We continue our studies of possible generalization of the Color Glass Condensate (CGC) effective theory of high energy QCD to include the high $p_t$ (or equivalently large $x$) QCD dynamics as proposed in [JJM-elastic]. Here we consider scattering of a quark from both the small and large $x$ gluon degrees of freedom in a proton or nucleus target and derive the full scattering amplitude by including the interactions between the small and large $x$ gluons of the target. We thus generalize the standard eikonal approximation for parton scattering which can now be deflected by a large angle (and therefore have large $p_t$) and also lose a significant fraction of its longitudinal momentum (unlike the eikonal approximation). The corresponding production cross section can thus serve as the starting point toward derivation of a general evolution equation that would contain DGLAP evolution equation at large $Q^2$ and the JIMWLK evolution equation at small $x$. This amplitude can also be used to construct the quark Feynman propagator which is the first ingredient needed to generalize the Color Glass Condensate (CGC) effective theory of high energy QCD to include the high $p_t$ dynamics. We outline how it can be used to compute observables in the large $x$ (high $p_t$) kinematic region where the standard Color Glass Condensate formalism breaks down.
A new geometrical scaling method with gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate the net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distribution…
Progresses towards the calculation and the understanding of NLO/NLL contributions to Deep Inelastic Scattering at low x with gluon saturation are being reviewed.
The discriminators of quark-gluon jets developed for $pp$ collisions at the LHC can be used to measure the gluon jet fraction in a jet sample. It allows to measure various characteristics of the quark and gluon jets. The methodology of such measurements for modern hadron colliders is discussed.
We present a short survey of the theoretical expectations on glueballs and hybrids as well as of the present phenomenological status. The possibility to obtain new information on gluonic mesons from the study of gluon jets in comparison to quark jets is discussed.
The leading order single inclusive soft gluon production in high energy proton-nucleus (pA) collisions has been studied by various approaches for more than two decades. The first correction due to the gluon saturation in proton was analytically attempted recently through a diagrammatic approach in which only partial results were obtained. An important feature of the first saturation correction is that it includes both initial state and final state interactions. In this paper, we present the complete result derived from the Color Glass Condensate framework. Our approach is to analytically solve…
We analyse forward-jet production at HERA in the framework of the Golec-Biernat and Wusthoff saturation models. We obtain a good description of the forward jet cross sections measured by the H1 and ZEUS collaborations in the two-hard-scale region kT ~ Q >> Lambda_QCD with two different parametrisations with either significant or weak saturation effects. The weak saturation parametrization gives a scale compatible with the one found for the proton structure function F_2. We argue that Mueller-Navelet jets at the Tevatron and the LHC could help distinguishing between both options.
Deep inelastic scattering at low x can be described by essentially only two fitted parameters. The interpretation of J/Psi photoproduction in terms of the gluon structure function is elaborated upon.
We consider a novel mechanism for J/Psi production in nuclear collisions arising due to the high density of gluons. We calculate the resulting J/Psi production cross section as a function of rapidity and centrality. We evaluate the nuclear modification factor and show that the rapidity distribution of the produced J/Psi's is significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate that gluon saturation in the colliding nuclei is a significant source of J/Psi suppression that can be disentangled from the quark-gluon plasma effects.
We calculate the unintegrated gluon distribution at low intrinsic transverse momenta and its parameters are found from the best description of the SPS and LHC data on the $pp$ collision in the soft kinematical region. It allows us to study the saturation of the gluon density at low $Q^2$ more carefully and find the saturation scale.
We report on the interesting possibility of instanton-driven gluon saturation in lepton-nucleon scattering at small Bjorken-x. The explicitly known instanton gauge field serves as a concrete realization of an underlying non-perturbative saturation mechanism associated with strong classical fields. The conspicuous, intrinsic instanton size scale known from lattice simulations, turns out to determine the saturation scale. The ``colour glass condensate'' can be identified in our approach with the QCD-sphaleron state, dominating instanton-induced processes in the softer regime.
