Eur. Phys. J. C (2009) 64: 589-608
https://doi.org/10.1140/epjc/s10052-009-1171-3

Regular Article - Experimental Physics

Determination of the S-wave π π scattering lengths from a study of K ^±→π ^± π ⁰ π ⁰ decays

¹ Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
² CERN, 1211, Genève 23, Switzerland
³ Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia
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 dell’Università e Sezione dell’INFN di Ferrara, 44100, Ferrara, Italy
⁷ Dipartimento di Fisica dell’Università e Sezione dell’INFN di Firenze, 50019, Sesto Fiorentino, Italy
⁸ Sezione dell’INFN di Firenze, 50019, Sesto Fiorentino, Italy
⁹ Institut für Physik, Universität Mainz, 55099, Mainz, Germany
¹⁰ Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
¹¹ Dipartimento di Fisica dell’Università e Sezione dell’INFN di Perugia, 06100, Perugia, Italy
¹² Sezione dell’INFN di Perugia, 06100, Perugia, Italy
¹³ Sezione dell’INFN di Pisa, 56100, Pisa, Italy
¹⁴ Scuola Normale Superiore e Sezione dell’INFN di Pisa, 56100, Pisa, Italy
¹⁵ Dipartimento di Fisica dell’Università e Sezione dell’INFN di Pisa, 56100, Pisa, Italy
¹⁶ DSM/IRFU—CEA Saclay, 91191, Gif-sur-Yvette, France
¹⁷ Fachbereich Physik, Universität Siegen, 57068, Siegen, Germany
¹⁸ Sezione dell’INFN di Torino, 10125, Torino, Italy
¹⁹ Dipartimento di Fisica Sperimentale dell’Università e Sezione dell’INFN di Torino, 10125, Torino, Italy
²⁰ Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften, 10560, Wien, Austria

^* e-mail: madigo@mail.cern.ch
^** e-mail: madigo@mail.ru

Received: 5 May 2009
Revised: 27 July 2009
Published online: 20 October 2009

Abstract

We report the results from a study of the full sample of ∼6.031×10⁷ K ^±→π ^± π ⁰ π ⁰ decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the π ⁰ π ⁰ invariant mass (M ₀₀) distribution shows a cusp-like anomaly in the region around M ₀₀=2m ₊, where m ₊ is the charged pion mass. This anomaly has been interpreted as an effect due mainly to the final state charge exchange scattering process π ⁺ π ⁻→π ⁰ π ⁰ in K ^±→π ^± π ⁺ π ⁻ decay. Fits to the M ₀₀ distribution using two different theoretical formulations provide the presently most precise determination of a ₀−a ₂, the difference between the π π S-wave scattering lengths in the isospin I=0 and I=2 states. Higher-order π π rescattering terms, included in the two formulations, allow also an independent, though less precise, determination of a ₂.