Using the U(3)R x U(3)L extended Linear Sigma Model with the ordinary (pseudo)scalar and (axial)vector mesons as well as a scalar glueball, we study the vacuum phenomenology of the scalar-isoscalar resonances f0(1370), f0(1500) and f0(1710). We present here a solution, based only on the masses and not yet on decays, in which the resonances f0(1370) and f0(1500) are predominantly nonstrange and strange qbar-q states respectively, and the resonance f0(1710) is predominantly a scalar glueball.
Ground and first radially excited scalar isoscalar meson states and a scalar glueball are described in a nonlocal U(3)xU(3) quark model. The glueball is introduced into the effective meson Lagrangian by means of the dilaton model on the base of the scale invariance of the meson Lagrangian. The scale invariance breaking by current quark masses and gluon anomalies is taken into account. The glueball anomalies turn out to be important for the description of the glueball-quarkonia mixing. The masses of five scalar isoscalar meson states and their strong decay widths are calculated. The state f_0(1…
We analyze the mixing of the scalar glueball with the scalar-isoscalar quarkonia states above 1 GeV in a non-local covariant constituent approach. Similarities and differences to the point-particle Klein-Gordon limit and to the quantum mechanical case are elaborated. Model predictions for the two-photon decay rates in the covariant mixing scheme are indicated.
We investigate the hadronic two-body decay modes of the scalar-isoscalar $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ states as resulting from the mixture of the lowest lying scalar glueball with the isoscalar states of the ground state $^3P_0$ $Q\bar Q$ nonet. In the decay analysis we take into account the direct coupling of the quarkonia and glueball components of the $f_0$ states to the quarkonia components of the two-meson final state with the decay dynamics inspired by the strong coupling limit of QCD. We calculate partial decay widths for the $f_0$ states in the proposed three-state mixing s…
A coupled-channel analysis of BESIII data on radiative $J/ψ$ decays into $ππ$, $K\bar K$, $ηη$ and $ωϕ$ has been performed. The partial-wave amplitude is constrained by a large number of further data. The analysis finds ten isoscalar scalar mesons. Their masses, widths and decay modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet and mainly octet states. Octet isoscalar scalar states are observed with significant yields only in the 1500-2100\,MeV mass region. Singlet scalar mesons are produced over a wide mass range but their yield peaks in the same mass region. The…
We summarize the results of the investigation of the $IJ^{PC}=00^{++}$ wave which is devoted to the search for the lightest scalar glueball. In the framework of the K-matrix formalism, the $q\bar q$-nonet classification of the scalar/isoscalar states is performed in the mass region below 1900 MeV basing on the following data: GAMS data for $π^-p\toπ^0π^0n$, $ηηn$, $ηη'n$; CERN-Münich data for $π^-p\toπ^+π^-n$; Crystal Barrel data for $p\bar p\toπ^0π^0π^0$, $π^0π^0η$, $π^0ηη$; BNL data for $ππ\to K\overline K$. It is shown the existence of an extra state for $q\bar q$ classification: this state…
The mixing angles between scalar isoscalar resonances and a scalar glueball are determined from their decays into two pseudoscalar mesons. For $f_0(1370)$ and $f_0(1500)$, at most a small glueball component is admitted by the data. The decay modes of $f_0(1710)$, $f_0(1770)$, $f_0(2020)$, and $f_0(2100)$ require significant glueball fractions. Above this mass, the errors in the decay frequencies become too large to extract a glueball component. The summation of all observed glueball fractions up to 2100\,MeV yields (78\er18)\%. The glueball fractions as function of the mass are consistent with…
In a U(3)x U(3) quark chiral model of the Nambu-Jona-Lasinio type with the 't Hooft interaction, the ground scalar isoscalar mesons and a scalar glueball are described. The glueball (dilaton) is introduced into the effective meson Lagrangian written in a chirally symmetric form on the base of scale invariance. The singlet-octet mixing of scalar isoscalar mesons and their mixing with the glueball are taken into account. Mass spectra of the scalar mesons and glueball and their strong decays are described.
Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)xU(3) chiral quark model of the Nambu--Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the sc…
The gluonic widths of four leading glueball candidates are determined from their production in radiative quarkonium decays, allowing quantitative estimation of their glue content. Lattice predictions for the scalar and tensor channels seem to be in reasonable agareement with present data (allowing for mixing with $q \bar{q}$ states). However there is a glueball-like-state in the pseudoscalar spectrum whose mass is considerably lower than expected from lattice estimates.
