F0 Mesons Research Articles

TO LEARN LIGHT SCALARS FROM SEMILEPTONIC DECAYS OF HEAVY QUARKONIA

We study the mechanism of production of the light scalar mesons in the [Formula: see text] decays: [Formula: see text], and compare it with the mechanism of production of the light pseudoscalar mesons in the [Formula: see text] decays: [Formula: see text]. We show that the [Formula: see text] transition is negligibly small in comparison with the [Formula: see text] one. As for the the f0(980) meson, the intensity of the [Formula: see text] transition is not more thirty percent from the intensity of the [Formula: see text] ([Formula: see text]) transition. So, the [Formula: see text] decay supports the previous conclusions about a dominant role of the four-quark components in the σ(600) and f0(980) mesons.

Analysis of the pion scalar form factor provides model independent values off0(500) andf0(980) meson parameters

An existence of the scalar meson f0(500) is unambiguously confirmed by the pion scalar form factor analysis. The same is concerned also of the f0(980) scalar meson, though it is placed on the tail of the elastic region to be investigated in the analysis under consideration, therefore with less precise parameters values.

The scalar mesons in decays of the ψ and ϒ families

The f0 mesons are studied in a combined analysis of data on isoscalar S-wave processes ππ→ππ,KK¯,ηη and on decays J/ψ→ϕ(ππ,KK¯),ψ(2S)→J/ψ(ππ) and ϒ(2S)→ϒ(1S)ππ from the Argus, Crystal Ball, CLEO, CUSB, DM2, Mark II, Mark III, and BES III Collaborations. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. Some spectroscopic implications from results of the analysis are discussed.

Model independent [formula omitted] and [formula omitted] meson parameters by pion scalar form factor analysis

The f0(500) and f0(980) meson parameters are determined by the pion scalar form factor analysis, in which all existing S-wave iso-scalar ππ-scattering phase shift data in the elastic region are utilized.

Tetraquarks, hadronic molecules, meson-meson scattering, and disconnected contributions in lattice QCD

There are generally two types of Wick contractions in lattice QCD calculations of a correlation function --- connected and disconnected ones. The disconnected contribution is difficult to calculate and noisy, thus it is often neglected. In the context of studying tetraquarks, hadronic molecules and meson-meson scattering, we show that whenever there are both connected and singly disconnected contractions, the singly disconnected part gives the leading order contribution, and thus should never be neglected. As an explicit example, we show that information about the scalar mesons sigma, f0(980), a0(980) and kappa will be lost when neglecting the disconnected contributions.

Production representation of partial wave scattering amplitudes and the f 0(600) particle

The establishment of production representation of partial wave scattering amplitudes is reviewed in the context of quantum field theory. Its relation to the production representation, or Ning Hu representation in quantum mechanical scattering theory is pointed out. One of the most important application of the production representation is the physics of the f0(600) and K(700) scalar hadron resonances, on which we also give a brief review. It is emphasized that all evidences accumulated so far are consistent with the picture that the f0(600) meson is the chiral partner of the Nambu-Goldstone bosons in a linear realization of chiral symmetry.

Effective multiquark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.

Bs → f0(980) Transition Form Factors Within the kT Factorization Approach

In the paper, we apply the kT factorization approach to deal with the Bs → f0 (980) transition form factors in the large recoil regions, i.e. the small q2 regions. For the purpose, we adopt the B-meson wave-functions ΦB, and δ that include the three-Fock states contributions to do our discussion. Although the scalar meson f0(980) is widely perceived as the 4-quark bound state (scenario 2), but the distribution amplitudes of 4-quark states are still unknown to us, so we adopt 2-quark model (scenario 1) for scalar meson f0(980) in our discussion. By varying the B-meson wave-function parameters within their reasonable regions, we obtain F0(0) = F+(0) = 0.20 ± 0.02, FT(0) = 0.24 ± 0.02. Our present results for these form factors are consistent with the light-cone sum rule results obtained in the literature.

