The light σ-meson

Abstract

In the framework of the dispersion relation N/D-approach, we restore the low-energy ππ (IJ P C = 00 ++ )-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450-1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane near the ππ threshold, that is the light σ-meson.12.39. Mk, At present the understanding of scalar meson is one of the key problems for the Strong-QCD physics. The ππ low-mass data provide indications on the existence of a low-mass σ-meson. This state is beyond qq and gluonium systematics, which makes it necessary to confirm its existence as well as to study the possible mechanisms of its formation.Experimental data on meson spectra accumulated by the Crystal Barrel Collaboration [1], GAMS [2] and BNL [3] groups provided a good basis for setting up the qq/gluonium classification of the light scalars. For the (IJ P C = 00 ++ )-wave, the combined K-matrix analysis of the reactions ππ → ππ, KK, ηη, ηη ′ , ππππ has been carried out over the mass range 450-1900 MeV [4,5], then the K-matrix analysis was extended to the waves , thus making it possible to establish the qq systematics of scalars for 1 3 P 0 qq and 2 3 P 0 qq multiplets. The advantage of the K-matrix representation is that it allows us not only to determine the locations and partial widths of resonances but also to study characteristics of corresponding states with switched off decay channels: these "primary states", or "bare states" (i.e. states without a cloud of mesons produced by decay processes) are suitable objects for the qq/gluonium classification (see [7] for the details). The decay processes in the scalar/isoscalar sector cause a strong mixing which destroys the qq/gluonium classification. Another important effect generated by transitions (qq) 1 → real mesons → (qq) 2 is an accumulation of widths of neighbouring resonances by one of them, that results in appearance of a broad state.According to [4,5], five bare scalar/isoscalar states are located in the region 700-1800 MeV: f An important result of the article [4,5] is that the K-matrix 00 ++ -amplitude has no pole singularities in the region 500-800 MeV. Here the ππ-scattering phase δ 0 0 increases smoothly reaching 90• at 800-900 MeV. A straightforward explanation of such a behaviour of δ 0 0 might consist in the presence of a broad resonance, with a mass about 600-900 MeV and width Γ ∼ 500 MeV (for example, see Refs. [10,11] and references therein). However, according to the Kmatrix solution [4,5], the 00 ++ -amplitude does not contain pole singularities on the second sheet of the complex-M ππ plane inside the interval 450 ≤ Re M ππ ≤ 900 MeV: the K-matrix amplitude has a low-mass pole only, which is located on the second sheet either near the ππ threshold or even below it. In [4,5], the presence of this pole was not emphasized, for the left-hand cut, which is important for the reconstruction of analytic structure of the low-energy partial amplitude, was taken into account only indirectly; a proper way for the ...

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“…The above value is consistent with the result (6 ± 2)% that was obtained from the multichannel analysis [38].…”

Systematics of quark–antiquark states and scalar exotic mesons

“…As to experimental data, the position of pole is rather sensitive to the scattering length value, which in the fit [31] was taken in accordance to the paper [77]: a π , that agrees completely with the value (47) obtained in [31]. Such a coincidence favours undoubtedly the pole position (46).…”

“…see [28,29,30,31]. In this connection let us emphasize that the dispersion-relation N/D analysis [31], where the low-energy 00…”

Systematics of qq̄ states, scalar mesons and glueball

“…3 following the results of the dispersion relation N/D-analysis [6] (the mass region validated by this analysis is also shown in Fig. 3).…”