The central exclusive production of $χ_{c}$ and $χ_{b}$ at the LHC, RHIC and Tevatron energies is analyzed, using the recent unintegrated parton distribution (UGDs) functions available in the package TMDlib. Comparison with data is performed, which tests the underlying assumptions basing the theoretical approach and it can constrain the unintegrated gluon distribution function at the small-$x$ region. Predictions for LHC energies using recent UGDs based in CCFM formalism are provided. It is explored the underlying uncertainties on this production as the choice for the unintegrated gluon distribution and factorization scale is done. Moreover, based on the parton saturation model for the gluon distribution, analytical expressions for the rapidity distributions are proposed. The prompt production of $J/ψ+γ$ and $Υ+γ$ is computed for the first time for LHC energies within the very same formalism used for $χ$ production.
The exclusive production of vector mesons and photons in $ep$ collisions is investigated considering three phenomenological saturation models based on distinct assumptions for the treatment of the dipole - hadron scattering amplitude. The latest high precision HERA data for the reduced and vector meson cross sections are used to update the saturation model proposed by Marquet - Peschanski - Soyez (MPS), which predicts that the saturation model is dependent of the squared momentum transfer $t$. The MPS predictions for the photon virtuality, energy and $t$ - dependencies of the exclusive $ρ$, $J…
Two-particle azimuthal angle correlations have been proposed to be one of the most direct and sensitive probes to access the underlying gluon dynamics involved in hard scatterings. In anticipation of an Electron-Ion Collider (EIC), detailed studies of dihadron correlation measurements in electron-proton and electron-ion collisions at an EIC have been performed. The impact of such measurements on the understanding of the different gluon distribution functions, as a clean signature for gluon saturation and to constrain saturation models further, has been explored. It is shown that dihadron corre…
Being the "mother distributions" of all types of two-parton correlation functions, generalized transverse momentum dependent parton distributions (GTMDs) have attracted a lot of attention over the last years. We argue that exclusive double production of pseudoscalar quarkonia ($η_c$ or $η_b$) in nucleon-nucleon collisions gives access to GTMDs of gluons.
We present the results of recent work on the central exclusive production of meson pairs. We concentrate on the case of flavour-singlet pseudoscalar mesons eta, eta' and show that the central exclusive process, as modelled using a recent novel application of the 'hard exclusive' perturbative formalism, is potentially highly sensitive to the size of the gluon content of these states. We also discuss the exclusive production of meson pairs in the lower mass region, and present the first results of the new Dime Monte Carlo.
The exclusive production of axionlike particles (ALPs) by gluon -- induced interactions is investigated in this exploratory study considering $pp$ and $PbPb$ collisions for the energies of the next run of the Large Hadron Collider (LHC). Assuming the Duhram model, we estimate the associated cross sections for the rapidity ranges probed by central and forward detectors. A comparison with the predictions for the exclusive ALP production by photon -- induced interactions is presented. Our results indicate that the contribution of gluon -- induced interactions is nonnegligible and can become domin…
In this letter we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the $t$ - spectrum measured in exclusive $ρ$ and $J/Ψ$ photoproduction in $pA$ collisions at the LHC. We compute the differential cross sections considering two phenomenological models for the gluon saturation effects and present predictions for $pPb$ and $pCa$ collisions. Moreover, we compare our predictions with the recent preliminary CMS data for the exclusive $ρ$ photoproduction. We demonstrate that the gluon saturation models are able to des…
We present two NLO exclusive impact factors computed in the QCD shock wave approach. These are the very first steps towards precision studies of a wide range of high energy exclusive processes with saturation effects in $ep$, $eA$, $pp$ and $pA$ collisions.
The current uncertainty on the gluon density extracted from the global parton analysis is large in the kinematical range of small values of the Bjorken - $x$ variable and low values of the hard scale $Q^2$. An alternative to reduces this uncertainty is the analysis of the exclusive vector meson photoproduction in photon - hadron and hadron - hadron collisions. This process offers a unique opportunity to constrain the gluon density of the proton, since its cross section is proportional to the gluon density squared. In this paper we consider current parametrizations for the gluon distribution an…
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…
Using the framework of collinear factorization in perturbative QCD (pQCD), we analyze the recent data of the LHCb and ALICE collaborations on exclusive photoproduction of J/ψ in ultraperipheral pp and AA collisions, respectively. We demonstrate that the simultaneous analysis of the proton and Pb data allows us to reduce the ambiguity of the pQCD description of the $γp \to J/ψp$ and $γA \to J/ψp$ cross sections and, hence, to place additional constraints on the gluon distributions in the nucleon and nuclei at small x. We also make predictions for the cross section of coherent exclusive photopro…
In the framework of the QCD shock-wave approach, we review our results on the description of diffractive production of various final states (jets, meson) at next-to-leading order. This is applied to exclusive diffractive dijet electroproduction at HERA.