We perform a glueball-relevant study on isoscalars based on anisotropic $N_f=2$ lattice QCD gauge configurations. In the scalar channel, we identify the ground state obtained through gluonic operators to be a single-particle state through its dispersion relation. When $q\bar{q}$ operator is included, we find the mass of this state does not change, and the $q\bar{q}$ operator couples very weakly to this state. So this state is most likely a glueball state. For pseudoscalars, along with the exiting lattice results, our study implies that both the conventional $q\bar{q}$ state $η_2$ (or $η'$ in f…
The pseudoscalar mesons with the masses higher than 1 GeV are assumed to belong to the meson decuplet including the glueball as the basis state supplementing the standard $SU(3)_F$ nonet of light $q\bar{q}$ states $(u,d,s)$. The decuplet is investigated by means of an algebraic approach based on hypothesis of vanishing the exotic $SU(3)_F$ commutators of "charges" and their time derivatives. These commutators result in a system of equations determining contents of the isoscalar octet state in the physical isoscalar mesons as well as the mass formula including all masses of the decuplet: $π(130…
Within a nonlinear chiral Lagrangian framework the correlations between the quark and glueball admixtures of the isosinglet scalar mesons below 2 GeV and the current large uncertainties on the mass of the f0(600) and the f0(1370) are studied. The framework is formulated in terms of two scalar meson nonets (a two-quark nonet and a four-quark nonet) together with a scalar glueball. It is shown that while some properties of these states are sensitive to the mass of f0(600) and f0(1370), several relatively robust conclusions can be made: The f0(600), the f0(980), and the f0(1370) are admixtures of…
A coupled-channel analysis has been performed to identify the spectrum of scalar mesons. The data include BESIII data on radiative $J/ψ$ decays into $π^0π^0$,$K_SK_S$, $ηη$, and $ωϕ$, 15 Dalitz plots from $\bar pN$ annihilation at rest at LEAR, the CERN-Munich multipoles for $ππ$ elastic scattering, the $S$-wave from BNL data on $ππ$ scattering into $K_SK_S$, from GAMS data on $ππ\to π^0π^0, ηη$, and $ηη'$, and NA48/2 data on low-mass $ππ$ interactions from $K^\pm\toππe^\pmν$ decays. The analysis reveals the existence of ten scalar isoscalar resonances. The resonances can be grouped into two c…
We develop tools to determine the gluonic content of a resonance of known mass, width and $J^{PC}$ from its branching fraction in radiative quarkonium decays and production cross section in $γγ$ collisions. We test the procedures by applying them to known $q\bar{q}$ mesons, then analyze four leading glueball candidates. We identify inconsistencies in data for $J/ψ\to γf_0(1500)$ and $J/ψ\to γf_J(1710)$ whose resolution can quantify their glueball status.When $Γ(f_0(1500) \to γγ)$ and $Γ(f_J(1710) \to γγ)$ are known, the $n\bar{n}, s\bar{s},gg$ mixing angles can be determined. The enigmatic sit…
The quark/gluon content of eta(1295) and eta(1440) mesons is discussed, mesons being considered as members of the first radial excitation 2^1S_0 qqbar nonet. Recent results on eta(1295) and eta(1440) two-photon widths from L3 together with the information on radiative J/Psi decay allow one to evaluate the eta(1295)/eta(1440) mixing angle and the admixture of the glueball component. We found that eta(1440) is dominantly non-strange qqbar state, with a possible admixture of the glueball component (20 pm 20)%.
Scalar-isoscalar states (0++) are investigated within the large-Nc Regge approach. We elaborate on the consequences of including the lightest f0(600) scalar-isoscalar state into such an analysis, where the position of f0(600) fits very well into the pattern of the radial Regge trajectory. Furthermore, we point out that the pion and nucleon spin-0 gravitational form factors, recently measured on the lattice, provide valuable information on the low-mass spectrum of the scalar-isoscalar states on the basis of the scalar-meson dominance in the spin-0 channel. Through the fits to these data we find…
Recent results concerning the evidence and classification of the J^{PC}=0^{++} states, obtained with P. Minkowski, are presented: The isoscalars f_0(980) and f_0(1500) are classified as members of the 0^{++} nonet, while the broad state called f_0(400-1200) and the state f_0(1370) are considered as different components of a single broad resonance, the lowest-lying 0^{++} glueball. Furthermore, we propose the investigation of glueball production in the fragmentation region of gluon jets.