Dispersion theory of nucleon Compton scattering and polarizabilities

AbstractA status report on the topic nucleon Compton scattering and polarizabilities is presented with emphasis on the scalar t‐channel as entering into dispersion theory. Precise values for the polarizabilities are obtained leading to αp = 12.0 ± 0.6 (12.0), βp= 1.9∓ 0.6 (1.9), αn= 12.5 ± 1.7 (13.4), βn= 2.7 ∓ 1.8 (1.8) in units of 10−4 fm3 and γ(p)π= −36.4 ± 1.5 (−36.6), γ(n)π= 58.6 ± 4.0 (58.3), (γ(p)0 = −0.58 ± 0.20), (γ(n)0 = +0.38 ± 0.22) in units of 10−4 fm4, for the proton (p) and neutron (n), respectively. The data given with an error are recommended experimental values with updates compared to [1] where necessary, the data in parentheses are predicted values. These predicted values are not contained in [1], but are the result of a newly developed analysis which is the main topic of the present paper. The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the σ meson as part of the constituent‐quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the σ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the σ meson of mσ= 600± 70 MeV. From the experimental αp and predicted differences (αn‐αp) neutron polarizabilities in the range αn = 12.0 – 13.4 are predicted, where the uncertainties are related to the f0(980) and a0(980) scalar mesons.

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

The light scalar mesons below 1 GeV 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 f0(980) mesons are not described as KK̄ molecular states and nsn̄s̄ diquark-antidiquark states. However, the mass of the first radial excited state of the diquark-antidiquark state, nnn̄n̄ is 1019 MeV, is close to the experimental data of the f0(980).

Interpreting f0(600) and a0(980) as states from an Nf = 3 sigma model with (axial-)vectors

We address the question of whether it is possible to interpret the low-lying scalar mesons f0(600) and a0(980) as states within a U(3)×U(3) linear sigma model containing vector and axial-vector degrees of freedom.

Exotic mesons

We discuss possible exotic structure interpretations of the scalar mesons f0(1370), f0(1500) and f0(1710) and the charmonium-like state X(3872). The scalars are shown to result from a scheme where the excited quarkonia QQ̄ configurations mix with the lowest lying glueball. Within an effective chiral Lagrangian approach the strong decays of these states are shown to be consistent within this structure assumption. We also discuss the role of the scalar resonances f0(1370), f0(1500) and f0(1710) in the strong and radiative three-body decays of J/ψ, presenting further tests for this scenario. The charmonium-like X(3872) is assumed to consist dominantly of molecular hadronic components with an additional small admixture of a charmonium configuration. A potential model based on meson exchange is able to generate weak binding of the molecular hadronic components. The observed radiative (γJ/ψ and γψ(2s)) and strong (J/ψ2π and J/ψ3π) decays are shown to be consistent with the molecular structure assumption of the X(3872).

Search for and study of low-mass scalar mesons in reaction np → npπ+π− at neutron beam momentum P n = (5.20 ± 0.12) GeV/c

We present the results of a search for and study of the resonance effects in the system of π+π− from the reaction np → npπ+π− at the momentum of quasi-monochromatic neutrons Pn = (5.20 ± 0.12) GeV/c from the data obtained in an exposure of the 1-m hydrogen bubble chamber of Veksler and Baldin Laboratory of High Energies, Joint Institute for Nuclear Research (VBLHE JINR). After the supplementary selection of the events where a secondary proton was emitted in the forward hemisphere in the general c.m.s. of the reaction (cosθ*p> 0) in the effective mass spectrum of π+π− combinations, we found nine peculiarities at the masses (350 ± 3), (408 ± 3), (489 ± 3), (579 ± 5), (676 ± 7), (762 ± 11), (878 ± 7), (1036 ±13), and (1170 ± 11) MeV/c2 with experimental widths of no more than several tens of MeV/c2. We carried out a direct measurement of the spins of resonances and also obtained other quantum numbers. All of these peculiarities have a similar set of quantum numbers IG(JPC) = 0+ (0++). We investigated a sequence of scalar-isoscalar resonances f0(σ0) with masses in the range M ≤ 1200 MeV/c2. We found a phenomenological dependence of the resonance mass on its number. This dependence covered not only the resonances shown in this paper, but also those present in PDG tables with quantum numbers of f0(σ0) mesons.