Parton distributions in the small $x$ region are numerically predicted by using a modified DGLAP equation with the GRV-like input distributions. We find that gluon recombination at twist-4 level obviously suppresses the rapid growth of parton densities with $x$ decrease. We show that before the saturation scale $Q^2_s$ is reached, saturation and partial saturation appear in the small $x$ behavior of parton distributions in nucleus and free proton, respectively. The antishadowing contributions to the saturation phenomena are also discussed.
We present an overview of theoretical aspects of the phenomenon of gluon saturation in high energy scattering in Quantum Chromo Dynamics. Then we review the state-of-the-art of saturation-based phenomenological approaches to the study and characterisation of the initial state of ultra-relativistic heavy ion collisions performed at RHIC and the LHC. Our review focuses mostly in the Color Glass Condensate effective theory, although we shall also discuss other approaches in parallel.
We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $σ(x,r)/α(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.
The properties of quark and gluon jets depend on jet definitions and event selection. I discuss how these can be included in calculations and present jet definitions designed to give unbiased jets.
We show that the inclusion of parton density effects in the perturbative small-x evolution reduces the strength of the powerlike growth of total hadronic cross sections.
Our approach to low-x deep inelastic scattering based on the ell-perp factorization of perturbative QCD (the color-dipole picture) yields parameter-free absolute predictions for J/Psi production. The connection of J/Psi production to the low-x saturation scale and to the gluon structure function is clarified.
Signatures of dominant and central production of glueballs (binary gluonic mesons) in heavy ion and hadromic collisions are discussed. Search strategies are proposed.
We derive the medium-induced, coherent gluon radiation spectrum associated with the hard forward scattering of an energetic parton off a nucleus, in the saturation formalism and within the Gaussian approximation for the relevant correlators of Wilson lines. The calculation reproduces the simple expression for the spectrum previously obtained in the opacity expansion formalism, and rigorously specifies its validity range. The connection between the calculations in the opacity expansion and saturation formalisms is made apparent. This study may serve as a first step in order to implement consist…
Gluon distribution function at small x is computed using the extended McLerran-Venugopalan model. A lipatov like enhancement is seen as well as a non-trivial transverse momentum dependence which is estimated. It is shown that gluon density saturates at small x which would lead to unitarization of cross sections computed with this distribution function.
The CCFM equation and its extended form with a quadratic term (KGBJS equation) are solved with fixed and running coupling constant. The solution of the KGBJS equation is compared to gluon densities resulting from the CCFM and BK equations. As the saturation scale $Q_s$ now becomes available as a function of the hard scale $p$ we observe that low values of $p$ impede its growth with $\frac 1 x$. Also, at values much larger than partons transversal momentum the saturation effects become independent on the hard scale what we call liberation of saturation scale. We also introduce the hard-scale-re…
We construct a Gaussian approximation to the effective theory for the Colour Glass Condensate which describes correctly the gluon distribution both in the low density regime at high transverse momenta (above the saturation scale $Q_s$), and in the high density regime below $Q_s$, and provides a simple interpolation between these two regimes. At high momenta, the effective theory reproduces the BFKL dynamics, while at low momenta, it exhibits gluon saturation and, related to it, colour neutrality over the short distance scale $1/Q_s \ll 1/Λ_{QCD}$. Gauge--invariant quantities computed within th…
This is a summary of the latest results of the DELPHI Collaboration on the properties of identified quark and gluon jets. It covers the measurement of the fragmentation functions of gluons and quarks and their scaling violation behaviour as well as an analysis of the scale dependence of the multiplicities in gluon and quark jets. Further, a precision measurement of CA/CF from the multiplicities in symmetric three jet events is discussed.
At very high energies, the relevant component of the hadron wavefunction can be described as a Color Glass Condensate, i.e., a state of high density gluonic matter whose distribution is random, but frozen over the relevant time scales. The weight function for this distribution obeys a renormalization group equation in the form of a functional Fokker-Planck equation. Its solution leads to an effective theory which predicts gluon saturation at sufficiently high energy, or small Bjorken's $x$.
