Momentum-DependentKe4-Decay Form Factors

$K_{e4\mathrm{}}$ decays are considered within the framework of $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ algebra. An effort has been made to obtain the momentum dependence of the axial-vector form factors involved in these decays. To achieve this, we work with zero-mass external pions ($p^2,q^2\to 0$, where $p$ and $q$ are the four-momenta of the two pions), unlike the soft pions ($p,q\to 0$) incorporated in earlier current-algebra calculations of $K_{e4\mathrm{}}$ decays. Further, we use the recently developed on-mass-shell three-point functions throughout our analysis. We also make an estimate of the weak-amplitude term involving $K$- and $Q$-meson poles and the scalar term involving the $\sigma$ meson. In this way, we obtain momentum-dependent $K_{e4\mathrm{}}$-decay form factors. These are used to calculate the dipion energy spectrum, decay rates, and the vector form factor. The fair agreement obtained with the experimental data is indirect evidence of small $s$-wave final-state interactions. Our calculation neatly brings out the fact that the $K_{e4\mathrm{}}$-decay form factors have significant momentum dependence.