Dynamical coupled-channel approaches on a momentum lattice

Dynamical coupled-channel approaches are a widely used tool in hadronic physics that allow to analyze different reactions and partial waves in a consistent way. In such approaches the basic interactions are derived within an effective Lagrangian framework and the resulting pseudo-potentials are then unitarized in a coupled-channel scattering equation. We propose a scheme that allows for a solution of the arising integral equation in discretized momentum space for periodic as well as twisted boundary conditions. This permits to study finite size effects as they appear in lattice QCD simulations. The new formalism, at this stage with a restriction to S-waves, is applied to coupled-channel models for the sigma(600), f0(980), and a0(980) mesons, and also for the Lambda(1405) baryon. Lattice spectra are predicted.

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.

Recent results from BESIII

In this talk, I will report recent results from BESIII Collaboration. (1) The χcJ decay into π0π0, ηη and γV(V = ρ,ω,ϕ) are presented and compared with that of theory calculation. (2) The first observation of χc1 → ϕ ϕ and ωω is displayed. Doubly OZI suppressed decay of χcJ → ωϕ are observed for the first time. (3) The mass and decay of hc(1P1) is important to learn about hyperfine(spin-spin) interaction of P wave states, and the hyperfine or triplet-singlet splitting determined by spin-spin term in QCD potential models. The mass and width of hc are measured, and Br(hc → γηc) are firstly obtained. Some results are also compared with theory prediction. (4) In order to study nature of light scalar meson a0 and f0, The J/ψ → ϕf0 → ϕa0 → ϕηπ and χc1 → aπ00 → f0π0 → π+π−π0 are performed. (5) The result of X(1835) in the η′π+π− are also shown, the possibility that there are two new resonances is under further study.

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 $ \pi$ , K, $ \eta$ , $ \eta^{{\prime}}_{}$ mesons correspond exactly to the chiral nonet pseudoscalar fields $ \pi$ , K, $ \eta$ , $ \eta^{{\prime}}_{}$ in the chiral SU(3) quark model. The $ \eta$ , $ \eta^{{\prime}}_{}$ mesons are considered as the mixing of singlet and octet mesons, and the mixing angle $ \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) , $ \kappa$ , a 0(980) , f 0(980) mesons and the theoretical scalar nonet $ \sigma$ , $ \kappa$ , $ \sigma^{{\prime}}_{}$ , $ \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 $ \theta_{s}^{}$ = 19° mixing. The masses of the $ \sigma^{{\prime}}_{}$ and $ \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 $ \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 $ \theta_{s}^{}$ = 19° mixing, respectively. We find that, in order to reasonably describe the YN interactions, the mass of the $ \kappa$ meson is near 780MeV for the ideal mixing. However, we must enhance the mass of the $ \kappa$ meson for the $ \theta_{s}^{}$ = 19° mixing, the 1050MeV is favorably used in the present work. The experimental $ \sigma$ and $ \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.

Scalar mesons in a finite volume

Using effective field theory methods, we discuss the extraction of the mass and width of the scalar mesons f0(980) and a0(980) from the finite-volume spectrum in lattice QCD. In particular, it is argued that the nature of these states can be studied by invoking twisted boundary conditions, as well as investigating the quark mass dependence of the spectrum.

KLOE results on scalar and pseudoscalar mesons

The data collected by the KLOE Collaboration at the Frascati ϕ-factory DAΦ from 2001 to 2006 have been used for extensive studies in meson spectroscopy. The decays of the scalar mesons a0(980) and f0 (980) into two pseudoscalar mesons have been exploited to measure the relevant parameters of those resonances. The radiative decays ϕ → ηγ and η′γ have been used for the determination of the pseudoscalar mixing angle and to search for a possible gluonium content in the η′. The dynamics of the η → 3π decay has been studied and the Dalitz Plot parameters have been measured. The large amount of η mesons produced allowed also to study interesting rare η decays.

Ideal Mixing of Scalar Mesons and Hyperon-Nucleon Interaction

The mixing of scalar mesons is an open problem since their structure is unclear and controversial. By introducing the ideal mixing of scalar mesons, we dynamically investigate the hyperon-nucleon interaction in the chiral SU(3) quark model by solving the resonating group method (RGM) equation. The results show that when the ideal mixing of scalar mesons is considered and the mass of a κ meson is reduced to near 780 MeV, then the hyperon-nucleon scattering data can be reasonably described in the chiral SU(3) quark model. Hence we find that the experimental mass of the κ meson is around 780 MeV, and f0(600) and f0(980) mesons are the ideal mixing of scalar singlet and octet mesons.