Abstract
On the basis of analyticity and the soft-pion theorem, various exact bounds for the scalar ${K}_{l3}$ form factor $D(t)$ have been obtained, assuming that $D(t)$ satisfies at most a once-subtracted dispersion relation, and that $\mathrm{Im}D(t+i0)$ can change its sign at most only once on the cut. These bounds do not contain any arbitrary free parameters. Neither do we use any explicit Hamiltonian nor any approximation such as the pole-dominance model for its derivation. The results obtained disagree with present experiment. A connection of this method with the phase representation of $D(t)$ is also discussed, and we find that under some simple conditions, the result is at variance with present experiment.
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