HARD-MESON CURRENT ALGEBRA ANALYSIS OF KL3 DECAY

A hard-meson calculation of the Kl3, 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 f{hook}+(0) takes on its SU(3) symmetric value (f{hook}+(0) ≈ 1.0) then large breakdown of chiral invariance exists, while the chiral symmetric value (f{hook}+(0) ≈ 0.86) implies large breakdown of SU(3). A value of λ+ consistent with the Kl3 data and yielding also the correct K* width if one uses the chiral symmetric f{hook}+(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 Kl3 amplitude). © 1969.