We study the strong and electromagnetic decay properties of scalar mesons above 1 GeV within a chiral approach. The scalar-isoscalar states are treated as mixed states of quarkonia and glueball configurations. A fit to the experimental decay rates listed by the Particle Data group is performed to extract phenomenological constraints on the nature of the scalar resonances. A comparison to other theoretical approaches in the scalar meson sector is discussed.
Basing on the results of the K-matrix fit of $(IJ^{PC}=00^{++})$ wave, we analyze the analytic structure of the amplitude and $q \bar q$/glueball content of resonances in the mass region 1200-1900 MeV, where an extra state for $q \bar q$-systematics exists being a good candidate for the lightest scalar glueball. Our analysis shows that the pure glueball state dispersed over three resonances: $f_0(1300)$, $f_0(1500)$ and $f_0(1530^{+90}_{-250})$, while the glueball admixture in $f_0(1750)$ is small. The broad resonance $f_0(1530^{+90}_{-250})$ is the descendant of the lightest pure glueball. Th…
We study the strong and electromagnetic decay properties of scalar mesons above 1 GeV within a chiral approach. The scalar-isoscalar states are treated as mixed states of quarkonia and glueball configurations. A fit to the experimental mass and decay rates listed by the Particle Data group is performed to extract phenomenological constraints on the nature of the scalar resonances and to the issue of the glueball decays. A comparison to other experimental results and to other theoretical approaches in the scalar meson sector is discussed.
We consider a $N_f=3$ chiral Lagrangian which describes the interaction between the pseudoscalar glueball, $J^{PC}=0^{-+}$, and scalar and pseudoscalar mesons. We calculate the decay widths of the pseudoscalar glueball, where we fixed its mass to 2.6 GeV, as predicted by lattice QCD simulations, and take a closer look in the scalar-isoscalar decaying channel. We present our results as branching ratios which are relevant for the future PANDA experiment at the FAIR facility.
On the basis of a simultaneous description of the isoscalar s-wave channel of the $ππ$ scattering (from the threshold up to 1.9 GeV) and of the $ππ\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, a confirmation of the $σ$-meson at $\sim$ 660 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained.
Partial wave analysis of the reactions p anti-p -> pi-pi, eta-eta, eta-eta' in the region of invariant masses 1900-2400 MeV indicates to the existence of four relatively narrow tensor-isoscalar resonances f_2(1920), f_2(2020), f_2(2240), f_2(2300) and the broad state f_2(2000). The determined decay couplings of the broad resonance f_2(2000)-> pi0-pi0, eta-eta, eta-eta' satisfy the relations appropriate to those of tensor glueball, while the couplings of other tensor states do not, thus verifying the glueball nature of f_2(2000).
It is shown that new data on the $(J^{PC}=2^{++})$-resonances in the mass range $M\sim1700-2400 $MeV support the linearity of the $(n,M^2)$-trajectories, where $n$ is the radial quantum number of quark--antiquark state. In this way all vacancies for the isoscalar tensor $q\bar q$-mesons in the range up to 2450 MeV are filled in. This allows one to fix the broad $f_2$-state with $M=2000\pm30 $MeV and $Γ=530\pm40 $MeV as the lowest tensor glueball. PACS numbers: 14.40.-n, 12.38.-t, 12.39.-Mk
In the reactions $p\bar p\toπ^0π^0,ηη,ηη'$ there are four relatively narrow resonances $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$, and a broad one $f_2(2000)$ in the mass region 1990--2400 MeV. In the framework of quark combinatorics we carry out an analysis of the decay constants for all five resonances. It is shown that the relations for the decay constants corresponding to the broad resonance $f_2(2000)\toπ^0π^0,ηη, ηη'$ are the same as those corresponding to a glueball. An additional argument in favour of the glueball--nature of $f_2(2000)$ is the fact that $f_2(1920)$, $f_2(2020)$…
The evidence for the low mass J^{PC}=0^{++} states is reconsidered. We suggest classifying the isoscalars f_0(980) and f_0(1500) as members of the 0^{++} nonet, with a mixing rather similar to that of the pseudoscalars η' and η. The broad state called f_0(400-1200) or `sigma'' and the state f_0(1370) are considered as different signals from a single broad resonance, which we take to be the lowest-lying 0^{++} glueball. The main arguments in favor of these hypotheses are presented and compared with theoretical expectations.
