Gluon Component Research Articles

On the Decomposition Theorem for Gluons

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_\mu = A_\mu^{\text{phys}}+A_\mu^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition.

Di-gluonium sum rules, I = 0 scalar mesons and conformal anomaly

We revisit, scrutinize, improve, confirm and complete our previous results [1–4] from the scalar di-gluonium sum rules within the standard SVZ-expansion at N2LO without instantons and beyond the minimal duality ansatz: “one resonance ⊕ QCD continuum” parametrization of the spectral function which is necessary for a better understanding of the complex spectra of the I=0 scalar mesons. We select different (un)subtracted sum rules (USR) moments of degree ≤ 4 for extracting the two lowest gluonia masses and couplings. We obtain: [MσB,fσB]=[1.07(13),0.46(16)],[MG1,fG1]=[1.55(12),0.37(11)] GeV and the corresponding masses of the radial excitations: MσB′=1.11(12) and MG1′=1.56(14) GeV which are (unexpectedly) almost degenerated with the ground states. The 2nd radial excitation is found to have a much heavier mass: MG2≃ 2.99(22) GeV. Combining these results with some Low-Energy Vertex Sum Rules (LEV-SR), we predict some hadronic widths and classify these states into two groups: – The σ-like (σB,σB′) which decay copiously to ππ from OZI-violating process and the σB′ to 2(ππ)S through σσ. – The G-like (G1,G1′ and eventually G2) which decay into η′η,ηη through the U(1)A gluonic vertex. Besides some eventual mixings with quarkonia states, we may expect that the observed σ/f0(500) and f0(1.37) are σ-like while the f0(1.5) and f0(1.7) are G-like gluonia. The high mass G2(2.99) can also mix with the G1,G1′ to bring the gluon component of the gluonia candidates above 2 GeV. We also estimate the conformal charge ψG(0)=2.09(29) GeV4 and its slope 102×ψG′(0)=−22(29) GeV2. Our results are summarized in Table 1.

Excited and exotic bottomonium spectroscopy from lattice QCD

We explore the spectrum of excited and exotic bottomonia using lattice QCD. Highly excited states are identified with masses up to 11,000 MeV, many of which can be grouped into supermultiplets matching those of the quark model while exotic spin-parity-charge-conjugation quantum numbers JPC = 0+−, 1−+, 2+− that cannot be formed from overline{q}q alone are also identified. Single-meson operator constructions are used that have good JPC in the continuum, these are found to overlap well onto heavy quark states up to J ≤ 4. A continuum JPC is assigned to each level, based on the distribution amongst lattice irreps and dominant operator overlaps. States with a dominant gluonic component are identified and form a hybrid supermultiplet with JPC = (0, 1, 2)−+, 1−−, approximately 1500 MeV above the ground-state ηb, similar to previous computations with light, strange and charm quark systems.

Parton distribution functions of the charged pion within the xFitter framework

We present the first open-source analysis of parton distribution functions (PDFs) of charged pions using xFitter, an open-source QCD fit framework to facilitate PDF extraction and analyses. Our calculations are implemented at next-to-leading order (NLO) using APPLgrids generated by MCFM generator. Using currently available Drell-Yan and photon production data, we find the valence distribution is well constrained; however, the considered data are not sensitive enough to unambiguously determine sea and gluon distributions. Fractions of momentum carried by the valence, sea and gluon components are discussed, and we compare with the results of JAM collaboration and the GRV group.

Gluonic and Regulatory Solvents: A Paradigm for Tunable Phase Segregation in Polymers

A theoretical concept for phase segregation of polymers in the presence of multicomponent selective solvents is presented. Phase separation is caused by nonspecific attractive interactions between the polymers and a smaller component in the solution instead of repulsion between monomers and solvent molecules. We call the component that adsorbs on the polymers and thus causes condensation “gluonic”. It is shown that a discontinuous phase transition from a diluted or semidiluted state to the condensed state takes place if the fraction of the gluonic component is increased. The location of the phase coexistence can be shifted by influencing the binding efficiency of the gluonic component. This can be achieved by adding a regulator component to the solution. The latter is assumed to bind specifically to the polymer and interferes with the gluonic component. In this way a switching of the state of the polymer from dissolved to condensed can be achieved without changing the chemical properties of the system. Ap...

