We study coherent diffractive photon and vector meson production in electron-proton and electron-nucleus collisions within the Color Glass Condensate effective field theory. We show that electron-photon and electron-vector meson azimuthal angle correlations are sensitive to non-trivial spatial correlations in the gluon distribution of the target, and perform explicit calculations using spatially dependent McLerran-Venugopalan initial color charge configurations coupled to the numerical solution of small $x$ JIMWLK evolution equations. We compute the cross-section differentially in $Q^2$ and $|t|$ and find sizeable anisotropies in the electron-photon and electron-$\mathrm{J}/ψ$ azimuthal correlations ($v_{1,2} \approx 2 - 10 \%$) in electron-proton collisions for the kinematics of the future Electron-Ion Collider. In electron-gold collisions these modulations are found to be significantly smaller ($v_{1,2} <0.1 \%$). We also compute incoherent diffractive production where we find that the azimuthal correlations are sensitive to fluctuations of the gluon distribution in the target.
We calculate azimuthal correlations between the exclusively produced vector meson and the scattered electron in Deep Inelastic Scattering processes at the future Electron-Ion Collider (EIC). We identify "kinematical" and "intrinsic" contributions to these correlations, and show that the correlations are sensitive to the non-trivial correlations in the gluon distribution of the target. Realistic predictions at the EIC kinematics are provided using two different approaches to describe the dipole-proton interaction at relatively small $x$.
Azimuthal distributions in high-energy processes give information about the helicity structure of diffractive reactions. I discuss predictions of several dynamical mechanisms in this context, both for electron-proton and for hadron-hadron collisions.
We propose a new method of the determination of $R^{D}=σ_{L}^{D}/σ_{T}^{D}$ from the dependence of the diffractive cross section on the azimuthal angle between the electron scattering and proton scattering planes. The method is based on our finding of the model independence of the ratio of the $LT$ interference and transverse diffractive structure functions. The predicted azimuthal asymmetry is substantial and can be measured at HERA. We show that the accuracy of our reconstruction of $R^{D}$ is adequate for a reliable test of an important pQCD prediction of $R^{D}\gsim 1$ for large $β$.
We derive expressions for the gluon production cross sections in the single diffractive proton-nucleus scattering and DIS processes in a quasi-classical approximation. The resulting cross sections include the effects of all multiple rescatterings in the classical background field of the target proton or nucleus, which remains intact after the scattering. We also write down an expression for the inclusive gluon production cross section in DIS in the quasi-classical approximation.
We propose a new model for a homogeneous description of hadron-hadron and hadron-nucleus collisions, the Gluon Exchange Model, fundamentally based on color octet (gluon) exchange. In proton-proton collisions we provide an exact description of the final state proton and neutron spectrum including the proton diffractive peak. In proton-nucleus reactions we find that the projectile proton diquark cannot survive in more than about half of multiple proton-nucleon processes and consequently must be very frequently disintegrated, leading to long transfers of baryon number over rapidity space.
We investigate azimuthal correlations in deep inelastic diffractive scattering, e + p -> e + \tilde{p} + X. The dependence of the ep cross section on the angle between the lepton plane and some direction in the hadronic final state can be written in a simple form; its measurement can be used to constrain the cross section for longitudinally polarised photons. Using the model of nonperturbative two-gluon exchange of Landshoff and Nachtmann we calculate the distribution of the azimuthal jet angle in diffractive dijet production and find that useful bounds on the longitudinal cross section for su…
We discuss the leading particle spectra and diffractive mass spectra from the novel point of view, namely by treating them as particular examples of the general energy flow phenomena taking place in the multiparticle production processes. We argue that they show a high degree of universality what allows for their simple description in terms of the Interacting Gluon Model developed by us some time ago.
