New high statistics measurement of K_e4 decay form factors and ππ scattering phase shifts

We report results from a new measurement of the K_e4 decay K ^±→π⁺π^-e ^±ν by the NA48/2 collaboration at the CERN SPS, based on a partial sample of more than 670∈000 K_e4 decays in both charged modes collected in 2003. The form factors of the hadronic current (F,G,H) and ππ phase difference (δ=δ_s-δ_p) have been measured in ten independent bins of the ππ mass spectrum to investigate their variation. A sizeable acceptance at large ππ mass, a low background and a very good resolution contribute to an improved experimental accuracy, a factor two better than in the previous measurement, when extracting the ππ scattering lengths a₀ ⁰ and a₀ ². Under the assumption of isospin symmetry and using numerical solutions of the Roy equations, the following values are obtained in the plane (a₀ ⁰,a₀ ²): a₀ ⁰=0.233±0.016stat±0.007syst,a₀ ²=-0.0471±0.011stat±0.004syst. The presence of potentially large isospin effects is also considered and will allow comparison with precise predictions from Chiral Perturbation Theory.