The scalar glueball is observed in a coupled-channel analysis of the $S$-wave amplitude from BESIII data on radiative $J/ψ$ decays and further data. Ten scalar isoscalar resonances were required to fit the data. Five of them were interpreted as mainly-singlet, five as mainly-octet resonances in SU(3). The yield of resonances showed a striking peak with properties expected from a scalar glueball. The $D$ wave amplitude in the BESIII data on radiative $J/ψ$ decays reveales a high-mass structure which can be described by a single Breit-Wigner or by the sum of three $ϕϕ$ resonances interpreted as …
The search for the ground state scalar glueball G_0 is reviewed. Spin zero glueballs will have unique dynamical properties if the <G_0|\bar qq> amplitude is suppressed by chiral symmetry, as it is to all orders in perturbation theory: for instance, mixing of G_0 with \bar qq mesons would be suppressed, radiative J/psi decay would be a filter for new physics in the spin zero channel, and the decay G_0 \to \bar KK could be enhanced relative to G_0 \to ππ. These properties are consistent with the identification of f_0(1710) as the largely unmixed ground state scalar glueball, while recent BES dat…
We study the three-flavor chirally and dilatation invariant extended Linear Sigma Model with (pseudo)scalar and (axial-)vector mesons as well as a scalar dilaton field whose excitations are interpreted as a glueball. The model successfully describes masses and decay widths of quark-antiquark mesons in the low-energy region up to 1.6 GeV. Here we study in detail the vacuum properties of the scalar-isoscalar channel and find that (i) a narrow glueball is only possible if the vacuum expectation value of the dilaton field is (at tree-level) quite large (i.e., larger than what lattice QCD and QCD s…
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the fJ(2220), and one where the glueball is more distributed, with f2(1820) having the largest component. The f2(1565) and fJ(1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absense of significant coupling to decay channels. f2'(1525) -> pi pi is in agreement with experiment. The fJ(2220) decays neither flavour democratically nor is narrow.
We investigate the correlations between the scalar meson configurations and Okuba-Zweig-Iizuka (OZI) rule violations in the hadronic decays of heavy quarkonia, e.g. $J/ψ$ and $Υ$, into isoscalar vector meson ($ϕ$ and $ω$) and scalar mesons ($f_0(1710)$, $f_0(1500)$, and $f_0(1370)$). It shows that the dramatic change of the values of the branching ratio fraction of $ϕf_0/ωf_0$ from low (e.g. in $J/ψ$ decays) to high energies (e.g. in $Υ$ decays) will not only test the glueball-$Q\bar{Q}$ mixings, but also provide important information about the mysterious OZI-rule violations within the scalars…
We study the vacuum properties of the pseudoscalar glueball and charmed mesons by using the so-called extended Linear Sigma Model (eLSM). This model includes scalar and pseudoscalar mesons, as well as vector and axial-vector mesons. We calculate the mesonic and baryonic decays of the pseudoscalar glueball, where we fixed its mass to $2.6$ GeV, as predicted by lattice-QCD simulations, and take a closer look at the scalar-isoscalar decay channel. As a second step, we enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark to a global $U(4)_r\times U(4)_l$ chiral sym…
In the three-state mixing framework, considering the possible glueball components of $η$ and $η^\prime$, we investigate the hadronic decays of $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ into two pseudoscalar mesons. The quarkonia-glueball content of the three states is determined from the fit to the new data presented by the WA102 Collaboration. We find that these data are insensitive to the possible glueball components of $η$ and $η^\prime$. Furthermore, we discuss some properties of the mass matrix describing the mixing of the isoscalar scalar mesons.
Basing on the previously performed K-matrix analysis of experimental data, we investigate, in the framework of the propagator matrix (D-matrix) technique, the 1100-1900 MeV mass region, where overlapping resonances $f_0(1300)$, $f_0(1500)$, $f_0(1530^{+90}_{-250})$, and $f_0(1780)$ are located. Necessary elements of the D-matrix technique are developed. The D-matrix analysis confirms previous K-matrix results: in the region 900-1900 MeV five scalar/isoscalar states are located. Four of them are members of the two $q\bar q$-nonets, while one state is an extra for the $q\bar q$ systematics, bein…
The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the $a_0(980)$ could be the spin-partner of $a_2(1320)$, $a_1(1260)$, and $b_1(1235)$; $f_0(500)$ the spin-partner of $f_2(1270)$, $f_1(1285)$, and $h_1(1170)$; and $f_0(980)$ the spin-partner of $f_2'(1525)$, $f_1(1420)$, and $h_1(1415)$. From the decay and the production of light scalar mesons we find a consistent mixing angle $θ^{\rm s}=(14\pm4)^\circ$. We conclude that $f_0(980)$ is likely "octet-like" in SU(3…
In the framework of the extended Linear Sigma Model (eLSM) we investigate the masses and decays of the three scalar-isoscalar resonances $f_{0}(1370)$, $f_{0}(1500)$ and $f_{0}(1710)$. The degrees of freedom of the eLSM are (pseudo)scalars and (axial)vectors as well as the scalar glueball. Although still preliminary, present results, based on the physical masses of the above mentioned resonances, show that $f_{0}(1710)$ is the predominantly glueball state. However, acceptable decays for this resonance can be obtained only for a (very) large gluon condensate.
