Abstract
Upper and lower bounds on the scalar form factor of K ℓ3 decay are calculated using the analytic properties of the form factor, the experimental low-energy S-wave K π phase shift, and an estimate of the propagator Δ( t) of the divergence of the strangeness changing current at zero momentum. We release the condition given by the soft-pion theorem on ⨍(m K 2) that we considered in a previous work. For this reason the new bounds are less restrictive. However they are sufficiently strong to be inconsistent with some experimental data irrespective of the fit used for K π scattering.
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