We study the $p/π$ ratio in jets produced in simulated proton-proton collisions at $\sqrt{s_{NN}}=7~\mathrm{TeV}$ using Pythia $6.4$ Monte-Carlo generator. We compare the $p/π$ ratio in the selected quark-like and gluon-like jets to a reference samples of quark- and gluon-jets tagged at Monte-Carlo level. We observe that the contamination in the selected jets significantly influences the observed ratios. This suggests, that the origin of the jet fixes the value of the $p/π$ ratio within the model that we use.
Standard perturbative calculations lead to pathologically large NLO corrections to low-$x_{Bj}$ evolution equations like BFKL and BK. Using a more refined treatment of kinematics in mixed-space, relevant when gluon saturation sets on, one obtains an improved version of the BK equation, resumming to all orders the most severe of those large higher order corrections.
We review the recent developments of the QCD shockwave approach at Next-to-Leading Order. The general method of this effective action is sketched, and illustrated by the case of diffractive processes.
The characters of the angular distributions of quark jets and gluon jets with different flavors are carefully studied after introducing the cone angle of jets. The quark jets and gluon jets are identified from the 3-jet events which are produced by Monte Carlo simulation Jetset7.4 in e+e- collisions at $\sqrt s$=91.2GeV. It turns out that the ranges of angular distributions of gluon jets are obviously wider than that of quark jets at the same energies. The average cone angles of gluon jets are much larger than that of quark jets. As the multiplicity or the transverse momentum increases, the co…
We study a possibility of observation of the first Kaluza-Klein (KK) excitation of gluon in a warped extra dimension model at the LHC. In our analysis, we adopt the KK gluon mass and the b-quark coupling to the KK gluon as model parameters and study the sensitivity of the ATLAS experiment to observe the KK gluon through the two $b$-jets channel.
Three jets events in the e$^+$e$^-$ collisions at 91.2 GeV are investigated using both HERWIG and JETSET Monte Carlo generators. The angles between the three jets are used to identify the quark and gluon jets. The analysis at parton level is done to ensure the reasonableness of this method and an angular cut is ultilized to improve the purity of this identification. The multiplicity inside the identified quark or gluon jets agree with the QCD predictions.
We discuss the recent observation of f_0(980) in charmless B-decays and in gluon jets which hints toward a gluonic coupling of this meson similar to eta'. Further predictions on B-decays into scalar particles are presented. Charmless B decays also show a broad K Kbar (and possibly pi pi) S-wave enhancement which we relate to the 0^{++} glueball. These gluonic mesons represent a sizable fraction of the theoretically derived decay rate for b -> sg.
At very high energies we expect that the hadronic cross sections satisfy the Froissart bound, which is a well-established property of the strong interactions. In this energy regime we also expect the formation of the Color Glass Condensate, characterized by gluon saturation and a typical momentum scale: the saturation scale $Q_s$. In this paper we show that if a saturation window exists between the nonperturbative and perturbative regimes of Quantum Chromodynamics (QCD), the total cross sections satisfy the Froissart bound. Furthermore, we show that our approach allows us to describe the high …
We calculate the mean number of subjets in quark and gluon jets in the final state of e^+e^- annihilation. Since `quark' and `gluon' jets are scheme-dependent objects, we stress the importance of using the same definition as in experimental analyses. We define the jets using the k_perp algorithm at a coarse scale y_1, and the subjets using a finer scale y_0, in the same algorithm. Gluon jets are anti-tagged by the presence of heavy quarks in both other jets. Our result is exact to leading order in alpha_s, and resums leading and next-to-leading logarithmic terms in the ratio y_1/y_0 to all ord…
The high energy limit of QCD is controlled by very high energy density gluonic matter, the Color Glass Condensate. In the first instants of the collisions of two sheets of Colored Glass Condensate, a Glasma is formed with longitudinal flux tubes of color electric and magnetic fields. These flux tubes decay and might form a turbulent liquid that eventually thermalizes into a Quark Gluon Plasma
We study the effects of gluon saturation on pion production in high energy proton-nucleus collisions using the color glass condensate model. At high p_perp, we show that the p_perp-distribution of gluons behaves as ~ 1/(p_perp^7) in accordance with both conventional perturbative QCD calculations and experiment. Fragmentation of gluons into pions leads to a rapidity dependent depletion of pions relative to the conventional perturbative QCD predictions. We argue that these clear and systematic differences provide a signal for the onset of gluon saturation which is accessible in upcoming experime…
In this paper we complete our calculation of the NLO jet vertex which is part of the cross section formulae for the production of Mueller Navelet jets at hadron hadron colliders and of forward jets in deep inelastic electron proton scattering.
