Pseudoscalar Glueball Research Articles

Determination of Spin-Parity Quantum Numbers of X(2370) as 0^{-+} from J/ψ→γK_{S}^{0}K_{S}^{0}η^{'}.

Based on (10087±44)×10^{6} J/ψ events collected with the BESIII detector, a partial wave analysis of the decay J/ψ→γK_{S}^{0}K_{S}^{0}η^{'} is performed. The mass and width of the X(2370) are measured to be 2395±11(stat)_{-94}^{+26}(syst) MeV/c^{2} and 188_{-17}^{+18}(stat)_{-33}^{+124}(syst) MeV, respectively. The corresponding product branching fraction is B[J/ψ→γX(2370)]×B[X(2370)→f_{0}(980)η^{'}]×B[f_{0}(980)→K_{S}^{0}K_{S}^{0}]=(1.31±0.22(stat)_{-0.84}^{+2.85}(syst))×10^{-5}. The statistical significance of the X(2370) is greater than 11.7σ and the spin parity is determined to be 0^{-+} for the first time. The measured mass and spin parity of the X(2370) are consistent with the predictions of the lightest pseudoscalar glueball.

Branching Ratios of the Pseudoscalar Glueball and Its First Excited State

Branching Ratios of the Pseudoscalar Glueball and Its First Excited State

Radiative meson and glueball decays in the Witten-Sakai-Sugimoto model

We calculate radiative decay rates of mesons and glueballs in the top-down holographic Witten-Sakai-Sugimoto model with finite quark masses. After assessing to what extent this model agrees or disagrees with experimental data, we present its predictions for so far undetermined decay channels. Contrary to widespread expectations, we obtain sizeable two-photon widths of scalar, tensor, and pseudoscalar glueballs, suggesting in particular that the observed two-photon rate of the glueball candidate ${f}_{0}(1710)$ is not too large to permit a glueball interpretation, but could be even much higher. We also discuss the so-called exotic scalar glueball, which in the Witten-Sakai-Sugimoto model is too broad to match either of the main glueball candidates ${f}_{0}(1500)$ and ${f}_{0}(1710)$ but might be of interest with regard to the alternative scenario of the so-called fragmented scalar glueball. Employing the exotic scalar glueball for the latter, much smaller two-photon rates are predicted for the ground-state glueball despite a larger total width; relatively large two-photon rates would then apply to the excited scalar glueball described by the predominantly dilatonic scalar glueball. In either case, the resulting contributions to the muon $g\ensuremath{-}2$ from hadronic light-by-light scattering involving glueball exchanges are small compared to other single meson exchanges, of the order of $\ensuremath{\lesssim}{10}^{\ensuremath{-}12}$.

η -glueball mixing from Nf=2 lattice QCD

We perform the first lattice study on the mixing of the isoscalar pseudoscalar meson $\eta$ and the pseudoscalar glueball $G$ in the $N_f=2$ QCD at the pion mass $m_\pi\approx 350$ MeV. The $\eta$ mass is determined to be $m_\eta=714(6)(16)$ MeV. Through the Witten-Veneziano relation, this value can be matched to a mass value of $\sim 981$ MeV for the $\mathrm{SU(3)}$ counterpart of $\eta$. Based on a large gauge ensemble, the $\eta-G$ mixing energy and the mixing angle are determined to be $|x|=107(15)(2)$ MeV and $|\theta|=3.46(46)^\circ$ from the $\eta-G$ correlators that are calculated using the distillation method. We conclude that the $\eta-G$ mixing is tiny and the topology induced interaction contributes most of $\eta$ mass owing to the QCD $\mathrm{U_A(1)}$ anomaly.

Glueballs at physical pion mass* *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030300, XDPB15), the National Key Research and Development Program of China (2020YFA0406400), and the National Natural Science Foundation of China (NNSFC) under Grants ( 11935017, 12070131001) (CRC 110 by DFG and NNSFC). The computations were performed on the CAS ORISE computing environment, the

Glueballs are investigated through gluonic operators on two RBC/UKQCD gauge ensembles at the physical pion mass. The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor, and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential in the Coulomb gauge. These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions, where the ground state masses are extracted. These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point. The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.

