We prove a theorem in QCD stating that in the limit of strong coupling, $g\to\infty$, the observed spectrum of glueballs in QCD is the same of a pure Yang-Mills theory, being mixing effects due to the next-to-leading order. A full effective theory for QCD is obtained and the width of the $σ$ resonance decay is straightforwardly computed. This appears as the lowest glueball state. Vacuum gluon condensate is computed that consistently support studies on the identification of this meson as a glueball.
Glueballs, an old and firm prediction of various QCD approaches (lattice QCD, bag models, AdS/QCD, effective models, etc.), have not yet been experimentally confirmed. While for glueballs below $2.6$ GeV some candidates exist, the situation for heavy glueballs (above $2.6$ GeV) is cloudy. Here, after a brief review of scalar, tensor, and pseudoscalar glueballs, we present predictions for the decays of a putative pseudotensor glueball with a lattice predicted mass of $3.04$ GeV and a putative vector glueball with a lattice predicted mass of $3.81$ GeV. Moreover, we discuss in general the width …
The widths of a glueball decay to two pions or kaons are analyzed in the pQCD framework. Our results show that the glueball ground state has small branching ratio for two-meson decay mode, which is around $10^{-2}$. The predicted values are consistent with the data of $ξ\toππ, KK$ if $ξ$ particle is a $2^{++}$ glueball. Applicability of pQCD to the glueball decay and comparison with $χ_{cJ}$ decay are also discussed.
Based on a semiclassical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the $0^{++}$ scalar glueball current is given, and the properties of the $0^{++}$ scalar glueball are studied in the framework of Gaussian sum rules. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are come into play. Instead of the usual zero-width approximation for the resonance, the Breit-Wigner form for the spectral function of the finite-width resonance i…
We compute from lattice QCD in the valence (quenched) approximation the partial decay widths of the lightest scalar glueball to pairs of pseudoscalar quark-antiquark states. These predictions and values obtained earlier for the scalar glueball's mass are in good agreement with the observed properties of $f_J(1710)$ and inconsistent with all other observed meson resonances.
In the framework of a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the $0^{++}$ scalar glueball current is given. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are taken into account as well. Instead of the usual zero-width approximation for the resonance, the Brite-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Laplace sum rules for the scalar glueball in quant…
A quasiparticle description of pure glue QCD thermodynamics at T<T_c is proposed and compared to recent lattice data. Given that a gas of glueballs with constant mass cannot quantitatively reproduce the early stages of the deconfinement phase transition, the problem is to identify a relevant mechanism leading to the observed sudden increase of the pressure, trace anomaly, etc. It is shown that the strong decrease of the gluon condensate near T_c combined with the increasing thermal width of the lightest glueballs might be the trigger of the phase transition.
We calculate the mass spectrum and the decay widths of glueballs in the flux tube model. The glueball is assumed to be a closed flux tube. The breathing motion and the rotational motion are investigated using the WKB approximation. The calculated spectra is consistent with those by lattice QCD. The decay widths are also computed using Schwinger mechanism and it is shown that they have rather large values.
Based on correction from instanton-gluon interference to correlation function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated in a family of finite-width Gaussian sum rules. In the framework of semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the instanton liquid background, the contribution arising from the the interference between instantons and the quantum gluon fields is calculated, and included in the correlation function together with pure-classical contribution from instantons and the perturbative one. The interference contribution is turned t…
Computations in the quenched approximation on the lattice predict the lightest glueball to be a scalar in the 1.5-1.8 GeV region. Here we calculate the dynamical effect the coupling to two pseudoscalars has on the mass, width and decay pattern of such a scalar glueball. These hadronic interactions allow mixing with the $q \overline q$ scalar nonet, which is largely fixed by the well-established K_0^*(1430). This non-perturbative mixing means that, if the pure gluestate has a width to two pseudoscalar channels of ~100 MeV as predicted on the lattice, the resulting hadron has a width to these ch…
Using holographic QCD based on D4-branes and D8-anti-D8-branes, we have computed couplings of glueballs to light mesons. We describe glueball decay by explicitly calculating its decay widths and branching ratios. Interestingly, while glueballs remain less well understood both theoretically and experimentally, our results are found to be consistent with the experimental data for the scalar glueball candidate f_0(1500). More generally, holographic QCD predicts that decay of any glueball to 4 $π_0$ is surpressed, and that mixing of the lightest glueball with $q\bar{q}$ mesons is small.
