κ-Meson Mass and Weak-Decay Parameters from a Study ofKl3Form Factors

Current algebra, dispersion relations, and the postulate of a partially conserved vector current with which we associate a strangeness-carrying scalar meson $\kappa$ are employed to obtain the $K_{l3\mathrm{}}$ form factors and other weak-decay parameters. The values $f_{+}\mathrm{}\left(0\right)=0.96\mathrm{}$ and $\left|\frac{F_{\kappa }}{F_{\pi }}\right|\approx 0.1$ indicate that the $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry-breaking effect is negligibly small. The mass of the $\kappa$ meson is found to be greater than 1300 MeV, with a very large width for the decay $\kappa +K+\pi$. It is concluded that the existence of the $\kappa$ meson as a physically observable particle is extremely doubtful.