Gluonic Origin and Glueball Nature of Pomeron

The Pomeron-nucleon coupling vertex is theoretically derived from the fundamental theory of strong interaction QCD. The empirical vertex βγ^μF1 （t） used commonly in diffractive processes with a coupling strength β = 6.0 GeV^-1 is initially obtained from QCD theoretically. Our study not only reproduces the Pomeron-nucleon coupling from QCD but also clearly shows the gluonlc origin and glueball nature of Pomeron, which is a longstanding puzzle. From this investigation, we claim that Pomeron can be regarded as a Reggeized tensor glueball ζ（2230） with quantum numbers of I^GJ^PC = 0＋2＋＋. Since the tensor glueball ζ（2230） lies on the Pomeron trajectory αp（t = Mζ^2） = 2, the longstanding puzzle that no physical particle lies on the Pomeron trajectory, αp（t） = 1.08 ＋ 0.20 GeV^-2 .t, seems to be solved.

Pomeron as a Reggeized Tensor Glueball

We study gluonic content of the pomeron and propose that the pomeron could be a reggeized tensor glueball ζ(2230) with quantum numbers IG JPc = 0+2++.This conjecture is examined in high energy proton-proton elastic scattering,and the calculations lend a favorable support to our physical idea.

Reggeon, Pomeron and Glueball, Odderon-Hadron-Hadron Interaction at High Energies—From Regge Theory to Quantum Chromodynamics

Based on analysis of scattering matrix S, and its properties such as analyticity, unitarity, Lorentz invariance, and crossing symmetry relation, the Regge theory was proposed to describe hadron-hadron scattering at high energies before the advent of QCD, and correspondingly a Reggeon concept was born as a mediator of strongly interaction. This theory serves as a successful approach and has explained a great number of experimental data successfully, which proves that the Regge theory can be regarded as a basic theory of hadron interaction at high energies and its validity in many applications. However, as new experimental data come out, we have some difficulties in explaining the data. The new experimental total cross section violates the predictions of Regge theory, which shows that Regge formalism is limited in its applications to high energy data. To understand new experimental measurements, a new exchange theory was consequently born and its mediator is called Pomeron, which has vacuum quantum numbers. The new theory named as Pomeron exchange theory which reproduces the new experimental data of diffractive processes successfully. There are two exchange mediators： Reggeon and Pomeron. Reggeon exchange theory can only produce data at the relatively lower energy region, while Pomeron exchange theory fits the data only at higher-energy region, separately. In order to explain the data in the whole energy region, we propose a Reggeon-Pomeron model to describe high-energy hadron- hadron scattering and other diffractive processes. Although the Reggeon-Pomeron model is successful in describing high-energy hadron-hadron interaction in the whole energy region, it is a phenomenological model. After the advent of QCD, people try to reveal the mystery of the phenomenological theory from QCD since hadron-hadron processes is a strong interaction, which is believed to be described by QCD. According to this point of view, we study the QCD nature of Reggeon and Pomeron. We claim that the Reggeon exchange is an exchange of multigluon,the color singlet gluon bound state. In particular, the Pomeron could be a Reggeized tensor glueball ξ（2230） with mass of 2.23 GeV, quantum numbers I^G, J^PC = 0^＋, 2^＋＋ and decay width of about 100 MeV. The glueball exchange theory reproduces data quite well. Accordingly, we believe that the Odderon, consisting of three Reggeized gluons, and predicted by QCD, should also contribute to hadron-hadron scattering and many other diffractive processes. We search for the Odderon by studying pp and pp elastic scatterings at high energies. Our investigations on the differential cross section dσ/ dt of hadron-hadron scattering at various energies and comparisons with experimental data show that the Odderon plays an essential role in fitting to data. Therefore, we suggest that the measurements should be urgently done in order to confirm the existences of the Odderon and to test QCD.

Thied—Order Approximation of 0^＋＋ Glueball Mass and Wavefunction of （2＋1）—Dimensional SU（3） Lattice Gauge Theory

The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT). Using this method, wavefunctions are approximated by linear combination of graphs consisting of only one connected Wilson loop. We study the excited state energy and wavefunction in (2+1)-D SU(3) LGT up to the third order. The glueball mass shows a good scaling behavior.

Existence of Tensor Glueball ξ（2230） and Its Mass, Spin, and Decay Width

In order to solve the current experimental controversy on the existence of the tensor glueball ξ(2230), we examine whether the conclusion from Seth's experimental measurement, which rejects existence of ξ(2230), is reliable.We claim that the non-observation of the resonance structure by Seth is not a sound ground for rejecting the existence of ξ(2230) but it may just indicate that ξ(2230) has a broad width. We also study the tensor glueball properties: the mass, spin, and decay width. Our theoretical predictions of the mass and the spin of the ξ(2230) using QCD sum rule are about 2.23 GeV and J = 2, respectively. Our theoretical results also evidently show that the ξ(2230) must have a total decay width of about 100 MeV, which is much broader than the reported 20 MeV but a small partial decay width of 2 MeV into pp decay channel.

Fermion Corrections to Mass of Scalar Glueball in QCD Sum Rule

Contributions of fermions to the mass of the scalar glueball 0++are calculated at two-loop level in theframework of QCD sum rules.It slightly changes the coefficients in the operator product expansion （OPE） and shiftsthe mass of glueball to 1.72 ± 0.07 GeV.

A Lattice Study of the Glueball Spectrum

Glueball spectrum is studied using an improved gluonic action on asymmetric lattices in the pure gauge theory. The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the continuum limit more reliable. In particular, attention is paid to the scalar glueball mass which is known to have problems in the extrapolation. Converting our lattice results to physical units using the scale set by the static quark potential, we obtain the following results for the glueball masses: for the scalar glueball mass and for the tensor glueball.

1-16 Glueball Quarkonium Mixing in QCD

Despite of the fact that the quark model has been very successful in describing hadron spectrum, there are still some exotic states cannot be explained well. Glueball is one of the most interesting issue among the exotic states.The general wisdom is that QCD must have the glueballs made of gluons. And there are many models have been proposed to describe the physics of glueball[1?5].

1-17 Glueball Physics in QCD

An important issues in hadron spectroscopy is the identification of glueballs. The general wisdom is that QCD must have the glueballs made of gluons. The search for the glueballs has a long history . Several models of glueballs, such as the bag model, flux tube model and constituent model, have been proposed[1??5]. Moreover, the lattice QCD has been able to estimate the mass of the low-lying glueballs[6;7].

The radiative decay of scalar glueball from lattice QCD

We perform the first lattice QCD study on the radiative decay of the scalar glueball to the vector mesonφin the quenched approximation.The calculations are carried out on three gauge ensembles with different lattice spacings,which enable us to do the continuum extrapolation.We first revisit the radiative J/ψdecay into the scalar glueball G and obtain the partial decay widthΓ(J/ψ→γG)=0.578(86)keV and the branching fraction Br(J/ψ→γG)=6.2(9)×10^(-3),which are in agreement with the previous lattice results.We then extend the similar calculation to the process G→γφand get the partial decay widthΓ(G→γφ)=0.074(47)keV,which implies that the combined branching fraction of J/ψ→γG→γγφis as small as O(10^(-9))such that this process is hardly detected by the BESⅢexperiment even with the large J/ψsample of O(10^(10)).With the vector meson dominance model,the two-photon decay width of the scalar glueball is estimated to beΓ(G→γγ)=0.53(46)e V,which results in a large stickiness S(G)~O(10^(4))of the scalar glueball by assuming the stickiness of f_(2)(1270)to be one.

Glueballs at physical pion mass

Glueballs are investigated through gluonic operators on two N_(f)=2+1RBC/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 A_(μ)(x)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.

A Model of Grand Unified Theory: Suggested Solution for CP-Violation Using Ideas of Phase Paths

This study demonstrates that beyond standard model (BSM) cosmic fundamental interactions—weak, strong, and electromagnetic forces—can be unified through a common basis of representation. This unification allows for the derivation of the fine structure constant with running points of α(t) ≈ 1/(136.9038) at high energy scales, based on electroweak interactions. Through the application of the Ising model, the running point of the elementary charge e at high energy scales is determined, and Coulomb’s law is actually derived from the Yukawa potential. Theoretically, based on S. Weinberg’s electroweak interaction theory, this study unifies the strong and electromagnetic forces by representing them with rYuka, and further advances the reconstruction of the SU(3)C×SU(1)L×U(1)EMframework on the basis of electroweak interaction concepts. In fact, the cosmic fundamental forces can interchange at the mass gap, defined as the Yukawa turning phase at rYuka ≃1.9404 fm, with the SU(3)Diag structural constant fijk on glueballs calculated, estimating a spectrum mass gap of ∆0 > 0.

Abelian-Higgs phase of SU(2) QCD and glueball energy

It is shown that SU（2） QCD admits an dual Abelian-Higgs phase, with a Higgs vacuum of a type-Ⅱ superconductor. This is done by using a connection decomposition for the gluon field and the random-direction approximation. Using a bag picture with soft wall, we presented a calculational procedure for the glueball energy based on the recent proof for wall-vortices [Nucl. Phys. B 741（2006）1].

Two-gluon and trigluon glueballs from dynamical holography QCD

We study the scalar, vector and tensor two-gluon and trigluon glueball spectra in the framework of the 5-dimension dynamical holographic QCD model, where the metric structure is deformed self-consistently by the dilaton field. For comparison, the glueball spectra are also calculated in the hard-wall and soft-wall holographic QCD models. In order to distinguish glueballs with even and odd parities, we introduce a positive and negative coupling between the dilaton field and glueballs, and for higher spin glueballs, we introduce a deformed 5-dimension mass. With this set-up, there is only one free parameter from the quadratic dilaton profile in the dynamical holographic QCD model, which is fixed by the scalar glueball spectra. It is found that the two-gluon glueball spectra produced in the dynamical holographic QCD model are in good agreement with lattice data. Among six trigluon glueballs, the produced masses for 1±- and 2-- are in good agreement with lattice data, and the produced masses for 0--, 0＋- and 2＋- are around 1.5 GeV lighter than lattice results. This result might indicate that the three trigluon glueballs of 0--, 0＋- and 2＋- are dominated by the three-gluon condensate contribution.

Search for J^(PC) = even^(++) glueballs in radiative decay of J/Ψ

Based on the general analysis of decay width and branching ratio of two pseudo scalar meson channels, two sets of discriminants between mesons and glueballs for l = 0, J1PC = even++ un-flavored hadrons with the mass between 1.2 and 2.9 GeV are suggested. Known l = 0, JPC = 2++, f2(l525) particle is discriminated as a typical meson. The way to discriminate new l = 0, JPC = even++ unflavored hadrons is discussed.

Scalar glueball in a soft-wall model of AdS/QCD

The scalar glueball is investigated in a soft-wall model of AdS/QCD. Constraints of the mass of the scalar glueball are given through an analysis of a relation between the bulk mass and the anomalous dimension. The mass of the ground scalar glueball is located at 0.96＋-0.07 ＋0.04 GeV 〈 MG 〈 1.36＋0.05 -0.10 GeV. In terms of a background dilaton field θ（z）= cz2, the two-point correlation function for the scalar gluon operator is obtained. The two-point correlation function at A=4 gives a different behavior compared with the one in QCD.

Scalar mesons and glueballs in D_p-D_q hard-wall models

We investigate the light scalar mesons and glueballs in the Dp-Dq hard-wall models, including D3-Dq, D4-Dq, and D6-Dq systems. It is found that only in the D4-D6 and D4-Ds hard-wall models are the predicted masses of the clq scalar meson fo scalar glueball consistent with their experimental or lattice results. This indicates that D4-D6 and D4-Ds hard-wall models are the favorite candidates of the realistic holographic QCD model.

Glueball spectrum from Nf=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using Nf = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363（39） GeV and 2.384（67）GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573（55） GeV and 2.585（65） GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter（around 1 GeV） and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.

Revisiting the determining fraction of glueball component in f_(0) mesons via radiative decays of J/ψ

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 qq 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) mesonic series is an ideal place to study possible mixtures of glueballs and qq.In this paper,following the strategy proposed by Close,Farrar and Li,we try to determine the fraction of glueball components inf_(0)mesons using the measured mass spectra and the branching ratios of J/ψ radiative decays intof_(0)mesons.Since the pioneering papers by Close et al.,more than 20 years have elapsed and more accurate measurements have been done by several experimental collaborations,so it is time to revisit this interesting topic using new data.We suppose f_(0)(500)and f_(0)(980)to be pure quark states,while for f_(0)(1370),f_(0)(1500)and f_(0)(1710),to fit both the experimental data of J/ψradiative decay and their mass spectra,glueball components are needed.Moreover,the mass of the pure 0++ glueball is phenomenologically determined.

Picard–Fuchs Equation for Glueball Superfield for the SO(N) Gauge Group

In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.