Scalar Glueball Mass Research Articles

A comparative lattice analysis of SU(2) dark glueballs* *Supported in part by the Natural Science Foundation of China (12125503, 12335003), and the Natural Science Foundation of Shandong Province, China (ZR2022ZD26)

We study the mass and scattering cross section of glueballs as dark matter candidates using lattice simulations. We employ both naive and improved gauge actions in dimensions with several β values, and we adopt both the traditional Monte Carlo method and flow-based model based on machine learning techniques to generate lattice configurations. The mass of a dark scalar glueball with and the Nambu-Bethe-Salpeter wave function are calculated. Using a coupling constant of as an illustration, we compare the dark glueball mass calculated from the configurations generated from the two methods. While consistent results can be achieved, the two methods demonstrate distinct advantages. Using the Runge-Kutta method, we extract the glueball interaction potential and two-body scattering cross section. From the observational constraints, we obtain the lower bound of the mass of scalar glueballs as candidates of dark matter.

Phenomenology of strong interactions: towards an effective theory for low energy QCD

In this paper, we develop models applicable to phenomenological particle physics by using the string analogy of particles. These theories can be used to investigate the phenomenology of confinement, deconfinement, chiral condensate, QGP phase transitions, and even the evolution of the early universe. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, QCD vacuum, and color superconductivity can also be investigated in these model frameworks. We use one of the models to describe the phenomenon of color confinement among glueballs at the end of the paper. The models are built based on the Dirac–Born–Infeld (DBI) action modified for open strings with their endpoints on a Dp-brane or brane–anti-brane at a tachyonic vacuum.

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.

Spectrum of trace deformed Yang-Mills theories

In this paper we study, by means of numerical simulations, the behaviour of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on $ \mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. We find, by investigating both $SU(3)$ and $SU(4)$ pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size $l$ acquires a pleateau for large values of the strength $h$, with values which are compatible with a $1/l$ behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-$N$ predictions.

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.

Confinement of Fermions in Tachyon Matter at Finite Temperature

We study a phenomenological model that mimics the characteristics of QCD theory at finite temperature. The model involves fermions coupled with a modified Abelian gauge field in a tachyon matter. It reproduces some important QCD features such as confinement, deconfinement, chiral symmetry, and quark-gluon-plasma (QGP) phase transitions. The study may shed light on both light and heavy quark potentials and their string tensions. Flux tube and Cornell potentials are developed depending on the regime under consideration. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, and gluon and chiral condensates are exploited as well. The study is focused on two possible regimes, the ultraviolet (UV) and the infrared (IR) regimes.

Color dependence of tensor and scalar glueball masses in Yang-Mills theories

We report the masses of the lightest spin-0 and spin-2 glueballs obtained in an extensive lattice study of the continuum and infinite volume limits of $Sp(N_c)$ gauge theories for $N_c=2,4,6,8$. We also extrapolate the combined results towards the large-$N_c$ limit. We compute the ratio of scalar and tensor masses, and observe evidence that this ratio is independent of $N_{c}$. Other lattice studies of Yang-Mills theories at the same space-time dimension provide a compatible ratio. We further compare these results to various analytical ones and discuss them in view of symmetry-based arguments related to the breaking of scale invariance in the underlying dynamics, showing that a constant ratio might emerge in a scenario in which the $0^{++}$ glueball is interpreted as a dilaton state.

Mesons and Glueballs, the Strong Effective Coupling within Analytic Confinement

The phenomena of hadron mass generating, strong running coupling and radiative transitions of charmonium excited states have been studied in the framework of a relativistic field model with analytic confinement. A meson mass equation is derived and a specific new behavior of the mass-dependent strong coupling $$\mathop {\bar {\alpha }}\nolimits_s $$ is revealed in the time-like region. A new infrared fixed point $$\mathop {\bar {\alpha }}\nolimits_s (0) = 1.032$$ has been found at origin. Independent and new estimates on the scalar glueball mass, radius and gluon condensate value have been performed. The spectrum of conventional mesons have been calculated by introducing a minimal set of parameters with relative errors less than 1.8 percent compared to the latest data. Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have also been performed. Partial decay widths of the dominant radiative transitions of the charmonium orbital excitations have been estimated with reasonable accuracy.

