Kl3Form Factors and the Pion Charge Form Factor

Phenomenological Lagrangian models for $K_{l3\mathrm{}}$ decays and the pion charge form factor are introduced by assuming single-particle dominance and the trilinear meson interactions derived by Schwinger from his composite model for mesons. The usual pole models in the dispersion approach assume that the structure of a "particle" is entirely due to emission and absorption of another particle or particles by a point-like source. Our models differ from these by allowing the "structure" of the source to be included. In other words, we keep all $q^2$ dependences of the form factors where they are. For small momentum transfers, the form factors can be effectively put into the standard form ${(1+\frac{q^2}{m^2})}^{-1\mathrm{}}$, with $m$ an effective-mass parameter. Assuming $K^{*}$ dominance, we predict the effective-mass parameters in the $K_{l3\mathrm{}}$ form factors $f_{\pm }\left(q^2\right)$ to be about 700 MeV. By assuming ${\rho }^0$ dominance, the effective-mass parameter for the pion charge form factor $f_{\pi }\left(q^2\right)$ is predicted to be about 600 MeV.