Experimental status of the π πi isoscalar S wave at low energy: f_(0)(600) pole and scattering length
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2007
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Amer Physical Soc
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Abstract
The experimental results obtained in the last few years on kaon decays (K → 2 π and, above all, Ke4 decays) allow a reliable, model-independent determination of low energy π π scattering in the S0 wave. Using them and, eventually, other sets of data, it is possible to give a precise parametrization of the S0 wave as well as to find the scattering length and effective range parameter. One can also perform an extrapolation to the pole of the ‘‘sigma resonance’’ [f_0(600)]. We obtain the results a_(0)^(0) = 0,233 ± 0,013M_(π)^(-1), b_(0)^(0)=0,285 ± 0,012M_(π)^(-3), and, for the σ pole, M_(σ) = 484 ± 17 MeV, Γ_σ =255 ± 10 MeV.
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©2007 The American Physical Society.
Part of the results in this paper have been presented by J. R. Peláez at the NA48/2 meeting in Geneva, December 2006. We are grateful to Dr. Brigitte Bloch-Devaux for communicating to us the phase shifts obtained in the NA48/2 analysis [9], including the (as yet unpublished) analysis of the systematic errors, as well as to C. Gatti for communicating to us the K →ππ results before formal publication. Thanks are also due to I. Caprini and H. Leutwyler for pointing out the presence of the ghost in the expansion for cotδ_(0)^(0). Finally, discussions with P. Minkowski and W. Ochs have been very helpful to make us understand the interest of discussing the solutions B, C of Grayer et al.. This work was supported in part by the Spanish DGI of the MEC under Contract No. FPA2003- 04597. The research of R. G. M. and J. R. P. was partially funded by Spanish CICYT Contract No. FPA2005-02327, as well as Banco Santander/Complutense Contract No. PR27/05-13955-BSCH. J. R. P.’s research is also partially funded by CICYT Contract No. FIS2006-03438 and is part of the EU integrated infrastructure initiative HadronPhysics Project under Contract No. RII3-CT-
2004-506078.