Glueball Mass Spectrum Research Articles

Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

We review the current status of the long-term programme of numerical investigation of Sp(2N) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the Sp(2N) Yang–Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on Sp(4), and summarise the numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. We also describe our approach to open access.

Gluonic nature of the newly observed state X(2600)

Motivated by the newly observed resonance $X(2600)$ by BESIII Collaboration, we examine the trigluon glueball interpretation for it in the framework of QCD sum rules. We evaluate the mass spectra of the trigluon glueballs with quantum numbers $0^{-+}$ and $2^{-+}$ up to dimension 8 condensate in the operator product expansion. Our numerical results indicate that the mass of the $2^{-+}$ trigluon glueball is about $2.66\pm 0.06$ GeV, which is consistent with the mass of the X(2600) within the uncertainties, while $0^{-+}$ has a mass of $2.01\pm0.14$ GeV. The possible decay channels of the $2^{-+}$ state are analyzed, which are crucial in decoding $X(2600)$'s internal structure and are hopefully measurable in BESIII, BEllEII, PANDA, and LHCb experiments.

Glueballs and strings in Sp(2N) Yang-Mills theories

Motivated in part by the pseudo-Nambu Goldstone boson mechanism of electroweak symmetry breaking in composite Higgs models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-$N$ extrapolation, we perform lattice studies of the Yang-Mills theories with $Sp(2N)$ gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate two-point correlation functions of operators organized as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results for $N=1$, 2, 3, 4, combine them with data previously obtained for $N=2$, and extrapolate toward $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We confirm explicitly the expectation that, as already known for $N=1$, 2 also for $N=3$, 4 a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-$N$ limit. We find agreement with the known values of the mass of the ${0}^{++}$, ${0}^{++*}$, and ${2}^{++}$ glueballs obtained taking the large-$N$ limit in the $SU(N)$ groups. In addition, we determine for the first time the mass of some heavier glueball states at finite $N$ in $Sp(2N)$ and extrapolate the results toward $N\ensuremath{\rightarrow}+\ensuremath{\infty}$ taking the limit in the latter groups. Since the large-$N$ limit of $Sp(2N)$ is the same as in $SU(N)$, our results are relevant also for the study of QCD-like theories.

Odd-spin glueballs, AdS/QCD and information entropy

Odd-spin glueballs in the dynamical AdS/QCD model are scrutinized, in the paradigm of the configurational entropy (CE). Configurational-entropic Regge trajectories, that relate the CE underlying odd-spin glueballs to their mass spectra and spin, are then engendered. They predict the mass spectra of odd-spin glueballs, besides pointing towards the configurational stability of odd-spin glueball resonances. The exponential modified dilaton with logarithmic anomalous dimensions comprises the most suitable choice to derive the mass spectra of odd-spin glueballs, compatible to lattice QCD. It is then used in a hybrid paradigm that takes both lattice QCD and the AdS/QCD correspondence into account.

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.

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.

Higgs compositeness in Sp(2N) gauge theories — The pure gauge model

As a first step in the study of Sp(2N) composite Higgs models, we obtained a set of novel numerical results for the pure gauge Sp(4) lattice theory in 3+1 space-time dimensions. Results for the continuum extrapolations of the string tension and the glueball mass spectrum are presented and their values are compared with the same quantities in neighbouring SU(N) models.

Theta Dependence in Yang-Mills from Holography

In this contribution we review how holographic tools can be used to study the dependence on the CP-breaking θ parameter of various observables in a large Nc Yang-Mills model. Relevant examples are the ground-state energy density, the string tension, the glueball mass spectrum and the critical temperature for deconfinement. These observables have been also studied, in the small θ regime and up to very few powers of θ 2 , in pure Yang-Mills on the Lattice. The holographic results qualitatively agree with available Lattice data and, being exact in θ , provide benchmarks for higher order corrections.

Glueball spectrum in a gauge theory with two dynamical scales

We investigate the glueball spectrum of a strongly coupled gauge theory with two dynamical scales. The main tool is the use of the gauge/gravity duality. The model we study has a known graviational dual, which arises from a type IIB D-brane configuration. It exhibits two dynamical scales, separated by a nearly conformal region. Thus, it is of great interest for the study of walking in gauge theories. By using the gravitational description, we are able to compute analytically the glueball mass spectrum in a certain range of the parameter space of the theory. Within that range, we do not find a light state that could be associated with a slight breaking of conformal invariance. Finally, we show that in this model there can be an order of magnitude hierarchy between the scale of confinement, given by the lowest glueball mass, and the scale of chiral symmetry breaking, determined by the lowest vector-meson mass.

Gluons in glueballs: Spin or helicity?

In the past decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically noncovariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show, in particular, that this helicity formalism exactly reproduces the ${J}^{PC}$ numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.

