Gluon Operators Research Articles

Scale dependence of hadronic wave functions and parton densities

We study how the components of hadronic wave functions in light-cone quantization depend on the ultraviolet cut-off by relating them in a systematic way to the matrix elements of a class of quark–gluon operators between the QCD vacuum and the hadrons. From this, we derive an infinite set of scale-evolution equations for the individual contributions to parton distributions from the Fock expansion. When summed over all the contributions, we recover the well-known DGLAP equation.

Off-forward matrix elements in light-front Hamiltonian QCD

We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.

Hard electroproduction of mesons: Helicity flip amplitudes with tensor gluon contributions

We consider hard electroproduction of mesons at twist-3 level and focus our attention on helicity flip amplitudes corresponding to the production of transversely polarized mesons by transverse photons. We demonstrate that helicity-flip amplitude for the transversely polarized particles are closely related to the contributions of the matrix elements of the tensor gluon operator which can serve as pure gluonic probe of the hadrons. Using standard factorisation approach and Wanzura-Wilczek approximation for the twist-3 matrix elements we find that such amplitudes do not have divergencies from the endpoint regions which appear in the other twist-3 amplitudes.

Effective Lagrangian and equations for valence quark and gluon Green's functions

Starting from the QCD Lagrangian and separating background and valence degrees of freedom, one arrives at the effective Lagrangian for valence quarks and gluons. Each term in the Lagrangian contains a product of valence quark and gluon operators acting at the end of the fundamental or adjoint string, made of the background field. A simple procedure is described how to obtain from the Lagrangian self-coupled equations for quark and gluon Green's function.

QCD sum rules for [formula omitted] in the nuclear medium: calculation of the Wilson coefficients of gluon operators up to dimension 6

We calculate the Wilson coefficients of all dimension-6 gluon operators with nonzero spin in the correlation function between two heavy vector currents. For the twist-4 part, we first identify the three independent gluon operators, and then proceed with the calculation of the Wilson coefficients using the fixed-point gauge. Together with the previous calculation of the Wilson coefficients for the dimension-6 scalar gluon operators by Nikolaev and Radyushkin, our result completes the list of all the Wilson coefficients of dimension-6 gluon operators in the correlation function between heavy vector currents. We apply our results to investigate the mass of J/ψ in nuclear matter using QCD sum rules. Using an upper-bound estimate on the matrix elements of the dimension-6 gluon operators to linear order in density, we find that the density-dependent contribution from dimension-6 operators is less than 40% of the dimension-4 operators with opposite sign. The final result gives about −4 MeV mass shift for the charmonium at rest in nuclear matter.

The gluon spin in the chiral bag model

We study the gluon polarization contribution at the quark model renormalization scale to the proton spin, Γ, in the chiral bag model. It is evaluated by taking the expectation value of the forward matrix element of a local gluon operator in the axial gauge A +=0. It is shown that the confining boundary condition for the color electric field plays an important role. When a solution satisfying the boundary condition for the color electric field, which is not the conventionally used but which we favor, is used, the Γ has a positive value for all bag radii and its magnitude is comparable to the quark spin polarization. This results in a significant reduction in the relative fraction of the proton spin carried by the quark spin, which is consistent with the small flavor singlet axial current measured in the EMC experiments.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark–pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data.

Twist decomposition of nonlocal light-cone operators II: general tensors of 2nd rank

A group theoretical procedure, introduced earlier in 20, 21, to decompose bilocal light-ray operators into (harmonic) operators of definite twist is applied to the case of arbitrary 2nd rank tensors. As a generic example the bilocal gluon operator is considered which gets contributions of twist-2 up to twist-6 from four different symmetry classes characterized by corresponding Young tableaux; also the twist decomposition of the related vector and scalar operators is considered. In addition, we extend these results to various trilocal light-ray operators, like the Shuryak–Vainshtein, the three-gluon and the four-quark operators, which are required for the consideration of higher-twist distribution amplitudes. The present results rely on the knowledge of harmonic tensor polynomials of any order n which have been determined up to the case of 2nd rank symmetric tensor for arbitrary space-time dimension.

CPviolation in hyperon decays from supersymmetry

It was pointed out recently that supersymmetry can generate flavor-changing gluonic dipole operators with sufficiently large coefficients to dominate the observed value of ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}.$ We point out that the same operators contribute to direct $\mathrm{CP}$ violation in hyperon decay and can generate a $\mathrm{CP}$ violating asymmetry $A({\ensuremath{\Lambda}}_{\ensuremath{-}}^{0})$ in the range probed by the current E871 experiment. Interestingly, models that naturally reproduce the relation $\ensuremath{\lambda}=\sqrt{{m}_{d}{/m}_{s}}$ do not generate ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ but could lead to an $A({\ensuremath{\Lambda}}_{\ensuremath{-}}^{0})$ of ${O(10}^{\ensuremath{-}3}).$

Estimate of twist-four contributions at smallxBand lowQ2

We present a first study of gluonic twist-four corrections to the deep inelastic structure function ${F}_{2}$ at small x and small ${Q}^{2}.$ The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution equations of the gluonic twist-four operators that are expected to be dominant at small x. We first review the analytical results which are presently available and define the framework of our calculation. In the second part we discuss the connection with DIS diffractive dissociation which can be used to estimate the size of some of the twist-four corrections. In the final part we show, for three different choices of the input distributions, the relative magnitude of the leading-twist and the twist-four contributions.

Probing the Quark-Gluon Plasma with a New Fermionic Correlator

We present the first measurement of a new correlation function of fermion bilinears in finite temperature QCD with and without dynamical quarks in a quantum number channel in which nontrivial correlations are known to be present for purely gluonic operators. We find that the fermion correlator vanishes for $T\ensuremath{\ge}{3T}_{c}/2$, in agreement with the expectation for weakly interacting quarks in a quark-gluon plasma.

