The study of light scalar mesons at BESII

The production of σ and κ in J/ψ decays is presented using 58 million J/ψ events collected at BES II detector. We also report the study of the light scalar mesons f ₀(980), f ₀(1370), f ₀(1500) and f ₀(1710) etc. in J/ψ decays.     

Towards an understanding of the light scalar mesons

Although studied for many years the nature of the light scalar mesons remains controversial. Here we shall present a method, applicable for s-wave states located close to a threshold, that allows one to quantify the molecular part of a given state. When applied to the f ₀(980) a dominance of the molecular component is found. In the second part, we show that requirements of field-theoretic consistency and chiral symmetry, when applied to the scattering of light pseudo-scalars, naturally lead to the appearance of dynamical poles in the scalar sector. A program is proposed on how to further investigate experimentally the mixing between these dynamical states and possible genuine quark states.     

Vector-meson-dominance model for radiative decays involving light scalar mesons

We study a vector-dominance model which predicts quite a large number of currently interesting decay amplitudes of the types S-->gammagamma, V-->Sgamma, and S-->Vgamma, where S and V denote scalar and vector mesons, in terms of three parameters. As an application, the model makes it easy to study in detail a recent proposal to boost the ratio Gamma(phi-->f(0)gamma)/Gamma(phi-->a(0)(0)gamma) by including the isospin violating a(0)(0)-f(0) mixing. However, we find that this effect is actually small in our model.     

A QCD sum rule study of the light scalar mesons

We examine the interpretation of the light scalar meson nonet as bound states of the scalar diquark and the scalar antidiquark using the QCD sum rule approach. Our results are obtained by means of the operator product expansion (OPE) including operators up to dimension 8. They show no evidence of the coupling of the tetraquark states to the light scalar meson nonet.     

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states a₀(980), f₀(980), κ,σ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by     

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states a0(980), f0(980), κ,σ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the "fall apart" mechanism.     

Model of scalar mesons

A model containing a nonet of scalar mesonsS, a nonet of pseudoscalar mesonsP, and a nonet of baryons is constructed where the mesons enter in the form of the matrixM=e^i(S+iP), Several Lagrangians are introduced such that the mesons get their physical masses, and the decay widths of the scalar mesons are calculated. The model satisfies generalized PCAC. It is found that the coupling constants of the mesonsε(700) andε′(1060) to pions and nucleons satisfy the relations: $$\frac{{|G_{\varepsilon NN} |}}{{|G_{\varepsilon \pi \pi } |}} = 1 \cdot 4,\frac{{|G_{\varepsilon 'NN} |}}{{|G_{\varepsilon '\pi \pi } |}} = 0 \cdot 89,\frac{{|G_{\varepsilon \pi \pi } G_{\varepsilon NN} |}}{{4\pi }} = 4 \cdot 9,{\text{and}}\frac{{|G_{\varepsilon '\pi \pi } G_{\varepsilon 'NN} |}}{{4\pi }} = 0 \cdot 34.$$      

37 Years with the light scalar mesons. The learned lessons

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the σ(600) meson. We show that the kaon loop mechanism of the ? radiative decays, ratified by experiment, is four-quark transition and points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq? mesons that are produced via two-quark transitions γγ → qq?. We study the mechanism of production of the light scalar mesons in the D _s ⁺ → π⁺π^? e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → [σ(600) + f ₀(980)]e ⁺ν → π⁺π^? e ⁺ν, and compare it with the mechanism of production of the light pseudoscalar mesons in the D _s ⁺ → (η/η′)e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → (η/η′)e ⁺ν. As a result we find support to four-quark nature of light scalars. In the end, we outline the future research program.     

QCD sum rule study of the masses of light tetraquark scalar mesons

We study the low-lying scalar mesons of light u, d, s flavors in the QCD sum rule. Having all possible combinations of tetraquark currents in the local form, QCD sum rule analysis has been carefully performed. We found that using the appropriate tetraquark currents, the masses of σ, κ, f₀ and a₀ mesons appear in the region of 0.6–1 GeV with the expected ordering. The results are compared with that of the conventional currents, where the masses are considerably larger.     

