Eur. Phys. J. C (2008) 54: 411-423
https://doi.org/10.1140/epjc/s10052-008-0547-0

Regular Article - Experimental Physics

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

¹ Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
² CERN, 1211, Genève 23, Switzerland
³ Joint Institute for Nuclear Research, 141980, Dubna, Russian Federation
⁴ The Enrico Fermi Institute, The University of Chicago, Chicago, IL, 60126, USA
⁵ Department of Physics and Astronomy, University of Edinburgh, JCMB King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK
⁶ Dipartimento di Fisica, Università e Sezione dell’INFN di Ferrara, 44100, Ferrara, Italy
⁷ Dipartimento di Fisica, Università e Sezione dell’INFN di Firenze, 50125, Firenze, Italy
⁸ Institut für Physik, Universität Mainz, 55099, Mainz, Germany
⁹ Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208-3112, USA
¹⁰ Dipartimento di Fisica, Università e Sezione dell’INFN di Perugia, 06100, Perugia, Italy
¹¹ Dipartimento di Fisica, Università, Scuola Normale Superiore e Sezione dell’INFN di Pisa, 56100, Pisa, Italy
¹² DSM/DAPNIA – CEA Saclay, 91191, Gif-sur-Yvette, Bât 141, France
¹³ Fachbereich Physik, Universität Siegen, 57068, Siegen, Germany
¹⁴ Dipartimento di Fisica Sperimentale, Università e Sezione dell’INFN di Torino, 10125, Torino, Italy
¹⁵ Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften, 10560, Wien, Austria
¹⁶ Centre de Physique des Particules de Marseille, IN2P3-CNRS, Université de la Méditerranée, Marseille, France
¹⁷ Istituto di Fisica, Università di Modena, 41100, Modena, Italy
¹⁸ Istituto di Fisica, Università di Urbino, 61029, Urbino, Italy
¹⁹ University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
²⁰ Università di Roma “La Sapienza” e Sezzione dell’INFN di Roma, 00185, Roma, Italy
²¹ Istituto di Cosmogeofisica del CNR di Torino, 10133, Torino, Italy
²² Scuola Normale Superiore and INFN, 56100, Pisa, Italy
²³ Department of Physics and Astronomy, George Mason University, Fairfax, VA, 22030, USA
²⁴ Physikalisches Institut, Universität Bonn, 53115, Bonn, Germany
²⁵ SLAC, Stanford University, Menlo Park, CA, 94025, USA
²⁶ UCLA, Los Angeles, CA, 90024, USA

^* e-mail: bbloch@hep.saclay.cea.fr

Received: 29 October 2007
Revised: 24 January 2008
Published online: 19 February 2008

Abstract

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.