Bounds onKl3-Decay Form Factors

Abstract

We rederive certain bounds on ${K}_{l3}$ decay parameters found recently by Li, Pagels, and Okubo and obtain some new results with a simpler method based on a direct application of the maximum-modulus theorem for holomorphic functions. For an arbitrary value of the momentum-transfer variable $t$ in the complex cut $t$ plane, we find that the domain of values which can be taken by the form factor $d(t)$ of the divergence of the weak strangeness-changing vector current ${V}_{\ensuremath{\mu}}^{(K)}$ is bounded by a circle in the plane ($\mathrm{Re}d(t),\mathrm{Im}d(t)$). We express the radius and the position of the center of this circle in terms of ${f}_{+}(0)$ and of the propagator $\ensuremath{\Delta}(t)$ of the divergence of ${V}_{\ensuremath{\mu}}^{(K)}$.