Progresses towards the calculation and the understanding of NLO/NLL contributions to Deep Inelastic Scattering at low x with gluon saturation are being reviewed.
We compare the contributions from quark and from gluon exchange to the exclusive process gamma* p -> rho0 p. We present evidence that the gluon contribution is substantial for values of the Bjorken variable xB around 0.1.
We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing t…
Following recent predictions that the geometric scaling properties of deep inelastic scattering data in inclusive gamma*-p collisions are expected also in exclusive diffractive processes, we investigate the diffractive production of vector mesons. Using analytic results in the framework of the BK equation at non-zero momentum transfer, we extend to the non-forward amplitude a QCD-inspired forward saturation model including charm, following the theoretical predictions for the momentum transfer dependence of the saturation scale. We obtain a good fit to the available HERA data and make predictio…
We systematically study exclusive diffractive (photo) production of vector mesons ($J/ψ$, $ψ(2s)$, $ϕ$ and $ρ$) off protons in high-energy collisions and investigate whether the production is a sensitive probe of gluon saturation. We confront saturation-based results for diffractive $ψ(2s)$ and $ρ$ production at HERA and $J/ψ$ photoproduction with all available data including recent ones from HERA, ALICE and LHCb, finding good agreement. In particular, we show that the $t$-distribution of differential cross sections of photoproduction of vector mesons offers a unique opportunity to discriminat…
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 provide a universal expression of cross sections for the exclusive vector meson production and Deeply Virtual Compton Scattering (DVCS) in photon-proton and photon-nucleus interactions based on the geometric scaling phenomenon. The theoretical parameterization based on the scaling property depends only on the single variable $τ_A = Q^2/Q_{\mathrm{sat}}^2$, where the saturation scale, $Q_{\mathrm{sat}}$, drives the energy dependence and the corresponding nuclear effects. This phenomenological result describes all available data from DESY-HERA for $ρ,\,ϕ,\,J/ψ$ production and DVCS measurement…
We investigate the implication of uncertainties in the unintegrated gluon distribution for the predictions for central exclusive production of scalars at hadron colliders. We use parameterizations of the kT-unintegrated gluon density obtained from the Linked Dipole Chain model, applying different options for the treatment of non-leading terms. We find that the luminosity function for central exclusive production is very sensitive to details of the transverse momentum distribution of the gluon which, contrary to the kT-integrated distribution, is not very well constrained experimentally.
We estimate the value of the survival probability for central exclusive production, in a model, which is based on the CGC/saturation approach. Hard and soft processes are described in the same framework. At LHC energies, we obtain a small value for the survival probability. The source of the small value, is the impact parameter dependence of the hard amplitude. Our model has successfully described a large body of soft data: elastic, inelastic and diffractive cross sections,inclusive production and rapidity correlations, as well as the $t$-dependence of deep inelastic diffractive production of …
We perform the first next-to-leading order computation of the $γ^{(*)} \to V$ ($ρ, ϕ, ω$) impact factor in the QCD shockwave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order, in various processes to be measured in $ep$, $eA$, $pp$ and $pA$ collisions at existing and future colliders.
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 propose a method to introduce Sudakov effects to the unintegrated gluon density promoting it to be hard scale dependent. The advantage of the approach is that it guarantees that the gluon density is positive definite and that the Sudakov effects cancel on integrated level. As a case study we apply the method to calculate angular correlations and $R_{pA}$ ratio for p+p vs. p+Pb collision in the production of forward-forward dijets.
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.
The exclusive vector meson production cross section is one of the most promising observables to probe the high energy regime of the QCD dynamics. In particular, the squared momentum transfer ($t$) distributions are an important source of information about the spatial distribution of the gluons in the hadron and about fluctuations of the color fields. In this paper we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the $t$ - spectrum measured in exclusive $ρ$, $ϕ$ and $J/Ψ$ photoproduction in $pp$ and $PbPb$ col…
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.
