https://doi.org/10.1140/epjc/s10052-010-1480-6
Precise tests of low energy QCD from 
decay properties
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, Edinburgh, EH9 3JZ, UK
6
Dipartimento di Fisica dell’Università e Sezione dell’INFN di Ferrara, 44100, Ferrara, Italy
7
Sezione dell’INFN di Firenze, 50125, Firenze, Italy
8
Dipartimento di Fisica dell’Università e Sezione dell’INFN di Firenze, 50125, Firenze, Italy
9
Institut für Physik, Universität Mainz, 55099, Mainz, Germany
10
Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208-3112, USA
11
Sezione dell’INFN di Perugia, 06100, Perugia, Italy
12
Dipartimento di Fisica dell’Università e 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
21
University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
22
Università di Roma “La Sapienza” e Sezzione dell’INFN di Roma, 00185, Roma, Italy
23
Istituto di Cosmogeofisica del CNR di Torino, 10133, Torino, Italy
24
Department of Physics, Imperial College, London, SW7 2BW, UK
25
Faculty of Physics, University of Sofia “St. Kl. Ohridski”, 1164, Sofia, Bulgaria
26
Centre de Physique des Particules de Marseille, IN2P3-CNRS, Université de la Méditerranée, 13288, Marseille, France
27
Department of Physics and Astronomy, George Mason University, Fairfax, VA, 22030, USA
28
Dipartimento di Fisica, Università di Modena e Reggio Emilia, 41100, Modena, Italy
29
Istituto di Fisica, Università di Urbino, 61029, Urbino, Italy
30
SLAC, Stanford University, Menlo Park, CA, 94025, USA
31
Laboratory for High Energy Physics, 3012, Bern, Switzerland
32
UCLA, Los Angeles, CA, 90024, USA
33
Laboratori Nazionali di Frascati, 00044, Frascati (Rome), Italy
34
Institut de Física d’Altes Energies, UAB, 08193, Bellaterra (Barcelona), Spain
35
Dipartimento di Fisica Sperimentale dell’Università di Torino, 10125, Torino, Italy
36
Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Lyon I, 69622, Villeurbanne, France
37
University College Dublin School of Physics, Belfield, Dublin 4, Ireland
38
Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, 28040, Madrid, Spain
Received:
17
September
2010
Published online:
6
November
2010
We report results from the analysis of the 
() 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 
and 
, the I = 0 and I = 2 S-wave ππ scattering lengths: 
. Combination of this result with the other NA48/2 measurement obtained in the study of 
decays brings an improved determination of and the first precise experimental measurement of , 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: 
and 
.
© Springer-Verlag / Società Italiana di Fisica, 2010
