K_{l 3} and \pi_{e 3} transition form factors

Abstract

$K_{\ell 3}$ and ${\pi }_{e3}$ transition form factors are calculated as an application of Dyson-Schwinger equations. The role of nonanalytic contributions to the quark--W-boson vertex is elucidated. A one-parameter model for this vertex provides a uniformly good description of these transitions, including the value of the scalar form factor of the kaon at the Callan-Treiman point. The $K_{\ell 3}$ form factors, $f_{\pm }^K$, are approximately linear on $t\in [m_e^2,m_{\mu }^2]$ and have approximately the same slope. $f_{-}^K(0)$ is a measure of the Euclidean constituent-quark mass ratio: $M_s^E/M_u^E$. In the isospin symmetric limit: $-f_{+}^{\pi }(0)=F_{\pi }(t)$, the electromagnetic pion form factor, and $f_{-}^{\pi }(t)\equiv 0$.

Comments: 11 pages (incl. 3 figures), elsart.sty, epsf.sty