Strong Effective Coupling, Meson Ground States, and Glueball within Analytic Confinement

The phenomena of strong running coupling and hadron mass generating have been studied in the framework of a QCD-inspired relativistic model of quark-gluon interaction with infrared-confined propagators. We derived a meson mass equation and revealed a specific new behavior of the mass-dependent strong coupling α ^ s ( M ) defined in the time-like region. A new infrared freezing point α ^ s ( 0 ) = 1.03198 at origin has been found and it did not depend on the confinement scale Λ > 0 . Independent and new estimates on the scalar glueball mass, ‘radius’ and gluon condensate value have been performed. The spectrum of conventional mesons have been calculated by introducing a minimal set of parameters: the masses of constituent quarks and Λ . The obtained values are in good agreement with the latest experimental data with relative errors less than 1.8 percent. Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have been performed.

Comment on scalar glueball mass

We study the interaction of scalar glueball with quark–antiquark and four-quark spinless meson fields within the framework of a generalized linear sigma model in which the trace anomaly of QCD is exactly realized. To determine the pure scalar glueball mass (mh), we consider the decoupling limit in which the scalar glueball decouples from the meson fields. We find the exact relationship mh=2h0 where h0 is the vacuum expectation value of the scalar glueball field independent of the properties of the framework used.

Charmonium radiative transitions, meson and glueball particle properties with the effective strong coupling

The particle properties of conventional mesons and scalar glueball, radiative transitions of charmonium excited states χcJ (J = 0, 1, 2) are studied in the framework of relativistic quark models with infrared confinement by taking into account the mass dependence of the effective strong coupling. A specific behaviour of the mass-dependent strong coupling with a freezing point αs (0) = 1.032 has been revealed. The spectrum and leptonic (weak) decay constants of conventional mesons have been calculated in good agreement with the latest experimental data. New estimates on the scalar glueball mass, ’radius’ and gluon condensate value have been obtained. Dominant radiative transitions of the charmonium orbital excitations χcJ → J/ψ + γ have been studied and the partial decay widths have been estimated with reasonable accuracy.

Dynamical AdS/Yang-Mills model

The AdS/CFT correspondence has provided new and useful insights into the nonperturbative regime of strongly coupled gauge theories. We construct a class of models meant to mimic Yang-Mills theory using the superpotential method. This method allows us to efficiently address the problem of solving all the equations of motion. The conformal symmetry is broken in the infrared by a dilaton field. Using a five-dimensional action we calculate the mass spectrum of scalar glueballs. This spectrum contains a tachyon, indicating an instability in the theory. We stabilize the theory by introducing a cosmological constant in the bulk and a pair of 3-branes, as in the Randall-Sundrum model. The scalar glueball masses computed by lattice gauge theory are then described very well by just a few parameters. Prospects for extending the model to other spins and parities and to finite temperature are considered.

Morbidity of Pediatric Obstructive Sleep Apnea in Children: Myth, Reality, or Hidden Iceberg?

We study the interaction of scalar glueball with quark–antiquark and four-quark spinless meson fields within the framework of a generalized linear sigma model in which the trace anomaly of QCD is exactly realized. To determine the pure scalar glueball mass (mh), we consider the decoupling limit in which the scalar glueball decouples from the meson fields. We find the exact relationship mh=2h0 where h0 is the vacuum expectation value of the scalar glueball field independent of the properties of the framework used.

