Scalar Nonet, SemileptonicKDecays, and Spectral-Function Sum Rules

Abstract

In this paper we show that if one takes $\ensuremath{\epsilon}(700)$, the broad isoscalar $s$-wave dipion resonance for which there exists considerable evidence, along with the as yet not firmly established ${\ensuremath{\eta}}_{V}(1071)$ and ${\ensuremath{\pi}}_{V}(1016)$ and a ${K}_{V}$ (perhaps the one at 1080), as forming a scalar nonet, then the widths and branching ratio for the decay of these resonances into two pseudoscalar mesons are quite consistent with observation. In addition, the mixing of $\ensuremath{\epsilon}$ and ${\ensuremath{\eta}}_{V}$ explains the puzzling smallness of the branching ratio $\frac{({\ensuremath{\eta}}_{V}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi})}{({\ensuremath{\eta}}_{V}\ensuremath{\rightarrow}K\overline{K})}$ and simultaneously accounts for the ${K}_{e4}$ axial-vector form factors. Finally, these scalar resonances are found to fit quite well in the framework of current algebra and spectral-function sum rules stemming from $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ symmetry.