Chiral Lagrangian Treatment of 0^＋＋ Mesons and 0^＋＋ Glueballs

Within the framework of a nonlinear chiral Lagrangian the mass spectra and the decay properties of 0^＋＋ states below 2 GeV are studied. Assuming that f0（980）, a0（980）, K0（1430）, and f0（1500） comprise an SU（3） nonet, we make a detailed prediction about the static properties of the 0^＋＋ mesons. The substructure analysis of these states in terms of two- and four-quark components as well as a glueball component is carried out. We also consider the interaction Lagrangian and provide a preliminary study of the strong and radiative decays of the 0＋＋ mesons. The scalar glueball masses and partial widths are also presented. In view of the fact that few data of 0＋＋ mesons are clearly given in the present PDG （Particle Data Group） list and that the four-quark content of mesons is a hot issue both experimentally and theoretically, the predicted results of the paper may be helpful for upcoming experimental and theoretical studies of these mesons.     

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     

Positive parity scalar mesons in the 1–2 GeV mass range

Based on the observation that K₀ ^*(1430) is lighter than its SU₃ counterpart, a₀(1450), we examine the possibility that these particles, together with f₀(1370), f₀(1500) and f₀(1710), fill a tetraquark recurrence of the sub-GeV 0⁺⁺ nonet mixed with a glueball state. We find the picture to be consistent with the known data about the three f₀ resonances, more than the qq̄ hypothesis. Conventional spin–orbit coupling suggests the qq̄, P-wave, nonet to lie around 1200 MeV. We review possible experimental indications of a scalar isovector resonance at 1.29 GeV, first observed by OBELIX in pp̄ annihilation. PACS 12.39.Mk; 12.40.-y; 13.25.Jx     

Two-photon mechanism of scalar meson production by colliding beams

Cross sections of scalar mesons f ₀(980), a ₀(980), and σ(600) production by colliding electron-positron beams are calculated. Two-photon decay widths of scalar mesons obtained in the Nambu-Jona-Lasinio model are used with quark and meson loops taken into account.     

Two photon decay of the glueball and scalar isoscalar mesons in a scaled NJL model

We use a modified version of the Nambu-Jona-Lasinio (NJL) model which implements the QCD trace anomaly to calculate the two photon decay width of the glueball (f₀(1500)) and of the two scalar mesons (f₀(1370), f_J=0(1710)) to which it is mixed. We investigate the effect of the mixing over the coupling constants of the f₀ states to the quarks and over the widths. We show that mass and phase space effects are crucial, at least in the NJL model, in determining the relative strength of the 2γ widths.     

K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

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.     

The mixing of scalar mesons and the baryon-baryon interaction

By introducing the mixing of scalar mesons in the chiral SU(3) quark model, we dynamically investigate the baryon-baryon interaction. The hyperon-nucleon and nucleon-nucleon interactions are studied by solving the resonating group method (RGM) equation in a coupled-channel calculation. In our present work, the experimental lightest pseudoscalar p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} mesons correspond exactly to the chiral nonet pseudoscalar fields p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} in the chiral SU(3) quark model. The h \eta,h^￠ \eta^{{\prime}}_{} mesons are considered as the mixing of singlet and octet mesons, and the mixing angle q_ps \theta_{{ps}}^{} is taken to be -23^° . For scalar nonet mesons, we suppose that there exists a correspondence between the experimental lightest scalar f ₀(600) , k \kappa , a ₀(980) , f ₀(980) mesons and the theoretical scalar nonet s \sigma , k \kappa , s^￠ \sigma^{{\prime}}_{} , e \epsilon fields in the chiral SU(3) quark model. For scalar mesons, we consider two different mixing cases: one is the ideal mixing and another is the q_s \theta_{s}^{} = 19^° mixing. The masses of the s^￠ \sigma^{{\prime}}_{} and e \epsilon mesons are taken to be 980MeV, which are just the masses of the experimental a ₀(980) , f ₀(980) mesons. The mass of the s \sigma meson is an adjustable parameter and is decided by fitting the binding energy of the deuteron, the masses of 560MeV and 644MeV are obtained for the ideal mixing and the q_s \theta_{s}^{} = 19^° mixing, respectively. We find that, in order to reasonably describe the YN interactions, the mass of the k \kappa meson is near 780MeV for the ideal mixing. However, we must enhance the mass of the k \kappa meson for the q_s \theta_{s}^{} = 19^° mixing, the 1050MeV is favorably used in the present work. The experimental s \sigma and k \kappa scalar mesons are very strange, both have larger widths. Hence, no matter what kind of mixing is considered, all the masses of scalar mesons we used in the present work seem to be consistent with the present PDG information.     