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…
We present a new calculation of the mass and width of the exotic $0^{--}$ glueball in the framework of the QCD sum rules. We next construct a new current which couples to a pure $0^{--}$ gluon state and derive consistent and stable sum rules. A previously used current in this approach was shown to be inconsistent. We obtain for this state a mass $M_G=6.3^{+0.8}_{-1.1}$ GeV and an upper limit for the total width $Γ_G\leq 235$ MeV. These values can be used as an important guide for the experimental search of this exotic state. We argue that the mixing of this glueball state with $0^{--}$ tetraqu…
We investigate the two-meson decay modes for $f_0(1500)$. In this calculation we consider this resonance as a glueball. The Fock-Tani formalism is introduced to calculate the decay width.
We estimate the I=0 scalar meson sigma/f_0(600) parameters from pi-pi and gamma-gamma scattering data below 700 MeV using an improved analytic K-matrix model. A fit of the hadronic data gives a complex pole mass M_sigma= 422-i290 MeV, while simultaneous best fits of the gamma-gamma to pi+pi-, pi0pi0 data give a direct width of (0.13+-0.05)keV, a rescattering component of (2.7+-0.4)keV and a total (direct+rescattering) width of (3.9+-0.6)keV. "Running" these results to the physical real axis, the small "direct" gamma-gamma and the large hadronic widths at the "on-shell" mass are compatible with…
Matrix elements of the form $ <0| Tr \; g^{2}GG |G> $ are calculated using the lattice QCD Monte Carlo method. Here, $|G>$ is a glueball state with quantum numbers $ 0^{++}$, $ 2^{++}$, $ 0^{-+}$ and $G$ is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the $12^{4}$ and $14^{4}$ lattices at $β= 5.9 $ and $5.96$ respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the non-perturbative matrix elements needed in t…
We study the decay of a pseudovector glueball with quantum numbers $J^{PC}=1^{+-}$, the lightest glueball with spin different from zero or two, in the top-down holographic Witten-Sakai-Sugimoto model. This glueball is dual to the string-theoretic Kalb-Ramond tensor field, which completely fixes all its couplings by gauge invariance and $D$-brane anomaly inflow. The dominant decay channels are determined by a Chern-Simons-like action for the flavor branes; couplings from the Dirac-Born-Infeld action turn out to be subdominant. While the resulting width is parametrically of order $N_c^{-2}λ^{-1}…
We predict glueball/oddball resonances lying on the pomeron/odderon trajectories. A simple new form of the trajectories, with threshold and asymptotic behaviour required by analyticity and unitarity, is proposed. The parameters of these (pomeron and odderon) trajectories are fitted to the data on high-energy elastic proton-proton scattering. The fitted trajectories are extrapolated to the resonance region to predict masses and widths of glueballs and oddballs. The (pomeron and odderon) trajectories may be used to calculate processes of central exclusive diffraction (CED).