NLO corrections and contribution of a tensor gluon operator to the process [formula omitted

We have calculated the NLO corrections for the leading twist amplitude of the reaction γ ∗γ→ππ at large virtuality of the photon and at W 2≪ Q 2. With a simple model for the two-pion quark and gluon distribution amplitudes we have estimated that the NLO effects may reduce the leading-order amplitude by as much as 30%. We have found that besides the usual twist-2 quark and gluon operators the NLO amplitude receives contribution from a distribution associated with twist-2 tensor gluon operator. The new gluon distribution can be investigated by studying the azimuthal asymmetry of the cross section for e+ γ→ e′+ ππ.

Additional isospin-breaking effects in ϵ′/ ϵ

In the analysis of ϵ ′/ ϵ it has been traditional to consider the isospin-breaking effects arising from electroweak-penguin contributions and from π 0– η,η′ mixing, yet additional isospin-violating effects exist. In particular, we study the isospin violation which arises from the u– d quark mass difference in the hadronization of the gluonic penguin operator, engendering contributions of an effective ΔI=3/2 character. Using chiral perturbation theory and the factorization approximation for the hadronic matrix elements, we find within a specific model for the low-energy constants that we can readily accommodate an increase in ϵ ′/ϵ by a factor of two.

Masses ofJ/ψandηcin the Nuclear Medium: QCD Sum Rule Approach

We investigate the masses of the lowest $c\overline{c}$ states, the $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$, in nuclear matter using QCD sum rules. Up to dimension four, the differences between the operator product expansions in vacuum and in medium arise from the density-dependent change in the gluon condensate and from a new contribution proportional to the nucleon expectation value of the twist-2 gluon operator. Both terms together give an attractive shift of about 5--10 MeV to the $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ masses in nuclear matter.

J/ -Nucleon Scattering Length and In-Medium Mass Shift of J/ in QCD Sum Rule Analysis

We calculate the spin-averaged $J/\psi$-nucleon scattering length $a_{J/\psi}$ by directly applying QCD sum rule to $J/\psi$-$N$ forward scattering amplitude. Our result $a_{J/\psi} = - 0.10 \pm 0.02$ fm, predicts the possibility of bound states with nuclei, though the force is weaker than that of the light vector mesons ($\rho,\omega,\phi$)-$N$ cases. Up to dimension-4 gluonic operators, we evaluate the scattering length with twist-2 contribution, which increases the absolute value of the scattering length about 30%. If we apply $a_{J/\psi}$ to the effective mass of $J/\psi$ in nuclear matter on the basis of the linear density approximation, it shows very slight decrease ($4 \sim 7$ MeV) at normal matter density.

Instanton-induced charm contribution to polarized deep-inelastic scattering

Recent data on B decays involving η′ may be explained if the singlet axial current of charmed quarks has a large matrix element to η′, and instantons were shown to be able to generate this effect. We study the magnitude of charm contributions to nucleon polarized structure functions generated in a similar way. Comparing the charm contribution, which is related to a dim(6) gluonic operator, to that of light quarks, which are related by the anomaly equation to G G ̃ , we found that Δ c/Δ Σ≃−0.03. Future experiments like COMPASS at CERN identifying charm production in DIS can measure this “intrinsic polarized charm” component of the nucleon.

Anomalous dimension of gluonic operator in polarized deep inelastic scattering at O(1/ Nf)

We compute the O(1/ N f ) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three loop contribution at O(1/ N f ). The treatment of the ϵ-tensor in the large N f d-dimensional critical point formalism is also discussed.

Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/ Nf)

Using large N f methods we compute the anomalous dimension of the predominantly gluonic flavour singlet twist-2 composite operator which arises in the operator product expansion used in deep inelastic scattering. We obtain a d-dimensional expression for it which depends on the operator moment n. Its expansion in powers of e = (4 − d)/2 agrees with the explicit exact three-loop MS results available for n ⩽ 8 and allows us to determine some new information on the explicit n-dependence of the three and higher order coefficients. In particular the n-dependence of the three-loop anomalous dimension γ gg ( a) is determined in the C 2( G) sector at O(1/ N f ).

Gluon excitations of the static quark potential and the hybrid quarkonium spectrum

A comprehensive determination of the rich, low-lying spectrum of gluonic excitations in the presence of a static quark-antiquark pair is presented. Our results are obtained from several simulations on anisotropic lattices using an improved action and a large set of gluonic operators. The hybrid quarkonium states are studied in the quenched approximation using the Born-Oppenheimer expansion and nonrelativistic lattice QCD.

Hadronic and electromagnetic interactions of quarkonia

We examine the hadronic interactions of quarkonia, focusing on the decays psi(2s)->psi pi pi and upsilon(2s)-> upsilon pi pi. The leading gluonic operators in the multipole expansion are matched onto the chiral lagrangian with the coefficients fit to available data, both at tree-level and loop-level in the chiral expansion. A comparison is made with naive expectations loosely based on the large-$N_c$ limit of QCD in an effort to determine the reliability of this limit for other observables, such as the binding of $\ps$ to nuclei. Crossing symmetry is used to estimate the cross-section for inelastic $\pi\ps\to\pi\pss$ scattering, potentially relevant for heavy ion collisions. The radiative decays psi(2s)->psi pi pi gamma and upsilon(2s)-> upsilon pi pi gamma are determined at tree-level in the chiral lagrangian. Measurement of such decays will provide a test of the multipole and chiral expansions. We briefly discuss decays from the upsilon(3s) and also the contribution from pions to the electromagnetic polarizability of quarkonia.