From controversy to precision on the sigma meson: A review on the status of the non-ordinary f(0)(500) resonance

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TThe existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleonnucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: f_0(500). We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position √ sσ = 449^(+22)_ (−16)−i(275±12). In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD 1/N_c expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.
I want to especially thank J. Nebreda for her very careful reading of the whole manuscript, her endless patience with corrections and help with many figures, as well as J. Ruiz de Elvira and F. J. Llanes-Estrada for carefully reading and helping me to correct parts of it. I am particularly indebted to C. Hanhart for his critical reading of most of the manuscript, particularly those sections concerning the RPP and chiral symmetry as well as for his suggestions and constructive feedback. Many thanks also to J.A. Oiler and E. Oset for their careful reading of the whole manuscript, their numerous corrections and their suggestions and clarifications in several specific sections: the former on the different mixing schemes, the chiral unitary approach and the radiative sigma decay, and the latter on the section of the sigma from decays of heavier mesons. Thanks also to A. Gómez Nicola for his advice with the chiral symmetry restoration subsection and the references therein. In addition, and more or less in order of appearance at different stages of the elaboration of the manuscript, I also thank I. Caprini for her comments on rigorous analytic continuations and extractions of the σ pole, H. Leutwyler for pointing out the usefulness of Roy equations in different aspects, and the two of them together with G. Colangelo for kindly providing their files to display the Regge behavior. Thanks also to: J. Nieves for his explanations on his results on the Nc behavior, F. Giacosa and D.Parganlija for their explanations of their extended LσM, M. Nielsen for some clarifications on sum rules as well as G. Rupp for his comments on the Quark-level LσM, the Chiral Quark Model and on NJL models in general. I also want to thank W. Ochs for his comments on the sigma as a glueball, on his critical view of the κ resonance situation as well as on the difficulties of his Ph.D. thesis ππ scattering analysis with the CERN-Munich Collaboration, which is the closest one to the Madrid–Krakow final dispersive result. This work has been partially supported by the Spanish projects FPA2011-27853-C02-02, FPA2014-53375-C2-2 and FIS2014-57026-REDT.
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