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 peak is interpreted as scalar glueball. Its mass and width are determined to $M=1865$\er25$^{+10}_{-30}$ {\rm MeV} and $Γ= 370$\er$50^{+30}_{-20}$ {\rm MeV}, its yield in radiative $J/ψ$ decays to ($5.8\pm 1.0)\,10^{-3}$.
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.
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.
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…
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…
A new meson mass relation for meson nonet is given after considering mixing with glueball. The mixing between pseudoscalar mesons and pseudoscalar glueball will decrease the mass of glueball by about 500 Mev. So, according to the predicted mass of the pure pseudoscalar glueball given by lattice calculation and effective Hamiltonian, the expected mass of mixed pseudoscalar glueball is about 1.7 Gev. This result is helpful for experimemtal search for the mixed Isoscalar pseudoscalar glueball.
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…
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.
Using a bound-state model of weakly bound gluons for glueballs made of two gluons and a natural generalization of the perturbative QCD formalism for exclusive hadronic processes, we present results for glueball production in radiative J/psi, Upsilon decays into several possible glueball states, including L \not= 0 ones. We perform a detailed phenomenological analysis, presenting results for the more favored experimental candidates and for decay angular distributions.
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.
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.
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 …
We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar mesons is discussed. For pseudoscalar mesons, the inclusion of the glue field in an effective low energy theory is presented leading to a third isoscalar $η''$ partner of the $η$ and $η'$. Branching ratios for processes involving $η''$ are given and, when available, compatible with data for $η(1405)$.
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.
The mass of the lowest scalar glueball is discussed by using QCD sum rules. We find that the glueball mass is sensitive to the choice of moments and slightly depends on the radiative corrections. With the help of suitable moments and stability criteria, we get the scalar glueball mass: $1710\pm110$ MeV without radiative corrections and $1580\pm150$ MeV with radiative corrections.
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.
QCD theory predicts the existence of glueballs, but so far all experimental endeavors have failed to identify any such states. To remedy this discrepancy between QCD, which has proven to be a successful theory for strong interactions, and the failure of experimental searches for glueballs, one is tempted to accept the promising interpretation that the glueballs mix with regular $q\bar q$ states of the same quantum numbers. The lattice estimate of the masses of pure $0^{++}$ glueballs ranges from 1 to 2 GeV, which is the region of the $f_0$ family. Thus many authors suggest that the $f_0$ meson…
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…
The $0^{++}$ glueball mass is analyzed in the QCD sum rules. We show that in order to determine the $0^{++}$ glueball mass by using the QCD sum rules method, it is necessary to clarify the following three ingredients: (1) to choose the appropriate moment with acceptable parameters which satisfy all of the criteria; (2) to take account into the radiative corrections; (3) to estimate an additional contribution to the glueball mass from the lowest lying ${\bar q}q$ resonance. We conclude that it is the key point to choose suitable moments to determine the $0^{++}$ glueball mass, the radiative cor…
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 $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained. It is shown that the large $ππ$-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at $\sim$ 665 MeV. The coupling constants of the obs…
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.
We establish the factorization formula for scalar Glueball production through radiative decays of vector states of heavy quarkonia, e.g. $J/ψ$, $ψ(2S)$ and $Υ(nS)$, where the Glueball mass is much less than the parent heavy quarkonium mass. The factorization is demonstrated explicitly at one-loop level through the next-to-leading order (NLO) corrections to the hard kernel, the non-relativistic QCD (NRQCD) long-distance matrix element (LDMEs) of the heavy quarkonium, and the light-cone distribution amplitude (LCDA) of scalar Glueball. The factorization provides a comprehensive theoretical appro…
On the basis of the results of $ξ(2230)\rightarrowπ^{+}π^{-}, p\bar{p}$ and $K\bar{K}$, measured by the BES Collaboration in radiative J/$ψ$ decays, combined with the upper limit of Br($ξ\rightarrow p\bar{p}$)Br($ξ\rightarrow K\bar{K}$), measured by PS185 experiment, we argue that the distinctive properties of $ξ$(2230), the flavor-symmetric decays and the narrow partial decay widths to $ππ$ and $K\bar{K}$ as well as its copious production in radiative J/$ψ$ decay, would strongly favor the glueball interpretation of $ξ$(2230).
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…
Given a resonance of known mass, width, and J^{PC}, we can determine its gluonic branching fraction, b(R->gg), from data on its production in radiative vector quarkonium decay, V -> gamma+R. For most resonances b(R->gg) is found to be O(10%), consistent with being q-qbar states, but we find that both pseudoscalars observed in the 1440 MeV region have b(R->gg) ~ 1/2 - 1, and b(f_0^{++}->gg) ~ 1/2. As data improves, b(R->gg) should be a useful discriminator between q-qbar and gluonic states and may permit quantitative determination of the extent to which a particular resonance is a mixture of gl…
The tensor glueball is searched for in BESIII data on radiative $J/ψ$ decays into $π^0π^0$ and $K_sK_s$. The $ππ$ invariant mass distribution exhibits an enhancement that can be described by a pole at $(2210\pm 60) -i(180\pm 60)$\,MeV. We speculate if the tensor glueball could be distributed among high-mass tensor mesons.
This is a contribution to the review "50 Years of Quantum Chromdynamics" edited by F. Gross and E. Klempt [arXiv:2212.11107], to be published in EPJC. The contribution remembers the early searches and explains how to find a glueball, based on its properties. The results of a coupled-channel analysis are presented that provides evidence for the scalar glueball and first hints for the tensor glueball. Data on radiative decays of $ψ(2S)$ and $Υ(1S)$ show scalar intensity that is likely due to glueball production.
