Veneziano Formula,KAMeson Decays, and Weinberg Limits ofKl4Form Factors

Abstract

$s$- and $d$-wave ratios of ${g}_{{K}_{A}{K}_{\ensuremath{\rho}}}$ and ${g}_{{K}_{A}{K}^{*}\ensuremath{\pi}}$ couplings have been determined using Veneziano representations for ${K}_{A}\ensuremath{\pi}\ensuremath{\rightarrow}K\ensuremath{\pi}$ amplitudes. The results are in agreement with those obtained by the hard-meson techniques of current algebra. Assuming that the axial-vector current is dominated by ${K}_{A}$- and $K$-meson poles only, we obtain the ${K}_{l4}$ form factors from $K\ensuremath{\pi}\ensuremath{\rightarrow}{K}_{A}\ensuremath{\pi}$ and $K\ensuremath{\pi}\ensuremath{\rightarrow}K\ensuremath{\pi}$ scattering amplitudes when the ${K}_{A}$ and one of the $K$ mesons are taken off shell. Current-algebra constraints due to Weinberg, when both pions are soft, are then used to fix the arbitrary parameters of the theory. We find that consistency of our results with current-algebra predictions requires the presence of nonleading Veneziano amplitudes.