1. Precise tests of low energy QCD from $\mbox {$\mathrm {K}_{\mathrm {e}4}$}$ decay properties
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M. Holder, G. Bocquet, Yu. Potrebenikov, Lau Gatignon, B. Renk, R. Fantechi, Milene Calvetti, H. Dibon, Mauro Raggi, G. Lamanna, M. Wache, D. T. Madigozhin, Fabrizio Petrucci, Jacqueline Batley, P. Rubin, Anne Dabrowski, M. Pepe, P. Cenci, E. Iacopini, M. Scarpa, Stoyan Stoynev, Leander Litov, Peter Zahariev Hristov, P. Marouelli, E. Mazzucato, W. Kubischta, Marco Clemencic, A. Ceccucci, M. Szleper, Andrea Bizzeti, D. J. Munday, Rainer Wanke, E. Marinova, M. Sozzi, C. Morales Morales, S. A. Wotton, Vladimir Kekelidze, L. DiLella, G.M. Pierazzini, M. Markytan, M. Lenti, Cristina Lazzeroni, Simone Bifani, I. Polenkevich, C. Cerri, F. Marchetto, L. Widhalm, S. Balev, Cristina Biino, G. Kalmus, A. Peters, Nicola Cabibbo, C. Cheshkov, Ivan Mikulec, H. D. Wahl, M. Fidecaro, B. Peyaud, J. Derre, U. Moosbrugger, Evgueni Goudzovski, Konrad Kleinknecht, D. Coward, M. Valdata-Nappi, Alan W. Walker, N. A. Molokanova, K. Eppard, Mayda Velasco, J.B. Cheze, Luca Fiorini, M. D. Wood, M. Shieh, E. Monnier, G. Neuhofer, B. Vallage, D.C. Cundy, M. Martini, A. Cotta Ramusino, N. Doble, V. Kozhuharov, Massimiliano Fiorini, I. Mannelli, W. Baldini, L. Masetti, Roberta Arcidiacono, Nicolo Cartiglia, A. Winhart, T. Fonseca Martin, Mauro Piccini, G. Ruggiero, A. Gonidec, G. Collazuol, E. C. Swallow, Michael Ziolkowski, S. Venditti, M. Savrie, S. Giudici, A. A. Maier, E. Imbergamo, F. Costantini, B. Bloch-Devaux, A. I. Zinchenko, Maulik R. Patel, P. L. Frabetti, C. Damiani, A. Gianoli, M. Slater, M. De Beer, A. Michetti, Enrico Celeghini, V. Falaleev, M. C. Petrucci, A. Nappi, M. Veltri, P. F. Dalpiaz, S. Goy Lopez, M. Behler, Manfred Jeitler, A. Norton, Roland Winston, G. Anzivino, and G. Marel
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Phase difference ,Physics ,Quantum chromodynamics ,Chiral symmetry ,Particle physics ,Chiral perturbation theory ,Physics and Astronomy (miscellaneous) ,Nuclear Theory ,High Energy Physics::Phenomenology ,Hadron ,Lattice QCD ,Low energy ,High Energy Physics::Experiment ,Engineering (miscellaneous) ,Energy (signal processing) - Abstract
We report results from the analysis of the \(\mbox {$\mathrm {K}^{\pm}$}\rightarrow \pi^{+} \pi^{-} \mathrm{e}^{\pm} \nu\) (\(\mbox {$\mathrm {K}_{\mathrm {e}4}$}\)) 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 \(\mbox {$a_{0}^{0}$}\) and \(\mbox {$a_{0}^{2}$}\), the I = 0 and I = 2 S-wave ππ scattering lengths: \(\mbox {$a_{0}^{0}$}= 0.2220 \pm 0.0128 \mbox {$\mathrm {_{stat}}$}\pm 0.0050 \mbox {$\mathrm {_{syst}}$}\pm 0.0037\mbox {$\mathrm {_{th}}$},\mbox {$a_{0}^{2}$}= -0.0432 \pm 0.0086 \mbox {$\mathrm {_{stat}}$}\pm 0.0034 \mbox {$\mathrm {_{syst}}$}\pm 0.0028\mbox {$\mathrm {_{th}}$}\). Combination of this result with the other NA48/2 measurement obtained in the study of \(\mbox {$\mbox {$\mathrm {K}^{\pm}$}\rightarrow \mbox {$\pi ^{0}$}\mbox {$\pi ^{0}$}\mbox {$\scriptstyle \pi ^{\pm }$}$}\) decays brings an improved determination of \(\mbox {$a_{0}^{0}$}\) and the first precise experimental measurement of \(\mbox {$a_{0}^{2}$}\), 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: \(\mbox {$a_{0}^{0}$}=0.2196 \pm 0.0028\mbox {$\mathrm {_{stat}}$}\pm 0.0020 \mbox {$\mathrm {_{syst}}$}\) and \(\mbox {$a_{0}^{2}$}= -0.0444 \pm 0.0007 \mbox {$\mathrm {_{stat}}$}\pm 0.0005 \mbox {$\mathrm {_{syst}}$}\pm 0.0008 \mbox {$\mathrm {_{ChPT}}$}\).
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