Decay of the pseudoscalar glueball into vector, axial-vector, scalar and pseudoscalar mesons

We resume the investigation of the ground-state pseudoscalar glueball, J^{PC}=0^{-+}, by computing its two- and three-body decays into vector and axial-vector quark-antiquark meson fields additional to scalar and pseudoscalar mesons through the construction of an interaction chiral Lagrangian that produces these decays. We evaluate the branching ratio, via a parameter-free calculation, by setting the mass of the pseudoscalar glueball to 2.6 GeV as predicted by lattice QCD simulations. We duplicate the computation for the branching ratios for a pseudoscalar glueball mass 2.37 GeV which matches to the measured mass of the resonance X(2370) in the BESIII experiment. The present channels and states are potentially reached and are interesting for the running BESIII and Belle-II experiments and the planned PANDA experiment at FAIR/GSI which will be able to detect the pseudoscalar glueball within the accessible energy range.

Finite temperature 0−+ glueball spectrum from non-susy D3 brane of Type IIB string theory

Here, we calculate the pseudo-scalar glueball mass at finite temperature from the holographic QCD in 3+1 dimensions. The decoupled geometry of the non-supersymmetric (non-susy) D3 brane at finite temperature, which is the solution of type IIB supergravity, is considered as the dual theory of QCD. We calculate the mass spectrum from the axion fluctuation in this gravity background using WKB approximations. Approximating the WKB equation for various orders of mass, we derive the analytical expressions of the mass spectrum of 0−+ at finite temperature. Finally, we evaluate the masses of the ground state and the first excited state of the pseudo-scalar glueball numerically, as, m−+=2.5 GeV and m−+⁎=3.8 GeV respectively, from the complete WKB equation. The mass of a given state is found to decrease with increasing temperature and becomes zero at confinement-deconfinement transition temperature which is consistent with the idea of confinement and also matches with some recent lattice results. From this temperature variation, the QCD transition point is found to be about 186 MeV.

The glueball content of ηc

We carry out the first lattice QCD derivation of the mixing energy and the mixing angle of the pseudoscalar charmonium and glueball on two gauge ensembles with Nf=2 degenerate dynamical charm quarks. The mixing energy is determined to be 49(6) MeV on the near physical charm ensemble, which seems insensitive to charm quark mass. By the assumption that X(2370) is predominantly a pseudoscalar glueball, the mixing angle is determined to be approximately 4.6(6)∘, which results in a +3.9(9) MeV mass shift of the ground state pseudoscalar charmonium. In the mean time, the mixing can raise the total width of the pseudoscalar charmonium by 7.2(8) MeV, which explains to some extent the relative large total width of the ηc meson. As a result, the branching fraction of ηc→γγ can be understood in this cc¯-glueball mixing framework. On the other hand, the possible discrepancy of the theoretical predictions and the experimental results of the partial width of J/ψ→γηc cannot be alleviated by the cc¯-glueball mixing picture yet, which demands future precise experimental measurements of this partial width.

Glueballs in Radiative J/ψ Decays

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 mainlyoctet resonances in SU(3). The yield of resonances showed a striking peak with properties expected from a scalar glueball: • G0(1865) is produced abundantly in radiative J/ψ decays above a very low background. Its mass is 1σ compatible with the mass calculated in unquenched lattice QCD, and the yield is 1.6σ compatible with the yield calculated in lattice QCD. • The decay analysis of the scalar isoscalar mesons shows that the assignment of mesons to mainly-octet and mainly-singlet states is correct. Even the production of mainly-octet scalar mesons - which should be forbidden in radiative J/ψ decays - peaks at 1865 MeV. The decay analysis requires a small glueball content in the flavor wave function of several scalar resonances. The glueball content as a function of the mass shows a peak compatible with the peak in the yield of scalar isoscalar mesons. The sum of the fractional glueball contributions is compatible with one. • In the reaction Bs → J/ψ + K+K− reported by the LHCb collaboration, a primary ss̄ couples to mesons having a strong coupling to K+K−. Two peaks in the K+K− mass spectrum are seen due to ϕ(1020) and f′2(1525), but there is little evidence for the f0(1710) or other high-mass scalar mesons coupling strongly to KK̄. High-mass scalar mesons are strongly produced by two initial-state gluons but not by an ss̄ pair in the initial state. They must have sizable glueball fractions! • 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 tensor glueballs a long time ago. The structure - and further tensor resonances observed in radiative J/ψ decays - are tentatively interpreted as tensor glueball. • In J/ψ decays into γπ0π0η′ several resonances are reported. The possibility is discussed that the pseudoscalar glueball might be hidden in these data.

