Precise determination of the f_o(500) and f_o(980) parameters in dispersive analysis of the ππ data

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Use of the new and precise dispersive equations with imposed crossing symmetry condition to solve the longstanding puzzle in the parameters of the f_o(500), as well as the f_o(980) is presented. This puzzle is finally being settled thanks to analyzes carried out during the last years [1]. In this report we show how our very recent dispersive data analysis allowed for a precise and model independent determination of the amplitudes for the S, P, D and F waves [2–4]. Especially we present that the analytic continuation of once subtracted dispersion relations for the S 0 wave to the complex energy plane leads to very precise results for the f_o(500) pole: √S_ ¬(pole) = 457^(+14) _(−13) − i279^(+11) _(−7) MeV and for the f_o(980) √S_ ¬(pole) = 996 ± 7 − i25^(+10)_(−6) MeV. We also mention on first (or one of the first) practical application of presented dispersion relations in refitting and in significant improving of the ππ S –wave amplitudes below 1000 MeV
©2012 Elsevier B.V. All rights reserved. International Conference on Quantum Chromodynamics (16. 2013. Montpellier, Francia). This work has been partly supported by the Polish Ministry of Science and Higher Education (grant No N N202 101 368).
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[1] J. Beringer et al. (Particle Data Group), Phys. Rev. D86, (2012) 010001 [2] R. García-Martín, R. Kaminski, J. R. Peláez, J. Ruíz de Elvira and F.J. Yndurain, Phys. Rev. D83, (2011) 074004 [3] R. García-Martín, R. Kamiński, J.R. Pelaez and J. Rúiz de Elvira, Phys. Rev. Lett. 107, (2011) 072001 [4] R. Kamiński, Phys. Rev. D83, (2011) 076008 [5] K. Nakamura et al. (Particle Data Group), J. Phys. G37, (2010) 075021