We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that bot…
We investigate the azimuthal distribution of quark-antiquark jets in DIS diffractive dissociation with large transverse momentum. In this kinematical region the matrix element is expressed in terms of the gluon structure function. For the transverse part of the cross section we find a $\cos(2 ϕ)$-distribution with the maximum at $ϕ= \pm π/2$, i.e.\ the jets prefer a direction perpendicular to the electron plane. This is in contrast to boson gluon fusion where the $q\bar{q}$ jet cross section for transversely polarized bosons peaks at $ϕ=0$ and $ϕ=π$. We discuss the origin of this striking diff…
Diffractive dijet production at the electron-ion collider (EIC) has been proposed to study the gluon Wigner distribution at small-$x$. We investigate the soft gluon radiation associated with the final state jets and an all order resummation formula is derived. We show that the soft gluon resummation plays an important role to describe E791 data on $π$-induced diffractive dijet production at Fermilab. Predictions for the EIC are presented, and we emphasize that the soft gluon resummation is an important aspect to explore the nucleon/nucleus tomography through these processes.
We study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
We investigate the close connection between the quantum phase space Wigner distribution of small-$x$ gluons and the color dipole scattering amplitude, and propose to study it experimentally in the hard diffractive dijet production at the planned electron-ion collider. The angular correlation between the nucleon recoiled momentum and the dijet transverse momentum will probe the nontrivial correlation in the phase space Wigner distribution. This experimental study will not only provide us with three-dimensional tomographic pictures of gluons inside high energy proton, but also give a unique and …
Fluctuations play an important role in diffractive production of vector mesons. It was in particular recently suggested, based on the Impact-Parameter dependent Saturation model (IPSat), that geometrical fluctuations triggered by the motion of the constituent quarks within the protons could explain incoherent diffractive processes observed at HERA. We propose a variant of the IPSat model which includes spatial and symmetry correlations between constituent quarks, thereby reducing the number of parameters needed to describe diffractive vector meson production to a single one, the size of the gl…
We have extended the Interacting Gluon Model (IGM) to calculate diffractive mass spectra generated in hadronic collisions. We show that it is possible to treat both diffractive and non-diffractive events on the same footing, in terms of gluon-gluon collisions. A systematic analysis of available data is performed. The energy dependence of diffractive mass spectra is addressed. They show a moderate narrowing at increasing energies. Predictions for LHC energies are presented.
Following our recent paper on the calculations of diffractive quark jet production at hadron colliders, we present here the calculations of gluon jet production at hadron colliders in the two-gluon exchange parameterization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formula. We find that for the gluon jet production the diffractive process is related to the differential off-diagonal gluon distribution function in the proton. We estimate the production rate for this process at the Fermilab Tevatron by approximating the off-diagonal gluon distributi…
We study exclusive dijet production in electron-proton deep inelastic scattering at a future Electron Ion Collider. We predict the elliptic modulation of the cross section as a function of the angle between the dijet transverse momentum and the recoil momentum, and show that this modulation is due to non-trivial angular correlations between the transverse coordinate and transverse momentum in the Wigner (or Husimi) distribution. The small-$x$ evolution is shown to decrease the elliptic modulation in the EIC kinematics, because of the growth of the proton with decreasing $x$.
We present a new technique to calculate the cross-section for diffractive vector meson production and DVCS in electron-ion collisions based on the dipole model. The measurement of these processes can provide valuable information on non-linear QCD phenomena, such as gluon saturation, and is the the only known way to gain insight into the spatial distribution of gluons in nuclei. We present predictions of differential cross-section distribution $dσ/dQ^2$ and $dσ/dt$ for $J/ψ$ and $ϕ$ meson production for diffractive processes of heavy nuclei and demonstrate the feasibility of extracting the gluo…
We have applied the Interacting Gluon Model (IGM) to calculate diffractive mass spectra measured recently in e-p collisions at HERA. We show that it is possible to treat them in terms of gluon-gluon collisions in the same way as was done before for hadronic collisions. Analysis of available data is performed.
