Unitarity, chiral perturbation theory, and Kl4 decays

Chiral perturbation theory at next-to-leading order has been successfully used to simultaneously describe the form factors in the decay K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}e\ensuremath{\nu} and low-energy \ensuremath{\pi}\ensuremath{\pi} scattering. However, since the one-loop corrections to the form factors are large, one would generally expect higher order corrections to also contribute significantly. With the use of unitarity and dispersion relations together with the chiral expansion, the effects of higher order corrections coming from \ensuremath{\pi}\ensuremath{\pi} rescattering are investigated. These results agree well with the experimental form factors, and agree even better than the chiral prediction with the data on low-energy \ensuremath{\pi}\ensuremath{\pi} scattering.