We calculate two- and three-body decays of the (lightest) vector glueball into (pseudo)scalar, (axial-)vector, as well as pseudovector and excited vector mesons\textbf{ }in the framework of a model of QCD. While absolute values of widths cannot be predicted because the corresponding coupling constants are unknown, some interesting branching ratios can be evaluated\textbf{ }by setting the mass of the yet hypothetical vector glueball to $3.8$ GeV as predicted by quenched Lattice QCD\textbf{.} We find that the decay mode $ωππ$ should be one of the largest (both through the decay chain $\mathcal{O…
The ratios of partial widths for the decay of a glueball into two pseudoscalar mesons are calculated under the assumption that the production of light quark pairs ($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 …
We present a two-flavour linear sigma model with global chiral symmetry and (axial-)vector mesons as well as an additional glueball degree of freedom. We study the structure of the well-established scalar resonances f0(1370) and f0(1500): by a fit to experimentally known decay widths we find that f0(1370) is predominantly a \bar{q}q state and f0(1500) is predominantly a glueball state. The overall phenomenology of these two resonances can be well described. Other assignments for our mixed quarkonium-glueball states are also tested, but turn out to be in worse agreement with the phenomenology. …
Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violat…
An effective meson Lagrangian including a scalar glueball is constructed on the base of $U(3)\times U(3)$ chiral symmetry. The glueball is introduced into the meson Lagrangian by using the principle of scale invariance of an effective Lagrangian and the dilaton model. The singlet-octet mixing of scalar meson states is described by means of 't Hooft interaction. The contribution of the scalar and pseudoscalar anomalies into the breaking of scale invariance is taken into account. The mixing of quarkonia with the glueball is described. The mass spectrum of scalar mesons together with the glueball…
We use the holographic AdS/QCD soft-wall model to investigate the spectrum of scalar glueballs in a finite temperature plasma. In this model, glueballs are described by a massless scalar field in an AdS_5 black hole with a dilaton soft-wall background. Using AdS/CFT prescriptions, we compute the boundary retarded Green's function. The corresponding thermal spectral function shows quasiparticle peaks at low temperatures. We also compute the quasinormal modes of the scalar field in the soft-wall black hole geometry. The temperature and momentum dependences of these modes are analyzed. The positi…
We study scalar glueballs and scalar mesons at $T \neq 0$ in the soft wall holographic QCD model. We find that, using the Anti-de Sitter-Black Hole metric for all values of the temperature, the masses of the hadronic states decrease and the widths become broader when T increases, and there are temperatures for which the states disappear from the scalar glueball and scalar meson spectral functions. However, the values of the temperatures in correspondence of which such phenomena occur are low, of the order of 40-60 MeV. A consistent holographic description of in-medium effects on hadron propert…
Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the a…
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…
We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.
We analyze the f_0(1810) state recently observed by the BES collaboration via radiative J/ψdecay to a resonant ϕωspectrum and confront it with DM2 data and glueball theory. The DM2 group only measured ωωdecays and reported a pseudoscalar but no scalar resonance in this mass region. A rescattering mechanism from the open flavored KKbar decay channel is considered to explain why the resonance is only seen in the flavor asymmetric ωϕbranch along with a discussion of positive C parity charmonia decays to strengthen the case for preferred open flavor glueball decays. We also calculate the total glu…
We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the $ρ$ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scala…
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…
The spectrum of glueballs in 2+1 dimensions is calculated within an extended class of Isgur-Paton flux tube models and is compared to lattice calculations of the low-lying SU(N) glueball mass spectra. Our modifications of the model include a string curvature term and different ways of dealing with the flux tube width. We find that the generic model is remarkably successful at reproducing the positive charge conjugation, C=+, sector of the spectrum. The only large (and robust) discrepancy involves the 0-+ state. This raises the interesting possibility that the lattice spin identification is mis…
Central exclusive diffractive (CED) production of meson resonances potentially is a factory producing new particles, in particular a glueball. The produced resonances lie in trajectories with vacuum quantum numbers, essentially on the pomeron trajectory. A tower of resonance recurrences, the production cross section and the resonances widths are predicted. A new feature is the form of the non-linear pomeron trajectory, producing resonances (glueballs) with increasing widths. At LHC energies, in the nearly forward direction the $t$-channel both in elastic, single or double diffraction dissociat…
We present a detailed study of the interactions among scalar and pseudoscalar mesons and glueballs within the framework of the generalized linear sigma model in the SU(3) flavor limit. The basis of our approach is to develop a global understanding of light scalar and pseudoscalar mesons (up to around 2 GeV) and thereby explore the underlying mixings among composite quark matter fields and glueballs. The chiral sector of the Lagrangian is formulated in terms of two chiral nonets representing quark-antiquarks and tetraquarks (in the leading order, this sector contains terms with eight or fewer n…
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.
