A Dispersive Treatment of $K_{\ell4}$ Decays

Understand

$K_{\ell4}$ decays offer several reasons of interest: they allow an accurate measurement of $\pi\pi$-scattering lengths; they provide the best source for the determination of some low-energy constants of ChPT; one form factor is directly related to the chiral anomaly, which can be measured here.

• We present a dispersive treatment of $K_{\ell4}$ decays that provides a resummation of $\pi\pi$- and $K\pi$-rescattering effects.
• The free parameters of the dispersion relation are fitted to the data of the high-statistics experiments E865 and NA48/2.
• The matching to ChPT at NLO and NNLO enables us to determine the LECs $L_1^r$, $L_2^r$ and $L_3^r$.