Unintegrated Gluon Distribution Research Articles

Study of the Linked Dipole Chain Model in heavy quark production at the Tevatron

We present calculations of charm and beauty production at Tevatron within the framework of kT-factorization, using the unintegrated gluon distributions as obtained from the Linked Dipole Chain model. The analysis covers transverse momentum and rapidity distributions and the azimuthal correlations between b and bbar quarks (or rather muons from their decay) which are powerful tests for the different unintegrated gluon distributions. We compare the theoretical results with recent experimental data taken by D0 and CDF collaborations at the Tevatron Run I and II.

Unintegrated parton distributions of pions and nucleons from the CCFM equations in the single-loop approximation

The unintegrated quark and gluon distributions in the pion and nucleon are analyzed using the CCFM equations in the single-loop approximation. We utilize the transverse-coordinate (or impact-parameter) representation which diagonalizes the equations and study in detail the dependence on the transverse coordinate induced by the CCFM evolution. We find considerable broadening of the transverse-momentum distributions with an increasing magnitude of the hard scale Q. For instance, at the Bjorken $x=0.1$ the root mean squared transverse momentum of the gluons is enhanced by about 1 GeV when evolved from the initial low scale to ${Q}^{2}=10{\mathrm{GeV}}^{2},$ and by about 2 GeV when evolved up to ${Q}^{2}=100{\mathrm{GeV}}^{2}.$ The broadening effect is enhanced with decreasing Bjorken x, and is stronger for the gluons than for the quarks. Analytic solution for the average transverse momentum corresponding to the x moments of the distributions is obtained. The parton luminosities are also discussed.

Electroproduction of J/ψ mesons within the semihard QCD approach and the color-singlet model

The deep-inelastic production of J/ψ mesons in electron-proton interactions at the HERA collider is considered within the semihard (kT-factorization) QCD approach and within the color-singlet model. The dependence of the Q2, pT2, z, y* and W distributions of J/ψ mesons on various sets of unintegrated gluon distributions and the dependence of the spin parameter α on pT2 and Q2 are investigated. The results of the calculations are compared with the latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider. It is shown that experimental investigations of the polarization properties of J/ψ mesons over the kinematical region Q2<1 GeV2 may provide an additional test of the statement that the dynamics of gluon distributions is governed by the Balitsky-Fadin-Kuraev-Lipatov equations.

Dynamics of particle production in relativistic nuclear collisions

Saturation models for particle production in relativistic nuclear collisions are discussed. In particular, I show that the predictions from the high density QCD for the qualitative shape of dN/ dy are very sensitive to the form of the unintegrated gluon distribution.

Heavy-quark production in p $$\bar p$$ collisions and unintegrated gluon distributions

The inclusive production of heavy (c and b) quarks in high-energy p\(\bar p\) collisions are considered within the semihard approach in QCD. The dependence of the cross section for heavy-quark production, σ(pT>p T min ), on unintegrated gluon distributions is studied. The results of this consideration are compared with experimental data obtained by the D0 and CDF Collaborations at Tevatron.

$J/\psi$ production at HERA in the color singlet model with $k_{\mathrm{T}}$ -factorization

In the framework of the $k_{\mathrm{T}}$ -factorization QCD approach and the color singlet model we consider $J/\psi$ inelastic photo- and leptoproduction processes at HERA. We investigate the dependences of the single differential and double differential cross section on various forms of the unintegrated gluon distribution. The z and ${\vec p}_{\mathrm {T}}$ dependences of the spin alignment parameter $\alpha$ are presented also. Our theoretical predictions agree well with the recent data taken by the H1 and ZEUS collaborations at HERA. It is shown that the experimental study of the polarization $J/\psi$ mesons at the low value $Q^2 < 1{\mathrm {GeV}}^2$ is an additional test of BFKL gluon dynamics.

Dynamics of particle production in relativistic nuclear collisions

Saturation models for particle production in relativistic nuclear collisions are discussed. In particular, I show that the predictions from the high density QCD for the qualitative shape of dN/dy are very sensitive to the form of the unintegrated gluon distribution.

