Hard-meson current algebra analysis of the K [formula omitted]3 decay

Abstract

A hard-meson calculation of the K l 3 , K ∗ and κ decays is given based upon (i) chiral SU(3) × SU(3) current algebra, (ii) pion and kaon PCAC, (iii) single meson saturation, (iv) approximation of meson vertices by low-order polynomials in momentum. No a priori assumption on the size of SU(3) or chiral breakdown, or type of chiral breakdown, is made. The possible existence of a κ-meson is included by (v) the PCVC condition on the strangeness changing vector current. If ƒ +(0) takes on its SU(3) symmetric value (ƒ +(0) ≈ 1.0) then large breakdown of chiral invariance exists, while the chiral symmetric value (ƒ +(0) ≈ 0.86) implies large breakdown of SU(3). A value of λ + consistent with the K l 3 data and yielding also the correct K ∗ width if one uses the chiral symmetric ƒ +(0) can be obtained, and implies the vanishing of the K ∗-K-π vertex asymptotically. If no κ-meson exists, the theory requires both |ξ| and λ − to be small. This is also generally the case if a κ meson exists and one assumes a (3 ∗, 3) + (3, 3 ∗) form of chiral breakdown. A large |ξ| and small λ − (which is consistent with both the polarization and the most recent branching ratio determinations) can only be achieved if both a κ-meson exists and one violates the (3 ∗, 3) + (3, 3 ∗) assumption. The theory than also predicts a κ width in agreement with recent data. It is further shown that the hard meson assumption are inconsistent with both a large |ξ| and a large λ −, and that the Callan-Treiman relation may be in error by as much as 50% (due to the presence of non-gentle terms in the K l 3 amplitude).