From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance

TL;DR

This review clarifies the long-standing controversy over the sigma meson, now called $f_0(500)$, by analyzing experimental data and dispersive formalisms, confirming its non-ordinary quark-antiquark structure and precise properties.

Contribution

It provides a comprehensive review of experimental and theoretical advances that settle the sigma meson controversy and establish its non-ordinary nature using modern dispersion and effective theories.

Findings

Precise determination of the $f_0(500)$ pole position: 449^{+22}_{-16} - i(275 b1 12)

Confirmation of the non-ordinary quark-gluon structure of the sigma meson

Resolution of the six-decade controversy over its existence and properties

Abstract

The 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 nucleon-nucleon 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 $\sqrt{s_\sigma}=449^{+22}_{-16}-i(275\pm12)$. 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.