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…
Basing on the latest results of the PNPI (Gatchina) and QM&W College (London) groups, I discuss systematics of the IJ^{PC} q anti-q states in terms of trajectories on the (n,M^2) plane, where n is the radial quantum number and M is its mass. In the scalar sector, which is the most interesting because of the presence of extra states with respect to the q anti-q systematics, I discuss: 1) the results of the K-matrix analysis of the spectra pi-pi, pi-pi-pi-pi, K anti-K, eta-eta, eta-eta', pi-eta and characteristics of the resonances in the scalar sector, 2) q anti-q nonet classification of scalar…
We present a chiral effective model which exhibits all the known symmetry features of the QCD Lagrangian. The extended Linear Sigma Model (eLSM) includes (pseudo-)scalar and (axial-) vector mesons, glueballs, and baryons. It has proven to be a useful tool to understand the nature of the low-energy resonances. It can be used to describe the masses and decay widths of the known low-energy mesons and to disentangle the complicated picture of resonances in the low-energy range. We can answer some of the open questions in the low-energy region, e.g. the resonance (f_0(1500)) is a predominantly glue…
We analyse data on pi pi and gamma gamma scattering below 700 MeV within an improved analytic K-matrix model. This model is based on an effective theory with couplings between resonances, hadrons and photons. The two-photon decay of a resonance can proceed through intermediate transition into charged hadrons (here: pi^+ pi^-) and their subsequent annihilation or through a ``direct'' transition into photons. Our analysis confirms the rather large total radiative width of the sigma/f_0(600) resonance which we find as (3.9 \pm 0.6) keV but suggests its dominance by the pi pi rescattering process.…
We calculate the decay widths of both the second and the third radial excitations of $η$ and $η'$ within the framework of $^3P_0$ model. After comparing the theoretical decay widths and decay patterns with the available experimental data of $η(1760)$, $X(1835)$, $X(2120)$ and $X(2370)$, we find that the interpretation of $η(1760)$ and $X(1835)$ as the second radial excitation of $η$ and $η'$ crucially depends on the measured mass and width of $η(1760)$, which is still controversial experimentally. We suggest that there may be sizable $p\bar{p}$ content in $X(1835)$. $X(2120)$ and $X(2370)$ can…
In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as $Γ=\frac\pi2 ATL$ where $T$ and $L$ are the tension and length of the string and $A$ is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by $Γ_i/Γ=Φ_i\exp(-2πCm_{sep}^2/T)$ where $Φ_i$ is a phase space factor, $m_{sep}$ is t…
We study the scalar glueball and vector meson spectral functions in a hot and dense medium by means of the soft-wall holographic model of QCD. Finite temperature and density effects are implemented through the AdS/RN metric. We analyse the behaviour of the hadron masses and widths in the $(T,μ)$ plane, and compare our results with the experimental ones and with other theoretical determinations.
We explore tensor mesons in AdS/QCD focusing on f2 (1270), the lightest spin-two resonance in QCD. We find that the f2 mass and the partial width for f2 -> gamma gamma are in very good agreement with data. In fact, the dimensionless ratio of these two quantities comes out within the current experimental bound. The result for this ratio depends only on Nc and Nf, and the quark and glueball content of the operator responsible for the f2; more importantly, it does not depend on chiral symmetry breaking and so is both independent of much of the arbitrariness of AdS/QCD and completely out of reach …