Heavy quark photoproduction in thek⊥-factorization approach

We investigate heavy quark photoproduction based on the ${\mathit{k}}_{\ensuremath{\perp}}$-factorization approach, focusing on the results from the saturation model. The deviations between the results using the unintegrated gluon distribution considering the saturation model and the derivative of the collinear gluon distribution are analyzed. Total cross sections and ${p}_{T}$ distributions are analyzed in detail, giving the deviations between the results of the color dipole approximation and the complete semihard approach.

Decomposition of the QCD string into dipoles and unintegrated gluon distributions

We present the perturbative and non-perturbative QCD structure of the dipole-dipole scattering amplitude in momentum space. The perturbative contribution is described by the two-gluon exchange and the non-perturbative contribution by the stochastic vacuum model which leads to confinement of the quark and antiquark in the dipole via a string of color fields. This QCD string gives important nonperturbative contributions to high-energy reactions. A new structure different from the perturbative dipole factors is found in the string-string scattering amplitude. The string can be represented as an integral over stringless dipoles with a given dipole number density. This decomposition of the QCD string into dipoles allows us to calculate the unintegrated gluon distribution of hadrons and photons from the dipole-hadron and dipole-photon cross section via $|{k}_{\ensuremath{\perp}}|$ factorization.

Saturation and Wilson line distribution

We introduce a Wilson line distribution function bar{W}_tau(v) to study gluon saturation at small Feynman x_F, or large tau=ln(1/x_F). This new distribution can be obtained from the distribution W_tau(alpha) of the Color Glass Condensate model and the JIMWLK renormalization group equation. bar{W}_tau(v) is physically more relevant, and mathematically simpler to deal with because of unitarity of the Wilson line v. A JIMWLK equation is derived for bar{W}_tau(v); its properties are studied. These properties are used to complete Mueller's derivation of the JIMWLK equation, though for bar{W}_tau(v) and not W_tau(alpha). They are used to derive a generalized Balitsky-Kovchegov equation for higher multipole amplitudes. They are also used to compute the unintegrated gluon distribution at x_F=0, yielding a completely flat spectrum in transverse momentum squared k^2, with a known height. This is similar but not identical to the mean field result at small k^2.

A simple model for nuclear structure functions at small x in the dipole picture

A simple model for nuclear structure functions in the region of small x and small and moderate $Q^2$, is presented. It is a parameter-free extension, in the Glauber-Gribov approach to nuclear collisions, of a saturation model for the nucleon. A reasonable agreement with experimental data on ratios of nuclear structure functions is obtained. Nuclear effects in the longitudinal-to-transverse cross section ratios are found to be small. Predictions of the model for values of $x$ smaller than those available to present experiments are given. The unintegrated gluon distribution and the behaviour of the saturation scale which result from this model are shown and discussed.

The contribution of off-shell gluons to the structure functions F 2 and $F_{\mathrm {L}}^c$ and the unintegrated gluon distributions

We calculate the perturbative parts of the structure functions $F_2^c$ and $F_L^c$ for a gluon target having nonzero transverse momentum squared at order $\alpha_s$. The results of the double convolution (with respect to the Bjorken variable $x_B$ and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with HERA experimental data for $F_2^c$. The contribution from $F_L^c$ structure function ranges (10-30)% of that of $F_2^c$ at the kinematical range of HERA experiments.

Enhanced minijet production in A–A collisions from gluons with large transverse momenta

We find supersaturation for the intrinsic gluon distribution of nuclei, i.e. the low $x$ unintegrated nuclear gluon distribution peaks at intermediate transverse momenta $k_t=Q_s$ and vanishes at zero $k_t$. Taking into account the intrinsic transverse momenta of the gluons and the saturation scale $p_s$ of the produced gluons, we calculate the minijet cross section arising from gluon gluon scattering for RHIC energies. For central collisions at $\sqrt{s}=200GeV$ the saturation scale $p_s \approx 1.4$ GeV is larger due to intrinsic $k_t$ effects and increases with energy. Our theoretical results on charged particle multiplicity agree very well with the recent experimental data from RHIC.