On the basis of the recent results of $ξ(2230)\rightarrow π^+π^-, p\bar p$ and $ξ(2230)\rightarrow K^+K^-,~K_SK_S$, measured by the BES Collaboration in $J/ψ$ radiative decays, combined with the PS185 experiment of $p\bar p\rightarrow ξ(2230)\rightarrow K\bar K$, we argue that because of its very narrow partial decay widths to $ππ$ and $K\bar K$ ( less than $1~MeV$ ), its large production rate in $J/ψ$ radiative decays, and its flavor- symmetric couplings to $ππ$ and $K\bar K$, the $ξ(2230)$ is very likely to be a $J^{PC}=(even)^{++}$ glueball.
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…
Existence of gluonic resonances is among the early expectations of QCD. Today, QCD calculations predict the lightest glueball to be a scalar state with mass within a range of about 900-1700 MeV but there is no consensus about its experimental evidence. In a re-analysis of the phase shifts for pi pi scattering up to 1800 MeV where such states should show up we find the broad resonance f_0(600)/σcontributing to the full mass range and the narrow f_0(980) and f_0(1500) but no evidence for f_0(1370). Phenomenological arguments for the broad state to be a glueball are recalled. It is argued that th…
The form factors in the radiative decay of $J/ψ$ to a scalar glueball are studied within quenched lattice QCD on anisotropic lattices. The continuum extrapolation is carried out by using two different lattice spacings. With the results of these form factors, the partial width of $J/ψ$ radiatively decaying into the pure gauge scalar glueball is predicted to be 0.35(8) keV, which corresponds to a branching ratio of 3.8(9)x10^{-3}. By comparing with the experiments, out results indicate that f_0(1710) has a larger overlap with the pure gauge glueball than other related scalar mesons.
The analysis of the experimental data of Crystal Barrel Collaboration on the p anti-p annihilation in flight with the production of mesons in the final state resulted in a discovery of a large number of mesons over the region 1900-2400 MeV, thus allowing us to systematize quark-antiquark states in the (n,M^2) and (J,M^2) planes, where n and J are radial quantum number and spin of the meson with the mass M. The data point to meson trajectories in these planes being approximately linear, with a universal slope. Basing on these data and results of the recent K-matrix analysis a nonet classificati…
We study the radiative decay of $Υ$ into a scalar glueball $Υ\to γG_s$ using QCD factorization. We find that for this process the non-perturbative effects can be factorized into a matrix element well defined in non-relativistic QCD (NRQCD) and the gluon distribution amplitude. The same NRQCD matrix element appears also in leptonic decay of $Υ$ and therefore can be determined from data. In the asymptotic limit the gluon distribution amplitude is known up to a normalization constant. Using a QCD sum-rule calculation for the normalization constant, we obtain $Br(Υ\to γG_s)$ to be in the range $(1…
We study whether the pseudoscalar glueball mass in full QCD can differ from the prediction of quenched lattice calculations. Using properties of the correlator of the vacuum topological susceptibility we derive an expression for the upper bound on the QCD glueball mass. We show that the QCD pseudoscalar glueball is lighter than the pure Yang-Mills theory glueball studied in quenched lattice calculations. The mass difference between those two states is of order of $1/N_c$. The value calculated for the $0^{-+}$ QCD glueball mass can not be reconciled with any physical state observed so far in th…
We show that the newly discovered scalar meson $f_0(1500)$ at LEAR has properties compatible with the lightest scalar glueball predicted by lattice QCD and incompatible with a $\qqbar$ state. We suggest that decays of glueballs are into pairs of glueballs (including $η, η'$ or $(ππ)_S$) or by mixing with nearby $Q\bar{Q}$ states. The partial widths of $f_0(1500)$ are in accord with this hypothesis, tests of which include characteristic radiative decays to $γϕ,γω, γρ$ and the prediction of a further scalar state, $f_0'(1500 - 1800)$ which couples strongly to $K\bar{K}$, $ηη$ and $ηη'$.
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.
In the model-independent approach consisting in the immediate application to the analysis of experimental data of such general principles as analyticity and unitarity, a confirmation of the $σ$-meson at $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained 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 where the 2-channel unitarity is valid). A parameterless description of the $ππ$ background is …
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…
Masses and topological charges of the eta and eta' mesons are expressed in terms of the singlet-octet mixing angle theta. Contributions of the pseudoscalar 0- continuum are evaluated in a model independant way. Applications to the decay eta --> 3pi and to the radiative decay of vector mesons involving eta and eta' are considered. Agreement with experiment is in general good and the results quite stable for -30.5 <= theta <= -18.5
Some recent developments in the phenomenology of the lightest scalar glueball are summarised. Tools for determining 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 are presented. Two $q\bar{q} - G$ mixing schemes for $J^{PC} = 0^{++}$, inspired by the lattice, are shown to lead to similar phenomenology that may be tested at BEPC and in $γγ$ production at LEP2.
The ratios of partial widths for the decay of a glueball into two pseudoscalar mesons are calculated under the assumption that the production of light quark pairs ($u\bar u,d\bar d,s\bar s$) in soft gluon-\-induced reactions goes on within universal symmetry breaking. Parameter of the violation of flavour symmetry is fixed by the central hadron production data in high energy hadron collisions and/or by the ratios of radiative decay amplitudes $J/Ψ\to γη/γη'$ and $J/Ψ\to γϕϕ/γωω$. The ratios of coupling constants $glueball\toππ,K\bar K, ηη,ηη'$ which are calculated with this parameter coincide …
