Precise tests of low energy QCD from decay properties

University of Birmingham, Edgbaston, Birmingham, B15 2TT UK
European Physical Journal C (Impact Factor: 5.44). 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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