QCD factorization for the pion diffractive dissociation to two jets

We calculate the cross section of a pion diffraction dissociation in two jets with large transverse momenta originating from a hard gluon exchange between the pion constituents. To the leading logarithmic accuracy (in energy), the contribution coming from small transverse separations between the quark and the antiquark in the pion acquires the expected factorized form, the longitudinal momentum distribution of the jets being proportional to the pion distribution amplitude. The hard gluon exchange can in this case be considered as a part of the unintegrated gluon distribution. Beyond the leading logarithms (in energy) this proportionality does not hold. Moreover, the collinear factorization appears to be broken by the end-point singularities. Remarkably enough, the longitudinal momentum distribution of the jets for the non-factorizable contribution is calculable, and turns out to be the same as for the factorizable contribution with the asymptotic pion distribution amplitude.

Gluon shadowing in the low x region probed by the LHC

Starting from an unintegrated gluon distribution which satisfies a ‘unified’ equation which embodies both BFKL and DGLAP behaviour, we compute the shadowing corrections to the integrated gluon in the small x domain that will be accessible at the LHC. The corrections are calculated via the Kovchegov equation, which incorporates the leading ln(1/ x) triple-pomeron vertex, and are approximately resummed using a simple Padé technique. We find that the shadowing corrections to xg( x, Q 2) are rather small in the HERA domain, but lead to a factor of 2 suppression in the region x∼10 −6, Q 2∼4 GeV 2 accessible to experiments at the LHC.

Mapping the proton unintegrated gluon distribution in dijets correlations in real and virtual photoproduction at HERA

We discuss how the dijet azimuthal correlations in DIS and real photoproduction at HERA probe the differential (unintegrated) gluon distribution in the proton. We find a strong dependence of the azimuthal correlation pattern on Bjorken- x, photon virtuality and the cut on the jet transverse momenta. A rise of the azimuthal decorrelations is observed with decreasing Bjorken- x due to the interplay of perturbative and nonperturbative effects. We predict a strong rise of the same-side jet rate with photon energy for real photoproduction. We discuss conditions for the correlation function to be dominated by hard perturbative gluons and ways of constraining the size of the nonperturbative soft component. We make some predictions for the THERA energy range. The analysis of the energy dependence of the isolated jet and two-jet cross sections in photoproduction would be a new way to study the not yet well constrained unintegrated gluon distributions and to explore the onset of the pQCD regime.

Unintegrated gluon distribution from the Ciafaloni-Catani-Fiorani-Marchesini equation

The gluon distribution ${f(x,k}_{t}^{2},{\ensuremath{\mu}}^{2}),$ unintegrated over the transverse momentum ${k}_{t}$ of the gluon, satisfies the angular-ordered CCFM equation which interlocks the dependence on the scale ${k}_{t}$ with the scale $\ensuremath{\mu}$ of the probe. We show how, to leading logarithmic accuracy, the equation can be simplified to a single-scale problem. In particular we demonstrate how to determine the two-scale unintegrated distribution ${f(x,k}_{t}^{2},{\ensuremath{\mu}}^{2})$ from knowledge of the integrated gluon obtained from a unified scheme embodying both BFKL $[\mathrm{log}(1/x)]$ and DGLAP $(\mathrm{log}{\ensuremath{\mu}}^{2})$ evolution.

HEAVY QUARK PHOTOPRODUCTION IN THE SEMIHARD QCD APPROACH AND THE UNINTEGRATED GLUON DISTRIBUTION

Processes of heavy quark photoproduction at HERA energies are considered using the semihard (k⊥ factorization) QCD approach with emphasis of the BFKL dynamics of gluon distributions. We investigate the dependences of the total cross-section of heavy quark photoproduction and also the pT distribution on different forms of the unintegrated gluon distribution. We present a comparison of the theoretical results with available H1 and ZEUS experimental data for charm and beauty photoproductions.

STUDY OF BFKL GLUON DYNAMICS IN HEAVY QUARKONIUM PHOTOPRODUCTION AT HERA

In the framework of semihard QCD approach we consider the processes of inelastic heavy quarkonium photoproduction at HERA with emphasis on the BFKL dynamics of gluon distributions. We investigate the dependences of the total cross-section of inelastic J/Ψ photoproduction and also pT and z spectra on different forms of the unintegrated gluon distribution. It is shown that the total cross-section is most sensitive to the Pomeron intercept parameter Δ. We compare the theoretical results with the available H1 and ZEUS experimental data.

Angular ordering and structure functions at small χ

We examine the effect of using an angular ordered evolution equation for the unintegrated gluon distribution at small χ.