Massless diquark jet and gluon jet productions at large transverse momentum in the coherent diffractive processes at hadron colliders are studied in the two-gluon exchange parametrization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formulas. We find that for the light quark jet and gluon jet production the diffractive process is related to t he differential off-diagonal gluon distribution function in the proton. We estimate the production rate for these processes at the Fermilab Tevatron by approximating the off-diagonal gluon distribution function…
We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating …
We study azimuthal asymmetries in diffractive J/$ψ$ production in ultraperipheral heavy-ion collisions at RHIC and LHC energies using the color glass condensate effective theory. Our calculation successfully describes azimuthal averaged $J/ψ$ production cross section measured by STAR and ALICE. We further predict very large $\cos 2ϕ$ and $\cos 4ϕ$ azimuthal asymmetries for diffractive $J/ψ$ production both in UPCs at RHIC and LHC energies and in eA collisions at EIC energy. These novel polarization dependent observables may provide complementary information for constraining gluon transverse sp…
We discuss diffractive dissociation of gluons into heavy quark pairs. The particular mechanism is similar to the diffractive dissociation of virtual photons into quarks, which drives diffractive deep inelastic production of charm in the low-mass diffraction, or large $β$-region. There, it can be understood, with some reservations, in terms of a valence heavy quark content of the Pomeron. The amplitude for the $g p \to Q \bar Q p$ is derived in the impact parameter and momentum space. The cross section for single diffractive $p p \to Q \bar Q p X$ is calculated as a convolution of the elementar…
Diffractive dijet photoproduction is proposed as a probe of the off-diagonal gluon distribution and its evolution. Predictions for the transverse momentum distribution of the jets are given. Differences with DGLAP evolution are highlighted.
Presented here is a study of the large p_T J/psi production in hard diffractive process by the pomeron exchange at the Fermilab Tevatron. We find that this process (p\bar p \to p+J/psi+X) can be used to probe the gluon content of the pomeron and to measure the gluon fraction of the pomeron. And the diffractive direct J/psi production can also provide another crucial test for the color-octet fragmentation mechanism. Using the renormalised pomeron flux factor D\approx 1/9, the single diffractive J/psi production cross section at large p_T (\geq 8GeV) is found to be of order of 0.01 nb, and the r…
The amplitude of diffractive $ρ$ (and open quark) leptoproduction on a polarized target is calculated in the leading log approximation of pQCD using the hadron-parton duality hypothesis. The spin-spin asymmetry is expressed in terms of the spin dependent gluon and quark structure functions in the small $x$ region. Therefore the $γ^*+p\to ρ+p$ reaction provides a promising tool to study the spin dependent gluon distribution $ΔG(x,q^2)$.
It is proposed, that color-singlet gluon-clusters can be formed in hadrons as a consequence of self-organized criticality (SOC) in systems of interacting soft gluons, and that the properties of such spatiotemporal complexities can be probed experimentally by examing inelastic diffractive scattering. Theoretical arguments and experimental evidences supporting the proposed picture are presented --- together with the result of a systematic analysis of the existing data for inelastic diffractive scattering processes performed at different incident energies, and/or by using different beam-particles…
Diffractive hard scattering is interpreted as the effect of soft gluon exchanges between the emerging energetic quarks and the nucleon's color field, resulting in an overall color singlet exchange. Summing multiple gluon exchanges to all orders leads to exponentiation and an amplitude in analytic form. Numerical evaluation reproduces the precise HERA data and gives new insights on the density of gluons in the proton.
We calculate spectrum of diffractively produced gluons in onium-heavy nucleus collisions at high energies. We show that it exhibits a characteristic dependence on nucleus atomic number A and energy/rapidity. We argue that this dependence offers a unique possibility for determining the low-x structure of nuclear matter. Applications to RHIC, LHC and EIC experimental programs are discussed.
