Chiral Lagrangians, SU (3)×SU (3) field algebra, symmetry breaking and K ℓ4 decay

Abstract

We study the self-consistent method of implementing chiral symmetry and symmetry breaking assumptions through phenomenological Lagrangian techniques. The basic assumptions are octet PCAC and PCVC through (3 ∗,3) + (3,3 ∗) symmetry breaking, field algebra (and field-current identity) and smooth momentum dependence. These assumptions give hard pion results and a smooth extrapolation to the soft pion PCAC results. In general this may be applied to n-point functions. The main applications in this paper will be to the three and four point functions which contribute to the form factors of K ℓ3 and K ℓ4 decays. Strong decay rates of spin one resonances are used to determine unknown constants in these form factors. The results for the usual K ℓ3 parameters are λ + = 0.024 (0.022), λ − = 0.024 (0.027) and ξ = −0.27 (−0.23) for a K A mass of 1230 (1320) MeV. The new hard pion results from these assumptions give significant corrections to the soft pion results. The hard pion form factors are momentum dependent and contain some unknown parameters not determined by the general assumptions; explicit expressions for the axial vector K ℓ4 form factors are given.