Nature of the σ meson as revealed by its softening process

Abstract

The ππ scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the σ meson which is observed as the lowest scalar-isoscalar resonance. We compare several models with different origins of the σ meson, such as the chiral partner of the pion and the dynamically generated ππ molecule. We find that the dynamically generated σ meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. This behavior around the threshold energy region is universal as far as the bare σ pole stays away from the threshold throughout the symmetry restoration process. On the other hand, for m π = 0, the dynamically generated σ behaves similarly to the chiral partner in the symmetry restoration limit, implying the possibility of the dynamically generated chiral partner.

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

“…This is also a generic feature of poles in S -wave amplitudes [300]. Similar movements were found in potential models [76,301], unitarized quark models [302],finite density analysis [303], or in general studies of chiral symmetry restoration [304]. Moreover, the non-analyticity of the hadron mass when the conjugate poles reach the real axis has been recently studied in detail within the general formalism of Jost functions in [305,306].…”

“…Another example of the pole moving below threshold but keeping a finite width may also occur [304] when increasing the ππ attraction in the σ channel relatively to other scales, for instance in the process of chiral restoration with temperature or in medium.…”

“…These pole movements could in principle be helpful to discriminate different inner structures proposed for the σ through the so-called "σ-softening", i.e. its becoming a sharper resonance, in a medium with high temperature and/or density [304].…”

Preliminary lattice QCD calculation of the σ meson decay width

“…In 2010, Particle Data Group (PDG) lists the meson f 0 (600), which is usually called σ meson I(J P C ) = 0(0 ++ ), with mass 400 − 1200 MeV and width 600 − 1000 MeV [1]. Its existence has been established by some refinements of the experimental analyses [2][3][4][5][6][7][8] and some phenomenological studies [9][10][11][12][13][14][15][16][17]. The Dalitz plot analysis of E791 [6] yields its decay width about 324 MeV.…”

“…However, some theoretical efforts are still taken to investigate σ meson and estimate its resonance parameters [9][10][11][12][13][14][15][16][17]. σ meson was originally introduced to fit experimental data and its mass was chosen to reproduce the experimental results.…”