Recently performed investigations of meson spectra allow us to determine the resonance structure for the waves $IJ^{PC}=00^{++}$, $10^{++}$, $02^{++}$, $12^{++}$ = $IJ^P= 1/2 0^+$ in the mass region up to 1900 MeV, thus establishing the meson multiplets $1^3P_0q\bar q$ and $2^3P_0q\bar q$. Experimental data demonstrate that there are five scalar/isoscalar states in this mass region. Four of them are $q\bar q$ states, that is, members of the $1^3P_0q\bar q$ and $2^3P_0q\bar q$ nonets, while the fifth state is an extra one not accomodated by $q \bar q$ systematics; it has the properties of the l…
The lightest gluonic meson is expected with J^{PC}=0^{++}, calculations in full QCD point towards a mass of around 1 GeV. The interpretation of the scalar meson spectrum is hindered as some states are rather broad. In a largely model-independent analysis of pi+ pi- \to pi+ pi-, pi0 pi0 scattering in the region 600-1800 MeV a unique solution for the isoscalar S-wave is obtained. The resonances f_0(980), f_0(1500) and the broad f_0(600) or ``sigma'' are clearly identified whereas f_0(1370) is not seen at the level B(f_0(1370)\to pi pi)\gtrsim 10%. Arguments for the broad state to be a glueball a…
Scalar-isoscalar states are analyzed within the large-Nc Regge approach. We find that the lightest f0(600) scalar-isoscalar state fits very well into the pattern of the radial Regge trajectory. We confirm the obtained mass values from an analysis of the pion and nucleon spin-0 gravitational form factors, recently measured on the lattice. We find that a simple two-state model suggests a meson nature of f0(600), and a glueball nature of f0(980), which naturally explains the ratios of various coupling constants. Finally, matching to the OPE requires a fine-tuned mass condition of the vanishing di…
We study the phenomenology of the ground-state (pseudo-)scalar charmonia $η_c$ and $χ_{c0}$ in the framework of a $U(4)_r \times U(4)_l$ symmetric linear sigma model with (pseudo-)scalar and (axial-) vector mesons. Based on previous results for the spectrum of charmonia and the spectrum and (OZI-dominant) strong decays of open charmed mesons, we extend the study of this model to OZI-suppressed charmonia decays. This includes decays into 'ordinary' mesons but also particularly interesting channels with scalar-isoscalar resonances $f_0(1370),\, f_0(1500),\, f_0(1710)$ that may include sizeable c…
Scalar-isoscalar states ($J^{PC}=0^{++}$) are discussed within the large-$N_c$ Regge approach. We find that the lightest $f_0(600)$ scalar-isoscalar state fits very well into the pattern of the radial Regge trajectory where the resonance nature of the states is advantageously used. We confirm the obtained mass values from an analysis of the pion and nucleon spin-0 gravitational form factors, recently measured on the lattice. We provide arguments suggesting an alternating meson-glueball pattern of the 0++ states, which is supported by the pseudoscalar-isovector 0+- excited spectrum and asymptot…
A separable potential model of three coupled channels (pion-pion, kaon-antikaon and an effective four pion) has been constructed and applied in the analysis of the isoscalar S-wave pion-pion and kaon-antikaon phase shifts and inelasticities .A relatively narrow scalar resonance of mass 1400-1460 MeV has been found. This resonance is consistent with the recent CERN observation of an eventual scalar glueball at 1500 MeV. Other resonances at lower energies like a wide sigma meson and a narrow f0(980) have been confirmed.
