Bounds on K/sub l3/-decay form factors

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 $V_{\mu }^{\left(K\right)}$ is bounded by a circle in the plane (Red(t),Imd(t)). We express the radius and the position of the center of this circle in terms of f₊(0) and of the propagator Δ(t) of the divergence of $V_{\mu }^{\left(K\right)}$.