From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

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 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 √ s σ = 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.

Averages of b-hadron, c-hadron, and $$\tau $$ τ -lepton properties as of summer 2016

“…[258,267] show large contributions from the ρ(770) 0 and f 0 (500) states, together with smaller contributions from higher resonances. Since modelling the f 0 (500) structure is challenging [268], it is difficult to determine reliably its associated CP violation parameters. Corresponding parameters for the J/ψρ 0 decay can, however, be determined.…”

Extending chiral perturbation theory with an isosinglet scalar

“…As for the relevant interpretation in terms of a four-quark state [1][2][3][4][5][6][7][8][9][10][45][46][47][48][49][50][51] one can envision different underlying realisations that range from this state emerging prevalently as bound state of pions to having a more compact wave-function at the quark level. Each of these possibilities will lead to specific predictions for the LECs that can, in principle, be obtained within model computations.…”

Chiral and U(1)A restoration for the scalar and pseudoscalar meson nonets

“…Similar results have been obtained in [36] by studying the influence of quantum and thermal fluctuations on the η − η 0 mixing angle. The above aspects regarding chiral partners and patterns are also of fundamental relevance to clarify the nature of the scalar nonet, which has been a matter of debate over the recent past [37][38][39]. Thus, the restoration pattern could help to shed light on the nature of those states when compared to the predictions based upon theirqq assignment.…”