Pseudoscalars and the η′ in the holographic soft-wall model

Pseudoscalar mesons and glueballs are studied in a model based on the AdS/QCD correspondence. Glueball masses are obtained in the pure-gauge case, while the mixing between pseudoscalar glueballs and singlet pseudoscalar mesons produces the expected mass of the η′ meson. The topological susceptibility is computed as a function of the quark mass. The model reproduces partial conservation of axial current, the anomaly equation, and the Witten-Veneziano relation.

Confinement and Pseudoscalar Glueball Spectrum in the 2 + 1D QCD-Like Theory from the Non-Susy D2 Brane

We study two important properties of 2+1D QCD, namely confinement and Pseudoscalar glueball spectrum, using holographic approach. The confined state of the bounded quark-antiquark pair occurs in the self-coupling dominated nonperturbative regime, where the free gluons form the bound states, known as glueballs. The gauge theory corresponding to low energy decoupled geometry of isotropic non-supersymmetric D2 brane, which is again similar to the 2+1D YM theory, has been taken into account but in this case the coupling constant is found to vary with the energy scale. At BPS limit, this theory reduces to supersymmetric YM theory. We have considered NG action of a test string and calculate the potential of such confined state located on the boundary. The QCD flux tube tension for large quark-antiquark separation is observed to be a monotonically increasing function of running coupling. The mass spectrum of Pseudoscalar glueball is evaluated numerically from the fluctuations of the axion in the gravity theory using WKB approximation. This produces the mass to be related to the string tension and the levels of the first three energy states. The various results that we obtained quite match with those previously studied through the lattice approach.

Quenched glueball spectrum from functional equations

We give an overview of results for the quenched glueball spectrum from two-body bound state equations based on the 3PI effective action. The setup, which uses self-consistently calculated two- and three-point functions as input, is completely self-contained and does not have any free parameters except for the coupling. The results for JPC = 0±+, 2±+, 3±+, 4±+ are in good agreement with recent lattice results where available. For the pseudoscalar glueball, we present first results from a two-loop complete calculation, rendering also the bound state calculation fully self-consistent.

Dispersive analysis of glueball masses

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 $\rho$ 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 scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the $f_0(500)$ and $f_0(980)$ ($\eta$ ad $\eta'$) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ ($\eta(1760)$) mesons are the glue-rich states. We also predict the topological susceptability $\chi_t^{1/4}=75$-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE.

Spinless mesons and glueballs mixing patterns in SU(3) flavor limit

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 number of quark or antiquark lines). The Lagrangian also contains a sector that represents scalar and pseudoscalar glueballs and their interactions with the matter chiral fields, in a manner that the axial and trace anomalies of QCD are exactly realized. In this construct, the model has two scalar octets and two pseudoscalar octets (each a linear combination of two- and four-quark components), as well as three scalar SU(3) singlets and three pseudoscalar SU(3) singlets (each a linear combination of two- and four-quark components as well as a glueball component). With the inputs of the experimental masses of a0(980), a0(1450), and the masses of π(137), π(1300) and their decay constants, we perform an extensive numerical simulation to determine the boundaries of the parameter space of the model. We further incorporate experimental data on the mass spectrum of eta states as well as on several decay widths and decay ratios of f0 states to zoom in on the parameter space and make predictions for the substructure of pseudoscalar and scalar SU(3) octets and singlets as well as for the pseudoscalar and scalar glueball masses. We find the scalar and pseudoscalar glueball masses around 1.6 and 2.0 GeV, respectively.

Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball

We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the $\pi^0,\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $\langle 0 |G\tilde{G} |\gamma\gamma^*(q^2) \rangle$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The duality between the axial and the vector channels was observed: the values of duality intervals and mixing parameters in the axial channel were related to vector resonances' masses and residues. The possibility of a light pseudoscalar glueball-like state is conjectured.

