Vector couplings). We pred ict, in an almost model-independent way, a slope of K-L --> pi(+)pi(-) gamma in the range c similar or equal to -1.6, -1.8, consistently with the experimental value. We find that the experimental result for the width of K-L --> pi(+)pi(-)gamma is compatible with a bigger breaking of the nonet symmetry in the weak vertices than previously stated. Thu s we conclude that our analysis does not exclude an opposite sign to t he one given by the dominance of the pion pole in the poorly known K-L --> gamma gamma amplitude. A complete analysis of the O(p(3)) weak ve ctor-pseudoscalar-pseudoscalar (VPP) vertex is also performed. (C) 199 8 Elsevier Science B.V.