Coupled kinetic equations for fermions and bosons in the relaxation-time approximation

Kinetic equations for quarks and gluons are solved numerically in the relaxation time approximation for the case of one-dimensional boost-invariant geometry. Quarks are massive and described by the Fermi-Dirac statistics, while gluons are massless and obey Bose-Einstein statistics. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions which specify the coupling between the quark and gluon sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a non-equlibrium mixture of quarks and gluons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of quark and gluon components, while the bulk viscosity is given by the formula known for a gas of quarks, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless gluons contribute in a non-trivial way to the bulk viscosity of a mixture, provided quarks are massive. We further observe the hydrodynamization effect which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behaviour is connected with the existence of an attractor solution for conformal systems.

Structure of the Nucleon and its Excitations

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

Production of Charmonium at Threshold in Hall A and C at Jefferson Lab

We describe in this paper two approved experiments in Hall A and Hall C at Jefferson Lab that will investigate the pure gluonic component of the strong interaction of Quantum Chromodynamics by measuring the elastic $$J/\psi $$ electro and photo-production cross section in the threshold region as well as explore the nature of the recently discovered LHCb charmed pentaquarks.

χc decays and the gluon component of the η′, η mesons

The large mass of the η′ meson indicates that a sizeable gluon component is present in the meson wave function. However, the χc0 and χc2 decays to η′ mesons, which proceed via a purely gluonic intermediate state and we would therefore naïvely expect to be enhanced by such a component, are in fact relatively suppressed. We argue that this apparent contradiction may be resolved by a proper treatment of interference effects in the decay. In particular, by accounting for the destructive interference between the quark and gluon components of the η′ distribution function, in combination with a model for strange quark mass effects, we demonstrate that the observed χc(0,2)→η(′)η(′) branching ratios can be reproduced for a reasonable gluon component of the η′, η mesons.

Colored-hadron distribution in hadron scattering in SU(2) lattice QCD

In color SU(2) lattice QCD, we investigate colored-diquark distributions in two-hadron scatterings by means of Bethe-Salpeter amplitudes on the lattice. With colored-diquark operators in the Coulomb gauge, we measure components of two colored diquarks realized as intermediate states via one gluon exchange (OGE) processes in hadron scattering. From the colored-diquark distributions, we estimate the dominant range of gluon (color) exchanges between closely located two hadrons. We find that the colored-diquark components are enhanced at the short range ($\leq$0.2 fm) and their tails show the single-exponential damping. In order to distinguish the genuine colored-diquark components originating in the color exchange processes from trivial colored two-quark components contained in two color-singlet hadrons as a result of simple transformation of hadronic basis, we repeat the analyses on the artificially constructed gauge fields, where low- and high-momentum gluon components are decoupled and only restricted pair of quarks can share and exchange low-momentum gluons. We observe qualitatively the same behaviors and confirm that the short-range enhancement of the colored-diquark distributions is the genuine OGE-origin color excitation in hadron scattering.

StrongDs*Dsη(′)andBs*Bsη(′)vertices from QCD light-cone sum rules

The strong $D^{*}_sD_{s}\eta^{(\prime)}$ and $B^{*}_sB_{s}\eta^{(\prime)}$ vertices are studied and the relevant couplings are calculated in the context of the light-cone QCD sum rule method with twist-4 accuracy by including the next-to-leading order corrections. In the analysis, both the quark and gluon components of the $\eta$ and $\eta^{\prime}$ mesons and the axial anomaly corrected higher twist distributions are included.

