Kl3-Decay Form Factors, Current Algebra, and Subtracted Dispersion Relations

Abstract

The algebra of currents is used in combination with once-subtracted dispersion relations to investigate the form factors $f_{\pm }\mathrm{}\left(t\right)\mathrm{}$ which describe $K_{l3\mathrm{}}$ decays. The soft-pion approximation is made in the form of a pole-dominance assumption for $q^2\approx 0$ ($q$ is the pion four-momentum) rather than taking the limit $q\to 0$. Results are obtained for the scale as well as for the $t$ dependence of the form factors. The calculation is presented in some detail so that the various effects of $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking may be observed.