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Precise tests of low energy QCD from decay properties

Dipartimento di Fisica Sperimentale dell’Università e Sezione dell’INFN di Torino, 10125 Torino, Italy; University of Birmingham, Edgbaston, Birmingham, B15 2TT UK; Università di Roma “La Sapienza” e Sezzione dell’INFN di Roma, 00185 Roma, Italy; Department of Physics, Imperial College, London, SW7 2BW UK; Faculty of Physics, University of Sofia “St. Kl. Ohridski”, 1164 Sofia, Bulgaria; Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA; Dipartimento di Fisica, Università di Modena e Reggio Emilia, 41100 Modena, Italy; Istituto di Fisica, Università di Urbino, 61029 Urbino, Italy; SLAC, Stanford University, Menlo Park, CA 94025, USA; Laboratory for High Energy Physics, 3012 Bern, Switzerland; UCLA, Los Angeles, CA 90024, USA; Laboratori Nazionali di Frascati, 00044 Frascati (Rome), Italy; Institut de Física d’Altes Energies, UAB, 08193 Bellaterra (Barcelona), Spain; Dipartimento di Fisica Sperimentale dell’Università di Torino, 10125 Torino, Italy; Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Lyon I, 69622 Villeurbanne, France; University College Dublin School of Physics, Belfield, Dublin 4, Ireland; Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, 28040 Madrid, Spain
European Physical Journal C (Impact Factor: 5.25). 01/2010; 70(3):635-657. DOI: 10.1140/epjc/s10052-010-1480-6

ABSTRACT We report results from the analysis of the $\mbox {$\mbox { ($\mbox {$\mbox {) 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 $\mbox {$\mbox { and $\mbox {$\mbox {, the I = 0 and I = 2 S-wave ππ scattering lengths: $\mbox {$\mbox {. Combination of this result with the other NA48/2 measurement obtained in the study of $\mbox {$\mbox { decays brings an improved determination of $\mbox {$\mbox { and the first precise experimental measurement of $\mbox {$\mbox {, 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: $\mbox {$\mbox { and $\mbox {$\mbox {.

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