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.     

Meson loops in the f0(980) and a0(980) radiative decays into ρ , ω

We calculate the radiative decay widths of the a ₀(980) and f ₀(980) scalar mesons into ργ and ωγ considering the dynamically generated nature of these scalar resonances within the realm of the chiral unitary approach. The main ingredient in the evaluation of the radiative width of the scalar mesons are the loops coming from the decay into their constituent pseudoscalar-pseudoscalar components and the subsequent radiation of the photon. The dominant diagrams with only pseudoscalar mesons in the loops are found to be convergent while the divergence of those with a vector meson in the loop are written in terms of the two-meson loop function easily regularizable. We provide results for all the possible charge channels and obtain results, with uncertainties, which differ significantly from quark loops models and some version of vector meson dominance.     

2γ decays of scalar mesons (σ(600), f0(980), and a0(980)) in the Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980), and a ₀(980) are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c approximation, where N _c is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f ₀ decay the K-loop contribution turns out to play the dominant role. The results are in satisfactory agreement with modern experimental data.     

Radiative scalar-meson decays f0(980) → ρ(ω)γ and a0(980) → ρ(ω)γ within the local Nambu-Jona-Lasinio model

The widths with respect to the radiative decays f ₀(980) → ργ and a ₀(980) → ωγ were calculated within the local Nambu-Jona-Lasinio model. The contributions of both quark and meson loops were taken into account. The latter and the former play a dominant role for the radiative decays of, respectively, the f ₀(980) and the a ₀(980) meson.     

<Emphasis Type="Italic">B</Emphasis> decays into light scalar particles and glueball

The recent observations of f ₀(980) in charmless B decays motivate further studies of scalar particle and glueball production in these processes. Amplitudes for charmless two-body B decays involving the members of the scalar nonet are presented based on the symmetries of the dominant penguin contribution. Different scenarios for the lightest scalar nonet are investigated in view of the presently available data. We describe the evidence from B decays for f ₀(1500) with a flavor octet like mixing and the hints towards the members of the nonet of lowest mass. There is further support for the hypothesis of a broad 0 ^{+ +} glueball acting as coherent background especially in . The estimated B decay rates into gluonic mesons represent a sizable fraction of the theoretically derived decay rate for .Received: 23 April 2004, Revised: 27 October 2004, Published online: 21 December 2004Work supported in part by the Schweizerischer Nationalfonds.     

Analysis the f 0(980) and a 0(980) mesons as four-quark states with the QCD sum rules

In this article, we take the point of view that the scalar mesons f₀(980) and a₀(980) are the diquark-antidiquark states , and we devote our attention to the determination of their masses in the framework of the QCD sum rule approach with the interpolating currents constructed from scalar-scalar type and pseudoscalar-pseudoscalar type diquark pairs respectively. The numerical results indicate that the scalar mesons f₀(980) and a₀(980) may have two possible diquark-antidiquark substructures.Received: 27 January 2005, Revised: 22 March 2005, Published online: 31 May 2005PACS: 12.38.Lg; 13.25.Jx; 14.40.Cs     

Towards resolution of the scalar meson nonet enigma

By the application of a linear mass spectrum to a composite system of both the pseudoscalar and scalar meson nonets, we find three relations for the masses of the scalar states which suggest the assignment for the scalar meson nonet a₀(1320), K ₀ ^* (1430), f₀(1500), and f₀ ^′(980).     

Investigation of gf0ργ and coupling constants in light cone sum rules

We present a calculation of the coupling constant of f₀→ργ and a₀→ργ decays from the point of view of the light cone QCD sum rules. We estimate the coupling constants g_f0ργ, which are an essential ingredient in the analysis of physical processes involving the isoscalar f₀(980) and the isovector a₀(980) mesons. PACS 12.38.Lg, 13.40.Hq, 14.40.AqAn erratum to this article can be found at     

In search of non-exotic glueballs

Identification of a non-exotic glueball requires investigating the meson decuplet, including the \(q\bar q\) meson nonet and the glueball. The masses are a key factor in describing the decuplet. A particular feature of decuplet mixing is the possibility of hidden flavour being displaced between isosinglets. Some rules for searching for meson decuplets can be formulated.     

Radiative decays of scalar mesons σ(600), f 0(980) and a 0(980) in the local Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980) and a ₀(980) as well a ₀ → ju(ω)γ and f ₀ → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c -approximation where N _c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f ₀ decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a ₀ → ju(ω)γ and f ₀ → ju(ω)γ widths are given.