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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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    ABSTRACT: The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three-flavour condensate in a particularly clean way in the case of three degenerate quarks.
    Journal of High Energy Physics 09/2012; 2012(12). · 5.62 Impact Factor

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