Understanding The Lightest Scalar Mesons

The introduction to a new paper on the photo-production of the two lightest scalar mesons (the f0(500) and the f0(980) explains the still unsolved mystery of these composite hadrons:

Understanding the structure of low-lying scalar mesons has been one of the most challenging issues in hadronic physics. Their internal structure is still under debate. That the f0(500) scalar meson, which is also known as σ, is not an ordinary meson consisting of a quark and an anti-quark is more or less in consensus. Recent studies suggest that these scalar mesons may belong to the flavor SU(3) non-qq¯ nonet (see reviews [1, 2], a “note on scalar mesons below 2 GeV ” in Ref. [3], and references therein. A recent review provides also various information on the structure of the scalar meson [4], including a historical background of the σ meson). The f0(500) is also interepreted as one of the glueballs or gluonia, mixed with the ¯qq state [5–7], though this idea is criticized because the same analysis is rather difficult to be applied to explaining the strange scalar meson K∗ 0 (800) or κ, which is also considered as a member of the nonet. The f0(500) is often regarded as a tetraquark state in a broad sense [8]. The f0(500) as a tetraquark state has a multiple meaning: It can be described as a diquark-antidiquark correlated state [9, 10], ¯qqqq¯ state [11], or correlated 2π state [12, 13] arising from ππ scattering. This non ¯qq feature was employed in various theoretical approaches such as QCD sum rules [14], effective Lagrangians [15], and lattice QCD [16–18].  

The scalar mesons were also extensively studied phenomenologically. There are two scalar-isoscalar mesons (I G(J P C ) = 0+(0++)) below 1 GeV, that is, the lowest-lying f0(500) (or σ) and the first excited f0(980). Both the f0(500) and the f0(980) exist in ππ scattering and their pole positions were investigated based on many different processes, for example, such as πN → ππN reactions [19–21], Kl4 decay [22, 23], D → 3π [24, 25], J/ψ → ωππ [26], ψ(2S) → π +π −J/ψ [27], γγ → ππ [28], pp scattering [29], and so on (for details, we refer to Refs. [3, 4]). While the mass and the width of the f0(980) are more or less known to be mf0 = 990±20 MeV and Γ = 40−100 MeV, those of f0(500) are still far from consensus (see Ref. [3]). The upper bound of the f0(500) mass is given in the large Nc limit in terms of the Gasser-Leutwyler low-energy constant [30], which suggests that the f0 mass is quite possibly smaller than 700 MeV.