K_{l 3} and π_{e 3} transition form factors

Details K_{l 3} and π_{e 3} transition form factors K_{l 3} and π_{e 3} transition form factors

1996-10-30

arxiv.org/abs/nucl-th/9610047v1

Phys.Lett.B399:22-28,1997

Physics

Nuclear Physics

Nuclear Theory

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

Scientific paper

10.1016/S0370-2693(97)00271-2

$K_{\ell 3}$ and $\pi_{e 3}$ 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: $M^E_s/M^E_u$. In the isospin symmetric limit: $-f_+^\pi(0)= F_\pi(t)$, the electromagnetic pion form factor, and $f_-^\pi(t)\equiv 0$.

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