Confinement and pseudoscalar glueball spectrum in the 2+1D QCD-like theory from the non-SUSY D2 brane

Here we study two important properties of $2+1$ dimensional QCD -- confinement and pseudoscalar glueball spectrum -- with holographic approach. We consider the low energy decoupled geometry of the isotropic non-susy D$2$ brane. We find the corresponding gauge theory is similar to the $2+1$-dim Yang-Mills theory with the running coupling $\lambda^2$. At the extremal limit (i.e. BPS limit), this gauge theory reduces to the super-YM theory. From the Nambu-Goto action of a test string, the potential of a \qq pair located on the boundary is calculated. At large \qq separation it gives the tension $\sigma$ of the QCD flux-tube. The parametric dependencies of $\sigma$ is shown pictorially. It is found that $\sigma$ is a monotonically increasing function of the effective coupling $\lambda^2$. In comparison, $\sqrt{\sigma}/g_\text{YM}^2N_c$ is found to match accurately with the previous results. In the next part, we consider fluctuation of the axion field in the aforementioned gravity background. From the linearized field equation of the fluctuation we calculate the mass spectrum of $0^{-+}$ numerically using the WKB approximation. The pseudoscalar mass is found to be related to the string tension approximately as $M_{0^{-+}}/\sqrt{\sigma}\approx 3(n+2)$ for first three energy states, $n=0,\,1,\,2$.

Spectrum of scalar and pseudoscalar glueballs from functional methods

We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang–Mills theory using a parameter-free fully self-contained truncation of Dyson–Schwinger and Bethe–Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of 1.9,text {GeV} and 2.6,text {GeV} for the scalar and pseudoscalar glueballs, respectively, and 2.6,text {GeV} and 3.9,text {GeV} for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict masses for the second excited states at 3.7,text {GeV} and 4.3,text {GeV}. The quality of the results hinges crucially on the self-consistency of the employed input. The masses are independent of a specific choice for the infrared behavior of the ghost propagator providing further evidence that this only reflects a nonperturbative gauge completion.

Mass Spectrum of Pseudo-Scalar Glueballs from a Bethe–Salpeter Approach with the Rainbow–Ladder Truncation

We suggest a framework based on the rainbow approximation to the Dyson-Schwinger and Bethe-Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe-Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson-Schwinger equations is analysed in Landau gauge. Both, the Bete-Salpeter and Dyson-Schwinger equations, are solved numerically within the same rainbow-ladder truncation with the same effective parameters which ensure consistency of the approach. We found that with a set of parameters, which provides a good description of the lattice data within the Dyson-Schwinger approach, the solutions of the Bethe Salpeter equation for the pseudo-scalar glueballs exhibit a rich mass spectrum which also includes the ground and excited states predicted by lattice calculations. The obtained mass spectrum contains also several intermediate excitations beyond the lattice approaches. The partial Bethe-Salpeter amplitudes of the pseudo-scalar glueballs are presented as well.

Gluon-pair-creation production model of strong interaction vertices * * Supported in part by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100) and the National Natural Science Foundation of China (NSFC) (11975236, 11635009)

By studying the exclusive decay to double glueballs, we introduce a model to phenomenologically mimic the gluon-pair-vacuum interaction vertices, namely the model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly , , and processes. Among them and are well-known scalars possessing large glue components, while is a potential candidate for a pseudoscalar glueball. The preliminary calculation results indicate that these processes are marginally accessible in the presently running experiments BES III, BELLE II, and LHCb.

Witten-Veneziano mechanism and pseudoscalar glueball-meson mixing in holographic QCD

We revisit the $U(1)_A$ anomaly in the holographic model of low-energy QCD by Witten, Sakai, and Sugimoto, presenting a new and direct derivation of the Witten-Veneziano mechanism for generating the mass of the $\eta'$ through an anomalous mixing of the Ramond-Ramond $C_1$ field with the singlet component of the pseudoscalar mesons. The latter turns out to have a kinetic mixing with the normalizable modes of the $C_1$ field representing pseudoscalar glueballs, yielding additional vertices for their production and their decay that dominate over those of the unmixed case considered previously in the Witten-Sakai-Sugimoto model. The leading channel is predicted to be decay into two vector mesons, followed in importance by decay into three pseudoscalar mesons. The issue of production of pseudoscalar glueballs in radiative $J/\psi$ decays and in double diffractive processes is also discussed briefly.