Almost 40 years ago, Gribov and colleagues at the Leningrad Nuclear Physics Institute developed the ideas that led to the Dokhsitzer-Gribov-Altarelli-Parisi the Baltisky-Fadin-Kuraev-Lipatov equations. These equations describe the evolution of the distributions for quarks and gluon inside a hadron to increased resolution scale of a probe or to smaller values of the fractional momentum of a hadronic constituent. I motivate and discuss the generalization required of these equations needed for high energy processes when the density of constituents is large. This leads to a theory of saturation re…
This is a short presentation of our talks given at eRHIC Workshop at the BNL. We give here a status report of our attempts to understand how gluon saturation will manifest itself in deep inelastic scattering with nuclei. This summary reflects our current understanding and shows directions of our research rather then a final answer to the question. Nevertheless, we are able to share with our reader our tentative answer to the question:``Why do we need to measure DIS with nuclei and why these data will be complementary to the information obtained from proton DIS".
Higgs production in association with three jets via gluon fusion (GF) is an important channel for the measurement of the CP-properties of the Higgs particle at the LHC. In this letter, we go beyond the heavy top effective theory approximation and include at LO the full mass dependence of the top- and bottom-quark contributions. We consider the dominant sub-channel gg -> H ggg which involves the manipulation of massive rank-5 hexagon integrals. Furthermore, we present results for several differential distributions and show deviations from the effective theory as large as 100% at high pT for lig…
Using the Landshoff-Nachtmann two-gluon exchange model of the pomeron, the double pomeron exchange contribution to production of gluon pairs in the central region of rapidity is calculated. The results are compared with those for production of quark-antiquark pairs.
The solution of the equations for the generating functions of multiplicity distributions of quark and gluon jets in higher order 3NLO perturbative QCD is obtained. The non-perturbative effects are discussed as well. The results are compared to recent experimental data on mean multiplicities, their ratio and its slope, higher moments of the distributions.
We use data on the deep inelastic structure function F_2 in order to constrain the cross-section for scattering a colour dipole off a proton. The data seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r < r_s(x) where r_s(x) decreases monotonically as x decreases. Subsequent predicitions for the diffractive structure function F_2^{D(3)} also hint at saturation, although the data are not really sufficiently accurate.
We address aspects of jet physics at the Large Hadron Collider focusing on features of recent jet measurements which challenge the theory. We discuss examples illustrating the role of QCD parton showers, nonperturbative corrections, soft multi-gluon emission.
We investigate photo-production of vector mesons J/Psi and Upsilon measured both at HERA and LHC, using 2 particular fits of inclusive unintegrated gluon distributions, based on non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution (Hentschinski-Sabio Vera-Salas gluon; HSS). We find that linear next-to-leading order evolution can only describe production at highest energies, if perturbative corrections are increased to unnaturally large values; rendering this corrections to a perturbative size, the growth with energy …
We study the effect of soft gluon resummation on the gaps-between-jets cross-section at the LHC. We review the theoretical framework that enables one to sum logarithms of the hard scale over the veto scale to all orders in perturbation theory. We then present a study of the phenomenological impact of Coulomb gluon contributions and super-leading logarithms on the gaps between jets cross-section at the LHC.