Understanding the cross section ofe+e−→ηJ/ψprocess via nonrelativistic QCD

Motivated by the large cross section of $e^+e^-\to \eta J/\psi$ process measured by the BESIII and Belle Collaborations recently, we evaluate this process at $\mathcal{O}(\alpha_s^4)$ accuracy in the framework of nonrelativistic QCD. We find that the cross section at the center-of-mass energy $\sqrt{s}=4.009$ {GeV} is $34.6\mathrm{pb}$, which is consistent with the BESIII data. The comparison with the Belle data in the region from $4.0\ \mathrm{GeV}$ to $5.3\ \mathrm{GeV}$ is also presented. Concerning the $\eta$ and $\eta^\prime$ mixing and the potential gluonium component of $\eta^\prime$, we also estimate the rate of $e^+e^-\to \eta^\prime J/\psi$ process, which can be checked within the updated Belle data.

A fresh look at exclusive electroproduction of light vector mesons

Relying on the collinear factorization approach, we demonstrate that H1 and ZEUS measurements of exclusive light vector meson and photon electroproduction cross sections can be simultaneously described for photon virtualities of $${\mathcal {Q}}\gtrsim 2\, \mathrm{GeV}$$ . Our findings reveal that quark exchanges are important in this small $$x_\mathrm{Bj}$$ region and that in leading order approximation the gluonic component is suppressed, e.g., the skewness ratio can be much smaller than one.

Central exclusive production as a probe of the gluonic component of the η′ and η mesons

Currently, the long-standing issue concerning the size of the gluonic content of the eta' and eta mesons remains unsettled. With this in mind we consider the central exclusive production (CEP) of eta', eta meson pairs in the perturbative regime, applying the Durham pQCD-based model of CEP and the `hard exclusive' formalism to evaluate the meson production subprocess. We calculate for the first time the relevant parton-level processes gg --> qqbar gg and gg --> gggg, where the final-state gg and qqbar pairs form a pseudoscalar flavour-singlet state. We observe that these amplitudes display some non-trivial and interesting theoretical properties, and we comment on how this can be understood in a MHV framework. Finally, we present a phenomenological study, and show that the cross sections for the CEP of eta', eta meson pairs are strongly sensitive to the size of the gluon content of these mesons. The observation of these processes could therefore provide important and novel insight into this problem.

Hydrodynamics of anisotropic quark and gluon fluids

The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy parameters. The dynamical equations describing such mixtures are derived from kinetic theory, with the collisional kernel treated in the relaxation-time approximation, allowing for different relaxation times for quarks and gluons. Baryon number conservation is enforced in the quark and antiquark components of the fluid, but overall parton number nonconservation is allowed in the system. The resulting equations are solved numerically in the ($0+1$)--dimensional boost-invariant case at zero and finite baryon density.

η−η′mixing: From electromagnetic transitions to weak decays of charm and beauty hadrons

It has been realized for a long time that knowing the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ wave functions in terms of quark and gluon components probes our understanding of nonperturbative QCD dynamics. Great effort has been given to this challenge, yet no clear picture has emerged even with the most recent KLOE data. We point out which measurements would be most helpful in arriving at a more definite conclusion. A better knowledge of these wave functions will significantly help to disentangle the weight of different decay subprocesses in semileptonic decays of ${D}^{+}$, ${D}_{s}^{+}$, and ${B}^{+}$ mesons. The resulting insights will be instrumental in treating even nonleptonic $B$ transitions involving $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ and their $CP$ asymmetries; thus they can sharpen the case for or against new physics intervening there.