A classification of the $IJ^{PC}=00^{++}$ mesons is performed on the basis of the K-matrix analysis of meson spectra in the reactions: (i) GAMS data on $πp\to π^0π^0 n$, $ηηn$, $ηη' n$; (ii) Crystal Barrel data on $p\bar p~(at~rest)\to π^0π^0π^0$, $π^0π^0η$, $π^0ηη$; (iii) CERN-Münich data on $πp\to π^+π^- n$; (iiii) BNL data on $πN\to K\bar K N$. The analysis points to the existence of four comparatively narrow scalar resonances which correspond to the following poles of the scattering amplitude (in MeV): $(1015\pm 15)- i(43\pm 8)$, $(1300\pm 20)-i(120\pm 20)$, $(1499\pm 8)-i(65\pm 10)$ and $…
In the framework of the $U(2)_{R}\times U(2)_{L}$ symmetric linear sigma model with (axial)vector mesons generalized by including a dilaton field we study the phenomenology of the scalar-isoscalar resonances below 2 GeV. It turns out that, in our favoured scenario, the resonance $f_{0}(1370)$ is predominantly a $\bar{q}q$ state and $f_{0}(1500)$ is predominantly a glueball state. Additionally we are able to calculate the value of the gluon condensate, which is in agreement with lattice QCD results.
First radial excitations of the isoscalar and isovector scalar mesons f_0(400-1200), f_0(980) and a_0(980) are investigated in the framework of a nonlocal version of a chiral quark model of the Nambu--Jona-Lasinio type. It is shown that f_0(1370), f_J(1710) and a_0(1450) are the first radially excited states of f_0(400-1200), f_0(980) and a_0(980) which are ground states of the scalar meson nonet. The mesons' masses and strong decay widths are calculated. The scalar resonance f_0(1500) is supposed to be a glueball. The status of K_0^*(1430) is discussed.
Scalar glueball-$s\bar{s}$ mixing in one flavor lattice QCD
Hunan Normal University（湖南师范大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Combining the recent lattice calculation of $a_0(1450)$ and $σ(600)$ mesons with the overlap fermion in the chiral regime with the pion mass less than $300 {\rm MeV}$, the quenched lattice calculation of the scalar glueball, and the phenomenological study of the mixing of isoscalar scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ through their decays, a simple pattern for the light scalar mesons begins to emerge. Below 1 GeV, the scalar mesons form a nonet of tetraquark mesoniums. Above 1 GeV, the nonent $q\bar{q}$ mesons are made of an octet with largely unbroken SU(3) symmetry and a fairl…
A coherent study of the production of $f_0^i$ ($i=1$, 2, 3 corresponding to $f_0(1710)$, $f_0(1500)$, and $f_0(1370)$) in $J/ψ\to V f_0 \to V PP$ is reported based on a previously proposed glueball and $Q\bar{Q}$ nonet mixing scheme, and a factorization for the decay of $J/ψ\to V f_0^i$, where $V$ denotes the isoscalar vector mesons $ϕ$ and $ω$, and $P$ denotes pseudoscalar mesons. The results show that the $J/ψ$ decays are very sensitive to the structure of those scalar mesons, and suggest a glueball in the $1.5-1.7$ GeV region, in line with Lattice QCD. The presence of significant glueball m…
A K-matrix re-analysis of the K-pi S-wave is performed in the mass region 900-2100 MeV, and solutions which describe the data well are found. The solution with two resonances in the (IJ^P=1/2 0^+)-wave has poles at (1415 pm 25)- i(165 pm 25) MeV and (1820 pm 40) -i(125 pm 50) MeV, close to the previous result of D. Aston et al., Nucl.Phys., B296 (1988) 493. The corresponding bare states, which are the subjects of a qqbar classification, are: K_0^{bare}(1220^{+50}_{-60}) and K_0^{bare}(1885^{+50}_{-80}). Within the restored bare states, a construction of the 1^3P_0 qqbar and 2^3P_0 qqbar nonets…
We extract the K+K- couplings of the isoscalar scalar mesons sigma/f_0(600) and f_0(980) from pi pi to pi pi / K K scatterings and found: |g_{sigma K+K-}|/ |g_{sigma pi+pi-}|= 0.8 and |g_{f_0 K+K-}|/ |g_{f_0 pi+pi-}|= 1.7. These results, together with the tiny "direct" gamma gamma width of the sigma and its large hadronic width, are a strong indication for the gluonium/glueball nature of the sigma-meson, as predicted by QCD spectral sum rules (QSSR) + some low-energy theorems (LET), while some other assignements (pi pi molecule, tetraquark state and ordinary qq meson) do not satisfy simultaneo…