We analyze three jet production in the central-forward and forward rapidity regions in proton-proton and proton-lead collisions at LHC energies. Our calculation relies on high-energy factorization with a single off-shell gluon obeying small x evolution equation which includes saturation. The calculations are made using two independent Monte Carlo codes implementing tree-level gauge invariant off-shell matrix elements. We calculate differential cross sections for azimuthal decorrelations and unbalanced jet transverse momenta and discuss them in the context of differences in the evolution of the…
The QCD evolution equations in Modified Leading Log Approximation for the factorial moments of the multiplicity distribution in quark and gluon jets are numerically solved with initial conditions at threshold by fully taking into account the energy conservation law. After applying Local Parton Hadron Duality as hadronization prescription, a consistent quantitative description of available experimental data for factorial cumulants and factorial moments of arbitrary order and for their ratio both in quark and gluon jets and in $e^+e^-$ annihilation is achieved.
The complete QCD evolution equation for factorial moments in quark and gluon jets is numerically solved with initial conditions at threshold by fully taking into account the energy-momentum conservation law. Within the picture of Local Parton Hadron Duality, the perturbative QCD predictions can successfully describe the available experimental data.
We study the gluon content of a large nucleus (i) in the semi-classical McLerran-Venugopalan model and (ii) in the high energy limit as given by the quantum evolution of the Color Glass Condensate. We give a simple and qualitative description of the Cronin effect and high-pT suppression in proton-nucleus collisions.
In this paper we discuss the example of one rapidity gap process: the inclusive cross sections of the leading neutrons in deep inelastic scattering with protons (DIS). The equations for this process are proposed and solved, giving the example of theoretical calculation of the survival probability for one rapidity gap processes. It turns out that the value of the survival probability is small and it decreases with energy
The energy evolution of average multiplicities of quark and gluon jets is studied in perturbative QCD. Higher order (3NLO) terms in the perturbative expansion of equations for the generating functions are found. First and second derivatives of average multiplicities are calculated. The mean multiplicity of gluon jets is larger than that of quark jets and evolves more rapidly with energy. It is shown which quantities are most sensitive to higher order perturbative and nonperturbative corrections. We define the energy regions where the corrections to different quantities are important. The lates…
Recently, an exact conformal mapping between soft gluons emitted from jets at large angle in e+e- annihilation and those in the BFKL evolution of a high energy hadron has been proposed. We elucidate some remarkable aspects of this correspondence and use them to analytically compute the distribution and correlation of gluons in the interjet region. We also establish the timelike counterpart of Mueller's dipole model and discuss the resulting linear and nonlinear evolution equations.
The second and third factorial moments of the multiplicity distributions of gluon and quark jets are calculated up to the next-to-next-to-next-to leading order in perturbative QCD, using the equations for generating functions. The results are confronted with experimental data. A general discussion on high order corrections revealed by such an approach is given. Other possible corrections and approaches are discussed as well.
The difference between the ratio of multiplicities and the ratio of their derivatives on energy for gluon and quark jets is calculated up to next-to-next-to leading order of perturbative QCD. Its non-zero value is uniquely defined by the running property of the QCD coupling constant. It is shown that this difference is rather small compared to values which can be obtained from experimental data. This disagreement can be ascribed either to strong non-perturbative terms or to experimental problems with a scale choice, jets separation and inadequate assignement of soft particles to jets.
The paper presents a system of nonlinear Lorentz-invariant equations. The behavior of their localized solutions is analogous to the processes of formation of azimuthal-anisotropic elliptical flows of quark-gluon plasma and hadron jets. In contrast to the hydrodynamic models of an ideal fluid, the elliptic flow in this model has a significant negative acceleration. The presence of the negative acceleration allows us to propose a hypothesis about the direct elliptic flow of photons as braking radiation QGP.
We study the new relation [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments D_{q,g}(μ^2) of the fragmentation functions, which correspond to the average multiplicities of hadrons in jets initiated by quarks and gluons, respectively. This relation is shown to lead to probabilistic properties of the properly rescaled parton jet multiplicities obtained from standard ones by extracting the quark and gluon "color charges" C_F and C_A, respectively.
We test several BFKL-like evolution equations for unintegrated gluon distributions against forward-central dijet production at LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimuthal decorrelations for forward-central dijet production and compare with existing data.
