The $K\pi$ form factors from Analyticity and Unitarity

Abstract

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of $K\pi$ form factors up to an energy \tin=1 {\rm GeV}^2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.Comment: 6 pages, 5 figures; Seminar given at DAE-BRNS Workshop on Hadron Physics Bhabha Atomic Research Centre, Mumbai, India October 31-November 4, 2011, submitted to Proceeding