Kl4Form Factors in Current Algebra with Hard Pions and Kaon

The axial form factors in $K_{l4\mathrm{}}$ decays are calculated using the technique of current algebra, hard kaon and pions, the assumption of partially conserved axial-vector current, and the spectral-function sum rules. The assumption of meson dominance of certain vertex functions and inverse propagators as given by Schnitzer and Weinberg is inherent in such calculations. Taking the parameter $\xi$ from the experimental $K_{l3\mathrm{}}$ decays and using the predicted axial-vector form factors at their zero arguments, the decay rates for $K^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$ and $K^{+}\to {\pi }^{+}{\pi }^{-}{\mu }^{+}\nu$ are then calculated. On comparison with their recent observed rates, it is found that the value ${\xi }_{\mathrm{br}}=0.6\mathrm{}$ (from the branching ratio) is strongly favored, as opposed to ${\xi }_{\mathrm{pol}}=-1.0\mathrm{}$ (from polarization measurements). The values of the form factors for other $K_{l4\mathrm{}}$ decays are also given.