Low-Energy Axial-Vector Form Factors forKe4Decay Based on Broken Chiral Symmetry

We present an analysis of $K_{e4\mathrm{}}$ decay, particularly the process, $K^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$, using the techniques of current algebra and the $(3^{*},3)\oplus (3,3^{*})$-breaking model. The axial-vector form factors with explicit dependence on the chiral-symmetry parameters are obtained at the points $k^2=p^2=q^2=0\mathrm{}$ and $k^2=m_K^{}{}_{}{}^2$, $p^2=q^2=0\mathrm{}$ and predictions compared with experimental rates and distributions. Discussion and comparison of our results with other recent analyses are also given. In particular, we find that $f_K=f_{\pi }$ and $f_{\kappa }=0\mathrm{}$ gives good over-all agreement with the experimental rate, the fitted form factors, and the experimental distributions although small breakings in $\frac{f_K}{f_{\pi }}$ and somewhat larger breakings in $\frac{f_{\kappa }}{f_{\pi }}$ are not ruled out.