QCD sum rules and radial excitations of light pseudoscalar and scalar mesons

The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within the QCD sum rules method are briefly reviewed. The predictions are based on the 1/N _c -supported model spectra, which consist of an infinite number of infinitely narrow resonances, and on the assumption that the ground states of light scalar mesons may be considered as \(\bar qq\)-bound states. The results of the studies are compared with the existing experimental data and with the predictions of other theoretical approaches.     

Masses of light tetraquarks and scalar mesons in the relativistic quark model

Masses of the ground-state light tetraquarks are dynamically calculated in the framework of the relativistic diquark–antidiquark picture. The internal structure of the diquark is taken into account by calculating the form factor of the diquark–gluon interaction in terms of the overlap integral of the diquark wave functions. It is found that scalar mesons with masses below 1 GeV, f ₀(600) (σ), K ₀^*(800) (κ), f ₀(980) and a ₀(980), agree well with the light-tetraquark interpretation.     

Scalar mesons and scalar gluonium

We investigate the mixing of scalar mesons (S ^*, ?) with gluonium in the context of a potential model. We calculate the masses of the scalars and the branching ratios to ππ,KK, ηη and ηη′. The model can accomodate the stateG(1.59) and explain its peculiar rates. We also investigate other possibilities for gluonium mass and branching ratios and find that a gluonium state around 1 GeV may explain the unusual branching ratios in the scalar sector.     

Dynamical study of light scalar mesons below 1 GeV in a flux-tube model

The light scalar mesons below 1GeV configured as tetraquark systems are studied in the framework of the flux-tube model. Comparative studies indicate that a multi-body confinement,instead of the additive two-body confinement, should be used in a multiquark system.The σ and κ mesons could be well accommodated in the diquark-antidiquark tetraquark picture, and could be colour-confinement resonances. The a0(980) and fo(980) mesons are not described as KK molecular states and ns diquark-antidiquark states.However, the mass of the first radial excited state of the diquark-antidiquark state, nn is 1019 MeV,is close to the experimental data of the fo (980).     

Radiative decays with light scalar mesons and singlet–octet mixing in ChPT

We study different types of radiative decays involving f₀(980) and a₀(980) mesons within a unified ChPT-based approach at one-loop level. Light scalar resonances, which are seen in the ππ, πη and KK̄ channels of the φ(1020) radiative decays and in the J/ψ decays are responsible for key questions of low-energy dynamics in the strong interaction sector, and the decays φ(1020)→γa₀(980), φ(1020)→γf₀(980), a₀(980)→γγ and f₀(980)→γγ are of interest for current experimental programs in Jülich, Frascati and Novosibirsk. From the theoretical point of view it is important to verify whether light scalar mesons are members of some flavor octet or nonet. We find a value for the mixing angle dictated by consistency with experiment and the coupling structures of the ChPT Lagrangian. The decay widths f₀(980)/a₀(980)→γρ(770)/ω(782), which have not been experimentally studied yet, are predicted. We also obtain several relations between the widths, which hold independently of the coupling constants and which represent a fingerprint of the model. PACS 11.30.Hv; 12.39.Fe; 13.30.Eg; 14.40.-n     

Soliton bag model with scalar mesons

We propose a soliton bag model with scalar mesons which is a modification of the simple soliton bag model and the linear sigma model. Our model can give comparatively large quark mass, so that it is applicable to low energy scattering. We have solved the Euler-Lagrange equations in the mean-field approximation for the hedgehog baryon state. The static properties of the nucleon is calculated by a projection method. Our results are in reasonable agreement with the observed values.     

Elementary scalar mesons and Regge poles

We show, for the annihilation amplitude of π⁺π^? → two vector mesons, that parity conservation and rotational symmetry demand the existence of a triplet of Regge singularities crossing at t = 0. In the usual scalar-vector field theory, calculations of the leading terms of this amplitude up to the eight order show that these singularities are moving Regge poles. Contrary to common belief, the elementary scalar meson lies on one of them.