Blockspin renormalization-group study of color confinement due to violation of the non-Abelian Bianchi identity

Block-spin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VMABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce various techniques smoothing the vacuum. The effective action can be determined by adopting the inverse Monte-Carlo method. The coupling constants $F(i)$ of the effective action depend on the coupling of the lattice action $\beta$ and the number of the blocking step $n$. But it is found that $F(i)$ satisfy a beautiful scaling, that is, they are a function of the product $b=na(\beta)$ alone for lattice coupling constants $3.0\le\beta\le3.9$ and the steps of blocking $1\le n\le 12$. The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since $a\to 0$ as $n\to\infty$ for fixed $b$. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum. The infrared monopole action can be transformed into that of the string model. The physical string tension and the lowest glueball mass can be evaluated \textit{analytically} by the strong-coupling expansion of the string model. We get $\sqrt{\sigma}\simeq 1.3\sqrt{\sigma_{phys}}$ for $b\ge 1.0\ \ (\sigma_{phys}^{-1/2})$, whereas the scalar glueball mass is kept to be near $M(0^{++})\sim 3.7\sqrt{\sigma_{phys}}$. Also we can almost reproduce \textit{analytically} the scaling function of the squared monopole density determined numerically for large $b$ region $b>1.2\ (\sigma_{phys}^{-1/2})$.

Ultralight glueballs in Quark-Gluon Plasma

We consider the dynamics of the scalar and pseudoscalar glueballs in the Quark-Gluon Plasma (QGP). By using the instanton model for the QCD vacuum we give the arguments that the nonperturbative gluon-gluon interaction is qualitatively different in the confinement and deconfinement phases. Based on this observation it is shown that above $T_c$ the values of the scalar and pseudoscalar glueball masses might be very small. The estimation of the temperature of scale invariance restoration, at which the scalar glueball becomes massless, is given. We also discuss the Bose-Einstein condensation of the glueballs and the superfluidity of the glueball matter in QGP.

Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory

By relating the functional averages of a generic scalar operator in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. Numerical results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.

Renormalization group summation of Laplace QCD sum rules for scalar gluon currents

We employ renormalization group (RG) summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter $\mu^2$ once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.

Proximity off0(1500)andf0(1710)to the scalar glueball

Within a nonlinear chiral Lagrangian framework, the underlying mixings among quark-antiquark, four-quark and glue components of $f_0(1500)$ and $f_0(1710)$ are studied in a global picture that includes all isosinglet scalar mesons below 2 GeV. The quark components are introduced in the Lagrangian in terms of two separate nonets (a quark-antiquark nonet and a four-quark nonet) which can mix with each other and with a scalar glueball. The free parameters of the Lagrangian are studied by a simultaneous fit to more than 20 experimental data and constraints on the mass spectrum, decay widths, and decay ratios of the isosinglet scalars below 2 GeV. Moreover, constraints on the mass spectrum and decay widths of isodoublet and isovector scalars below 2 GeV as well as pion-pion scattering amplitude are also taken into account. The insights gained in this global picture, due to the complexities of the mixings as well as the experimental uncertainties, are mainly qualitative but are relatively robust, and reveal that the lowest scalar glueball hides between $f_0(1500)$ and $f_0(1710)$, resulting in a considerable mixing with various quark components of these two states. The overall current experimental and theoretical uncertainties do not allow to pin down the exact glue components of isosinglet states, nevertheless it is shown that the $f_0(1500)$ and $f_0(1710)$ have the highest glue component. While this global study does not allow precision predictions for each individual state, it provides useful "family" correlations among the isosinglet states that are found insightful in probing the substructure of all scalars, in general, and the isosinglets, in particular. The overall estimate of the scalar glueball mass is found to be $1.58 \pm 0.18$ GeV.

Notes on theta dependence in holographic Yang-Mills

Effects of the theta parameter are studied in Witten's model of holographic 4d Yang-Mills, where theta is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the theta parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole (T, theta) phase diagram - and the entanglement entropy. A simple rule is provided to derive the theta corrections to (at least) all the CP-neutral observables of the model. Some of the observables we consider can and have been in fact studied in pure 4d Yang-Mills on the lattice. In that framework the results, obtained in the small theta regime, are given up to very few powers of theta^2. The corresponding holographic results agree qualitatively with available lattice data and signal an overall mass scale reduction by theta. Moreover, being exact in theta, they provide a benchmark for higher order corrections in Yang-Mills.

Open boundary condition, Wilson flow and the scalar glueball mass

A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV ≤ $ \frac{1}{a} $ ≤ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV ≤ $ \frac{1}{a} $ ≤ 5.7 GeV.