Unsubtracted Dispersion Relation, Current Algebra, and Momentum-Dependent Vector Form Factor inKl4Decays

The momentum-dependent structure of the vector form factor in $K_{l4\mathrm{}}$ decays is obtained by using unsubtracted dispersion relations and hard-meson current algebra. A few of the coupling parameters in terms of which the vector amplitude is expressed are evaluated from the on-mass-shell three-point functions of currents obeying the algebra of $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$. The other parameters, involving $\mathrm{VVP}$ couplings, are related to the known decay rate for the process ${\pi }^0\to \gamma \gamma$. The contributions of the vector form factor to the decay rates and the so-called left-right asymmetry parameter have been obtained and compared with those of the previous calculations.