Precise tests of low energy QCD from Kₑ₄ decay properties

We report results from the analysis of the K±→ π⁺ π⁻ e± ν ( Kₑ₄ ) decay by the NA48/2 collaboration at the CERN SPS, based on the total statistics of 1.13 million decays collected in 2003–2004. The hadronic form factors in the S- and P-wave and their variation with energy are obtained. The phase difference between the S- and P-wave states of the ππ system is accurately measured and allows a precise determination of a₀⁰ and a₀² , the I = 0 and I = 2 S-wave ππ scattering lengths: a₀⁰= 0.2220 ± 0.0128 {ₛₜₐₜ}± 0.0050 {syst}± 0.0037 {ₜₕ},a₀²= -0.0432 ± 0.0086 {ₛₜₐₜ}± 0.0034 {syst}± 0.0028 {ₜₕ} . Combination of this result with the other NA48/2 measurement obtained in the study of K±→ π ⁰π ⁰π ± decays brings an improved determination of a₀⁰ and the first precise experimental measurement of a₀² , providing a stringent test of Chiral Perturbation Theory predictions and lattice QCD calculations. Using constraints based on analyticity and chiral symmetry, even more precise values are obtained: a₀⁰=0.2196 ± 0.0028 {ₛₜₐₜ}± 0.0020 {syst} and a₀²= -0.0444 ± 0.0007 {ₛₜₐₜ}± 0.0005 {syst}± 0.0008 {ChPT} .