Forward photoproduction of $J/ψ$ can be used to extract Generalized Parton Distributions(GPD's) of gluons. We analyze the process at twist-3 level and study relevant classifications of twist-3 gluon GPD's. At leading power or twist-2 level the produced $J/ψ$ is transversely polarized. We find that at twist-3 the produced $J/ψ$ is longitudinally polarized. Our study shows that in high energy limit the twist-3 amplitude is only suppressed by the inverse power of the heavy quark mass relatively to the twist-2 amplitude. This indicates that the power correction to the cross-section of unpolarized …
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.
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.
Exclusive J/psi production, gamma* p -> J/psi p, offers a unique opportunity to determine the gluon density of the proton in the small x domain. We use the available HERA data to determine the gluon distribution in the region 10^{-4} <~ x <~ 10^{-2} and 2 <~ Q^2 <~ 10 GeV^2, where the uncertainty on the gluon extracted from the global parton analyses is large. The gluon density is found to be approximately flat at the lower scale; it is compared with those of recent global analyses.
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.
We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.
In exclusive $J/ψ$ production by polarized photons incident on polarized protons, a finite polarization asymmetry arises because of $c\bar c$ Fermi-motion and binding-energy effects. The asymmetry depends on the polarized nonforward gluon distribution of the proton and thus gives information on gluon polarization in the proton. The analyzing power, however, is rather small.
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…
We study properties of high energy factorisable gluon densities focusing on saturation effects. In particular we show that the property of saturation of unintegrated gluon density allows for introduction of thermodynamical entropy associated with production of gluons. This is due to the observation that saturation scale acts like a mass of a gluon which related with temperature via thermodynamical relations allows for calculations of entropy. We also show that obtained entropy behaves like multiplicity of produced gluons.
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…
Groundbreaking studies of exclusive physics processes at the Tevatron have demonstrated that proton-(anti)proton colliders are not only quark-antiquark but also gluon-gluon colliders, photon-photon and photon - gluon colliders. These studies are briefly reviewed in this paper.
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 $x$.
Within the archetypal factorization procedure, we study the gluon pole contributions manifesting in the nucleon-lepton hard processes of hadron production. We prove the dominant role of gluon pole contributions in the processes of such kind. We analyse the different sources of complexity associated with the gluon pole functions. As a practical application, we derive a new single spin asymmetry related directly to the gluon poles which can be studied experimentally.
In a previous report we used the Linked Dipole Chain model unintegrated gluon densities to investigate the uncertainties in the predictions for central exclusive production of scalars at hadron colliders. Here we expand this investigation by also looking at other parameterizations of the unintegrated gluon density, and look in more detail on the behavior of these at small k_T. We confirm our conclusions that the luminosity function for central exclusive production is very sensitive to this behavior. However, we also conclude that the available densities based on the CCFM and LDC evolutions are…
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 modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
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.
We use recent results for the gamma*L -> rhoL and gamma*T -> rhoT impact factors, computed in the impact parameter representation within the collinear factorization scheme, to get predictions for the polarized cross-sections sigmaT and sigmaL of the diffractive leptoproduction of the rho meson at high energy. In this approach the helicity amplitude is a convolution of the scattering amplitude of a color dipole with a target, together with the virtual gamma wave function and with the first moments of the rho meson wave function (in the transverse momentum space), given by the distribution ampli…
In this paper, we study the application of the recently proposed soft gluon factorization (SGF) to exclusive quarkonium production or decay. We find that in the nonrelativistic QCD factorization framework there are too many nonperturbative parameters. Thanks to the factorization of kinematical physics from dynamical physics, the SGF significantly reduces the number of nonperturbative parameters. Therefore, the SGF can improve our predictive power of exclusive quarkonium production or decay. By applying to $η_c+γ$ production at B-factories, our result is the closest one to data among all theore…
New, more precise data on diffractive J/psi photoproduction and on exclusive J/psi production in the process pp -> p + J/psi + p at the LHC allow a better constraint on the low-x gluon distribution in the domain of relatively low scales Q^2 ~ 2-6 GeV^2. We account for the `skewed' effect and for the real part of the amplitude, as well as for the absorptive corrections in the case of the exclusive process pp -> p + J/psi + p. The predictions for exclusive J/psi production at \sqrt{s}=8 and 14 TeV and for exclusive Upsilon(1S) production at 7, 8 and 14 TeV are also given. We present results at l…