FRACTION OF THE GLUONIUM COMPONENT IN η′ AND η

It is interesting to determine the fraction of the gluonium component in η and η′ which has been under serious discussion for many years. Measurements on different decay and/or production modes were employed in literatures, thus larger uncertainties were unavoidable. In this paper we suggest to determine the mixing angles of η-η′-G using the data of semileptonic decays of D and Ds. We extract the mixing angles ϕ′, ϕG and the model parameters simultaneously. Thanks to the new measurements carried out by CLEO Collaboration and there are sufficient decay modes to determine both the model parameters and mixing angles. The mixing angles from data are ϕ′ = (41.5 ± 2.0)° and sin ϕG = 0.00 ± 0.36. Even though the central value of sin ϕG is still zero, an upper bound is set. Moreover, as suggested in literature, η(1405) is a glueball candidate whereas in our picture, η(1405) may be identified as G with glueonium being its main content. Using all the model-parameters obtained above, we estimate the branching ratios of [Formula: see text] where G is identified as η(1405).

σ and [formula omitted] substructures from [formula omitted], [formula omitted] radiative and [formula omitted] semi-leptonic decays

Using an improved “analytic K-matrix model”, we reconsider the extraction of the σ≡f0(600) and f0(980)γγ widths from γγ→ππ scatterings data of Crystal Ball and Belle. Our main results are summarized in Tables 3 and 4. The averaged σ “direct width” to γγ is 0.16(3) keV which confirms a previous result of Mennessier et al. (2007, 2008) [1] and which does neither favour a large four-quark/molecule nor a pure q¯q components. The “direct width” of the f0(980) of 0.28(2) keV is much larger than the four-quark expectation but can be compatible with a s¯s or a gluonium component. We also found that the rescattering part of each amplitude is relatively large indicating an important contribution of the meson loops in the determinations of the σ and f0(980)γγ total widths. This is mainly due to the large couplings of the σ and f0(980) to ππ and/or K¯K, which can also be due to a light scalar gluonium with large OZI violating couplings but not necessary to a four-quark or molecule state. Our average results for the total (direct + rescattering) γγ widths: Γσtot=3.08(82) keV, Γf0tot=0.16(1) keV are comparable with the ones from dispersion relations and PDG values. Using the parameters from QCD spectral sum rules, we complete our analysis by showing that the production rates of unmixed scalar gluonia σB(1) and G(1.5–1.6) agree with the data from J/ψ, ϕ radiative and Ds semi-leptonic decays.

The σ and [formula omitted] from [formula omitted] scatterings data

We systematically reconsider, within an improved “analytic K-matrix model”, the extraction of the σ≡f0(600) and f0(980) masses, widths and hadronic couplings using new Ke4≡K→ππeνe data on ππ phase shift below 390 MeV and different sets of ππ→ππ/KK¯ scatterings data from 400 MeV to 1.4 GeV. Our results are summarized in Tables 1, 2 and 5. In units of MeV, the complex poles are: Mσ=452(12)−i260(15) and Mf=981(34)−i18(11), which are comparable with some recent high-precision determinations and with PDG values. Besides some other results, we find: |gσK+K−|/|gσπ+π−|=0.37(6) which confirms a sizeable gσK+K− coupling found earlier, and which disfavours a large ππ molecule or four-quark component of the σ, while its broad ππ width (relative to the one of the ρ-meson) cannot be explained within a q¯q scenario. The narrow ππ width of the f0(980) and the large value: |gfK+K−|/|gfπ+π−|=2.59(1.34), excludes its pure (u¯u+d¯d) content. A significant gluonium component eventually mixed with q¯q appears to be necessary for evading the previous difficulties.

Gluonic components of the pion and the transition form factorγ*γ*→π0

We propose an effective Lagrangian for the coupling of the neutral pion with gluons whose strength is determined by a low-energy theorem. We calculate the contribution of the gluonic components arising from this interaction to the pion transition form factor ${\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$ using the instanton liquid model to describe the quantum chromodynamics vacuum. We find that this contribution is large and might explain the anomalous behavior of the form factor at large virtuality of one of the photons, a feature which was recently discovered by the BABAR Collaboration.