# New high statistics measurement of $K_{e4}$ decay form factors and $\pi\pi$ scattering phase shifts

Abstract : We report results from a new measurement of the $K_{e4}$ decay $K^{\pm} \pi^{+}\pi^{-}e^{\pm}\nu$ 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 $\pi\pi$ phase difference ($\delta=\delta_s-\delta_p$) have been measured in ten independent bins of the $\pi\pi$ mass spectrum to investigate their variation. A sizeable acceptance at large $\pi\pi$ 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 $\pi\pi$ scattering lengths a00 and a20 . Under the assumption of isospin symmetry and using numerical solutions of the Roy equations, the following values are obtained in the plane a00 , a20 : a00 = 0.233± 0.016stat ±0.007syst, a20 =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.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00311742
Contributor : Danielle Cristofol <>
Submitted on : Monday, August 25, 2008 - 10:04:27 AM
Last modification on : Monday, February 10, 2020 - 6:12:58 PM

### Citation

J.R. Batley, A.J. Culling, C. Lazzeroni, D.J. Munday, M.W. Slater, et al.. New high statistics measurement of $K_{e4}$ decay form factors and $\pi\pi$ scattering phase shifts. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2008, 54, pp.411-423. ⟨10.1140/epjc/s10052-008-0547-0⟩. ⟨in2p3-00311742⟩

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