Gravity multiplet on KS and BB backgrounds

In this paper we study the spectra of glueballs on the Klebanov-Strassler background and its extension to the baryonic branch. We numerically calculate the mass spectrum of glueballs from the spin 2 ``gravity'' multiplet, which contains the traceless part of the stress-energy tensor and the transverse part of the U(1) R-current. The mass spectra of the corresponding fluctuations in supergravity coincide due to supersymmetry, which is manifest in the effective five-dimensional theory through a Supersymmetric Quantum Mechanics transformation. We show that the glueball spectra grow as m^2 ~ Un^2 for large values of the baryonic branch parameter U.

GLUEBALL MASSES FROM ADS6 GRAVITY THEORY

In view of the general holographic principle between gauge theories and gravity, We calculate the mass spectra of several typical QCD4 glueballs in term of AdS 6 AdS -Schwarzschild black hole metric of Einstein gravity theory. The obtained mass spectra are numerically in consistent with those from the AdS 7 × S 4 black hole metric of the 11-dimensional supergravity. Besides, by separating the thermal circle from the extra dimensions, we find a novel exact D p-brane solution of Type IIB supergravity, which might provide a scenario for studying the non-perturbative dynamics of QCD4 from the perspective of Type IIB supergravity.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

Glueball mass spectra for supergravity duals of noncommutative gauge theories

We derive the glueball masses in noncommutative super Yang--Mills theories in four dimensions via the dual supergravity description. The spectrum of glueball masses is discrete due to the noncommutativity and the glueball masses are proportional to the noncommutativity parameter with dimension of length. The mass spectrum in the WKB approximation closely agrees with the mass spectrum in finite temperature Yang--Mills theory.

Bulk dynamics in confining gauge theories

We consider gauge/string duality (in the supergravity approximation) for confining gauge theories. The system under scrutiny is a 5-dimensional consistent truncation of type IIB supergravity obtained using the Papadopoulos–Tseytlin ansatz with boundary momentum added. We develop a gauge-invariant and sigma-model-covariant approach to the dynamics of 5-dimensional bulk fluctuations. For the Maldacena–Nuñez subsystem, we study glueball mass spectra. For the Klebanov–Strassler subsystem, we compute the linearized equations of motion for the 7-scalar system, and show that a 3-scalar sector containing the scalar dual to the gluino bilinear decouples in the UV. We solve the fluctuation equations exactly in the “moderate UV” approximation and check this approximation numerically. Our results demonstrate the feasibility of analyzing the generally coupled equations for scalar bulk fluctuations, and constitute a step on the way towards computing correlators in confining gauge theories.

QCD4 GLUEBALL MASSES FROM AdS6 BLACK HOLE DESCRIPTION

By using the generalized version of gauge/gravity correspondence, we study the mass spectra of several typical QCD4 glueballs in the framework of AdS 6 black hole metric of Einstein gravity theory. The obtained glueball mass spectra are numerically in agreement with those from the AdS 7× S 4 black hole metric of the 11-dimensional supergravity.

Determination of the Glueball Mass Spectrum with the Spin-Orbit Interaction

Based on the investigation of the asymptotic behaviour of the polarization loop function for scalar charged particles in an external gauge field we determine the interaction Hamiltonian including the nonperturbative corrections of the relativistic character of motion and the large coupling constant. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the bound-state forming particles is explained. The change of the bound-state mass and of the constituent mass of particles is analyzed by varying the coupling constant. The mass spectrum of the two-gluon glueball is calculated taking into account spin-orbit and spin-spin interactions.

Mesons in gauge/gravity dual with large number of fundamental fields

In view of extending gauge/gravity dualities with flavour beyond the probe approximation, we establish the gravity dual description of mesons for a three-dimensional super Yang-Mills theory with fundamental matter. For this purpose we consider the fully backreacted D2/D6 brane solution of Cherkis and Hashimoto in an approximation due to Pelc and Siebelink. The low-energy field theory is the IR fixed point theory of three-dimensional N=4 SU(N_c) super Yang-Mills with N_f fundamental fields, which we consider in a large N_c and N_f limit with N_f/N_c finite and fixed. We discuss the dictionary between meson-like operators and supergravity fluctuations in the corresponding near-horizon geometry. In particular, we find that the mesons are dual to the low-energy limit of closed string states. In analogy to computations of glueball mass spectra, we calculate the mass of the lowest-lying meson and find that it depends linearly on the quark mass.

Determination of the glueball mass spectrum with allowance for spin-orbital interactions

The mass spectrum of a coupled state is analytically determined. The mechanism of production of a constituent mass of particles forming a coupled state is explained. The change of the coupled state and constituent particle component masses attendant to changes of the coupling constant is analyzed. The mass spectrum of a two-gluon glueball is determined with allowance for spin-orbital and spin-spin interactions.

A model of glueballs

We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses.