Constituent Gluons Research Articles

Spin effects in heavy hybrid mesons on an anisotropic lattice

We present a quenched calculation of lowest bottomonium hybrid states on an anisotropic lattice with Landau mean-link tadpole improvement, using the improved NRQCD Hamiltonian. We investigate the quark-spin s=0,1 sectors which contain both the non-exotic 1 −− and the exotic 1 −+, and demonstrate their degeneracy in the case of the lowest order Hamiltonian. Both states are found at around 1.6 GeV above the ϒ ground state. We examine the spin-splitting for several hybrid states (1 −−, 1 −+, 0 −+, 2 −+) which is due to the −c 1 σ· B/2m b term in the NRQCD Hamiltonian, all other terms having negligible effect. The spin splittings are well resolved outside errors and are surprisingly large. We investigate their dependence on c 1 for several values of c 1. We calculate one contribution to these splittings using the Born-Oppenheimer picture for hybrids and show that the observed size of the effect is plausibly explained by mixing with hybrid states with more than one constituent gluon.

Light-quark meson spectroscopy with crystal barrel

Light-quark meson spectroscopy provides a powerful tool to study QCD in the non-perturbative sector. Crystal Barrel has developed a lively experimental activity over the last decade and different high-statistics results have been published which have led to stimulating theoretical interpretations. A selection of results concerning the quest of constituent gluons in hadrons will be discussed.

Glueball Calculations in Large-NcGauge Theory

We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wavefunctions in the leading order of the 1/N_c colour expansion. We find 0^{++}, 2^{++}, and 1^{+-} glueballs having masses consistent with N_c=3 data available from Euclidean lattice path integral methods. The wavefunctions exhibit a light-front constituent gluon structure.

Hybrid baryons in large-NcQCD

We study the properties and couplings of hybrid baryons in the large-${N}_{c}$ expansion. These are color-neutral baryon states which contain in addition to ${N}_{c}$ quarks also one constituent gluon. Hybrid baryons with both symmetric and mixed symmetric orbital wave functions are considered. We introduce a Hartree description for these states, similar to the one used by Witten for ordinary baryons. It is shown that the Hartree equations for ${N}_{c},{(N}_{c}\ensuremath{-}1)$ quarks for symmetric (mixed symmetric) states in hybrid baryons coincide with those in ordinary baryons in the large-${N}_{c}$ limit. The energy due to the gluon field is of order ${N}_{c}^{0}{\ensuremath{\Lambda}}_{\mathrm{QCD}}$ and can be interpreted as the mass of a constituent gluon. Under the assumption of color confinement, our results prove the existence of hybrid baryons made up of heavy quarks in the large ${N}_{c}$ limit and provide a justification for the constituent gluon picture of these states. The couplings of the hybrid baryons to mesons of arbitrary spin are computed in the quark model. Using constraints from the large ${N}_{c}$ scaling laws for the meson-baryon scattering amplitudes, we write down consistency conditions for the meson couplings of the hybrid baryons. These consistency conditions are solved explicitly with results in agreement with those in the quark model for the respective couplings.

Heavy hybrids with constituent gluons

Hybrid meson energies are calculated in the static quark limit with the Dynamical Quark Model (DQM). In the DQM, transverse gluons are represented as effective constituents with a dynamically generated mass. Hybrid masses are determined within the Tamm-Dancoff approximation for the resulting relativistic Salpeter equation. Although the general features of the adiabatic potential surfaces correspond with lattice data, the results disagree on level orderings. Similar problems appear to exist in all constituent glue models of hybrids. We conclude that constituent gluons do not accurately represent soft gluonic degrees of freedom. The steps necessary to correct this deficiency are discussed.

Higher Fock states and power counting in exclusive $P$ -wave quarkonium decays

Exclusive processes at large momentum transfer $Q$ factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in $1/Q$ . We show that for exclusive decays of $P$ -wave quarkonia the contribution from the next-higher Fock state $|{\rm Q}\bar{\rm Q}{\rm g}\rangle$ contributes at the same order in $1/Q$ . We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on $\chi_{{\rm c} J}$ decays into pairs of pions, kaons, and etas. We also comment on $J/\psi$ decays into two pions.

Higher Fock states and power counting in exclusive

Exclusive processes at large momentum transfer $Q$ factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in $1/Q$ . We show that for exclusive decays of $P$ -wave quarkonia the contribution from the next-higher Fock state $|{\rm Q}\bar{\rm Q}{\rm g}\rangle$ contributes at the same order in $1/Q$ . We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on $\chi_{{\rm c} J}$ decays into pairs of pions, kaons, and etas. We also comment on $J/\psi$ decays into two pions.

Possible Signatures of the 2++ Glueball and ξ(2230)11The project supported in part by National Natural Science Foundation of China, and the State Education Commission of China

Based on a bound constituent gluon picture and the gluon anomaly in QCD, I argue that the decay branching ratios of the 2++ glueball candidate ξ(2230) may satisfy and , . These features might provide a useful test for ξ(2230).

Hybrid mesons with heavy quarks

Abstract Model-independent features of hybrid meson states are discussed. These general arguments are applied to the QCD-based constituent gluon model based on the Vacuum Background Correlators Method (VBCM). The leading-order Hamiltonian is derived from the general formalism.The masses of heavy quark hybrids, including charmonium hybrid states, are calculated. We predict ccg hybrids at 4·1 ± 0·1 GeV and bbg ones at 10·5 ± 0·1 GeV. Comparison with some other models are made.

Measurement of the D ∗± cross section in two photon collisions at LEP

The inclusive production of D ∗± mesons in photon-photon collisions has been measured by the Aleph experiment at LEP with a beam energy of 45 GeV. The D ∗+ are detected in their decay to D 0 π + with the D 0 observed in three separate decay modes: (1) K − π +, (2) K − π + π 0 and (3) K − π + π − π +, and analagously for the D ∗− modes. A total of 33 events was observed from an integrated luminosity of 73 pb −1 which corresponds to a cross section for Σ( e +e − → e +e −D ∗±X ) of 155 ± 33 ± 21 pb. This result is compatible with both the direct production γγ → c c in the Born approximation and with a more complete calculation which includes both radiative QCD corrections and contributions in which one of the photons is first resolved into its quark and gluon constituents. The shapes of distributions for events containing a D ∗+ are found to be better described by the latter.

The triple-pomeron regime and structure function of the pomeron in diffractive deep inelastic scattering at very smallx

We develop the novel description of diffractive deep inelastic scattering based on the technique of lightcone wave functions of multiparton Fock states of the photon. The technique takes advantage of the exact diagonalization of the diffractiveS-matrix in the dipole-cross section representation. In this paper we derive properties of the diffractive dissociation of virtual photons in the triple-pomeron regime. We demonstrate that the photonpomeron interactions can be described by the partonic structure function, which satisfies the conventional GLDAP evolution equations. We identify the valence and sea (anti) quark and the valence gluon structure functions of the pomeron. We show how the gluon structure of the pomeron can be described by the constituent gluon wave function. We derive the leading unitarization correction to the rising structure functions at smallx and conclude that the unitarized structure function satisfies the linear GLDAP evolution equations. This result holds even when the multipomeron exchanges are included.

If the $$\widehat\rho $$ (1405) is the exotic 1−(1− +) hybrid, then where are the non-exotic ones?(1405) is the exotic 1−(1− +) hybrid, then where are the non-exotic ones?

The decays of hybrid\(q\bar qg\) mesons are considered with the assumption that the lowest hybrids are those containing 1+ constituent gluon. The selection rules for the hybrid decays into two mesons are obtained and compared with the experimentally observed decay pattern for the mesons in the mass region 1–2GeV. The estimate of partial widths for the 1− + hybrid shows that the hybrid assignment is compatible with the properties of exotic\(\widehat\rho \)(1405) state. Setting the absolute scale of mass for hybrids in this way one may look for hybrids with non-exotic quantum numbers, and it appears that large admixture of 0− + and 2− + hybrids may be allowed for the π(1300) and π2(1670) correspondingly. Similarly, the controversial data on e+e− annihilation into pions in the energy region around 1.5 GeV may be explained in terms of mixing of 23S1 quark-antiquark states to 1−− isovector and isoscalar hybrids.

Spin structure of nucleons in a quark model with constituent gluons.

We discuss the spin structure of nucleons in a quark model with gluonic degrees of freedom. The sum rules for polarized protons and neutrons are related to nucleon magnetic moments. In particular, when the ratio of the proton and neutron magnetic moments is larger than $\ensuremath{-}\frac{3}{2}$ the sum rule for polarized neutrons is negative, in agreement with recent experiments.

A possible glueball contribution to the Goldberger-Treiman relations

We discuss the influence of glueball coupling to nucleons on the weak axial-vector coupling constants including the singlet channel. We consider the possibility of the introduction of a constituent gluon contribution to the proton spin. The estimated value for this quantity seems to be rather small for moderate values of glueball nucleon coupling.

Decay properties of hybrid mesons with a massive constituent gluon and search for their candidates.

In a previous work we argued the possibility of the ${f}_{1}(1420)$ being our first hybrid meson with the configuration of $\frac{(u\overline{u}+d\overline{d})g}{\sqrt{2}}$, and gave a preliminary consideration to search for other hybrid mesons. In this paper we calculate respective decay widths of the other members of ground-state hybrid-meson nonets in the framework of the covariant oscillator quark model extended to describe bound systems composed of quarks, antiquarks, and/or gluons. Based upon these results we select eight "observed" candidates altogether, three of them on a rather firm basis, and give some remarks to search further for their candidates experimentally.

The search for scalar gluonium

Mesons without quark constituents should exist if our definition of quantum chromodynamics is correct. It appears likely, but not compelling, that the ℓ = 0 scalar gluonium is the lightest bound state of two constituent gluons. Notwithstanding concerted experimental efforts, there is no convincing evidence that such a state has been found. Avenues for promising future activities are pointed out.

Recent crystal ball results on resonance formation in γγ-reactions

The Crystal Ball detector has been used for γγ-production of final states consisting of π°'s and η's only. New results are obtained for γγ → π° π° π° where the π 2(1670) with Γ γγ ( π 2) = (1.41 ± 0.23 ± 0.23) keV has been observed. In γγ → η π° π° a hitherto unknown resonance X (1900) was found with Γ γγ ( X) BR( X → ηπ° π°) = (0.9 ± 0.3 ± 0.5) keV. The assignment is probably J PC = 2 −+ suggesting X = η 2. The 2 −+ mesons seem to be q q states. All data on γγ-formation of resonances are summarized and used to get information on the charged constituents (quarks) of the hadrons and on possible gluon constituents by comparing to radiative J/ Ψ-decays.

Mass spectra of gg, ggg and $$gq\bar q$$ states in a Bethe-Salpeter formalismstates in a Bethe-Salpeter formalism

A covariant 3-D form (under the null-plane ansatz) of the Bethe-Salpeter equation with a Lorentz-invariant vector type (γμ(1)γμ(2)), confining 3 kernel, which had earlier successfully predicted the mass spectra of\(q\bar q\) (all flavours) and qqq (u, d, s, flavours) hadrons, is extended in natural way to make spectral predictions for low-lying gg, ggg and\(gq\bar q\) states, with no free parameters, except for an input constituent gluon mass (mg) playing the role ofmq. The sensitivity of the glueball spectra tomg is studied for both gg and ggg systems, and a sharp increase in the hadron mass,M withmg is found for these systems. The large spin content of the gluon (compared to the quark's) induces large mass depressions in the spectra of low-J glueball states, which in turn require a fairly large gluon mass as a sort of threshold (for low-J states) to ensure a real solution for the corresponding BSE. (This problem is absent for pure quark states as well as for hybrids characterized by lower spin splittings.) The locations of «exotic» glueball states are explored in some detail, both in terms of the «normal»S3-classifications usually employed for qqq systems and from additional [2, 1] symmetries (termed «abnormal» in the text) which are available in principle for 3-body states ofL=0. Comparison of the BS results (as a function ofmg) on all the three sectors is made with those of other models, where the available results are mostly limited to gg states. Quantitative comparison with available experimental candidates (with overlappingJPC and masses) is relegated to a more systematic BS formulation (in progress) of the transition amplitudes connecting gg etc. states with the conventional\(q\bar q\) states.

Very energetic photons at HERA

We show that very energetic photons in the backward direction can be produced in deep inelastic Compton scattering at HERA. Assuming a fixed energy of 9 GeV for the initial photons and 820 GeV for the photons a high rate is found for the production of final photons with a transverse momentum equal to 5 GeV/ c and energy between 40 GeV and 300 GeV. These energetic photons arise mainly from the scattering of the soft gluonic constituents of the initial photon with quarks from the proton. They are produced in the backward direction in coincidence with a photon beam jet of energy ∼9 GeV in the forward direction.

Meson-proton scattering at high energies

We use a model in which the energy dependence of hadronic scattering is driven at high energies primarily by semihard scattering of constituent gluons and quarks to calculate the elastic differential and total cross sections for $\ensuremath{\pi}p$ and $\mathrm{Kp}$ scattering. Our model predicts that, as a direct consequence of the dominance of gluon and sea quark interactions at small $x$, the total cross sections for all the meson-proton processes should approach equality in the TeV energy regime. The cross sections are strikingly large for energies in the upper range of cosmic ray energies, and the expected evolution of hadronic air showers may be changed as a result.