Massless quark and antiquark jet production at large transverse momentum in the coherent diffractive processes at hadron colliders is calculated in the two-gluon exchange parametrization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formula. We find that for the light quark jet production the diffractive process is related to the differential off-diagonal gluon distribution function in the proton. We estimate the production rate for this process at the Fermilab Tevatron by approximating the off-diagonal gluon distribution function by the usual diagon…
Order $α_s$-corrections to the diffractive structure functions $F_L^D$ and $F_2^D$ at large $Q^2$ and small $x$ are evaluated in the semiclassical approach, where the initial proton is treated as a classical colour field. The diffractive final state contains a fast gluon in addition to a quark-antiquark pair. Two of these partons may have large transverse momentum. Our calculations lead to an intuitive picture of deep-inelastic diffractive processes which is very similar to Bjorken's aligned-jet model. Both diffractive structure functions contain leading twist contributions from high-$p_{\perp…
We present a calculation of diffractive charm jet production at hadron colliders in perturbative QCD based on the two-gluon exchange model. Differing from the previous calculations, we abandon the use of the effective color-singlet vitual gluon simplification, and use the real gluon in the calculations for the partonic process. We find the final result is free of the linear singularities due to the small transverse momenta of the exchanged two gluons. In the leading logarithmic approximation (LLA) in QCD, this process is related to the off-diagonal gluon density in the proton. As a result, thi…
We discuss diffractive hadron leptoproduction in terms of skewed gluon distributions and within two-gluon exchange model. Connection of the two-gluon approach with skewed gluon distributions is found. The double spin asymmetries for longitudinally polarized leptons and transversely polarized protons in diffractive vector meson and $Q \bar Q$ production at high energies within the two-gluon model is analysed. The asymmetry predicted for meson production is found to be quite small. The $A_{lT}$ asymmetry for $Q \bar Q$ production is large and can be used to obtain information on the polarized sk…
We study the diffractive production of $q\bar{q}g$ jets with large transverse momenta in the region of large diffractive masses (small $β$). Cross sections for transverse and longitudinal photons are obtained in the leading log $1/x_{\fP}$ and log $1/β$ approximation, keeping all powers in log $k_t^2/Q^2$. We perform a numerical study and illustrate the angular distribution of the three jets. We also estimate the integrated diffractive three jet cross section and compare with the dijet cross section obtained before.
We use perturbative QCD, beyond the leading $\ln Q^2$ approximation, to show how measurements of diffractive $J/ψ$ production at HERA can provide a sensitive probe of the gluon density of the proton at small values of Bjorken $x$. We estimate both the effect of the relativistic motion of the $c$ and $\overline{c}$ within the $J/ψ$ and of the rescattering of the $c\overline{c}$ quark pair on the proton. We find that the available data for diffractive $J/ψ$ photoproduction can discriminate between the gluon distributions of the most recent sets of partons.
To test the model of the polarized gluon distribution $ΔG(x, Q^2)$ in the proton, we propose a new process, diffractive $Λ_c^+$ productions in polarized $pp$ reactions, which will be observed in the forthcoming RHIC and also the proposed HERA-$\vec {\rm N}$ experiments. The spin correlation between the target proton and the $Λ_c^+$ produced in the target fragmentation region largely depends on $ΔG(x, Q^2)$ and thus, the process is quite promising for testing the models of $ΔG(x, Q^2)$.
We propose exclusive diffractive dijet photoproduction as an ideal measure of the off-diagonal gluon distribution at high scales. We solve the off-diagonal evolution equations for the gluon and quark singlet over the full kinematic domain. We discuss the nature of the solutions of these equations, which embody both DGLAP and ERBL evolution. We give predictions for the transverse momentum distribution of the jets. In particular we quantify the enhancement arising from the evolution of the off-diagonal parton distributions.
The modifications induced in the calculation of the cross section of the diffractive process gamma gamma -> J/Psi J/Psi when the gluon propagator is changed are analyzed. Instead of the usual perturbative gluon propagator, alternative forms obtained using non-perturbative methods like Dyson-Schwinger equations are used to consider in a more consistent way the contributions of the infrared region. The result shows a reduction in the differential cross-section for low momentum transfer once compared with the perturbative result, to be confirmed with future experimental results from TESLA.
Based on the hard-scattering factorization which decomposes the diffractive structure function into a pomeron flux and a pomeron structure function, we study the single diffractive Lambda_c^+ production in polarized pp scattering: p + p -> p + Lambda_c^+ + X, which will be observed at forthcoming RHIC experiment. By analyzing the cross section and correlation of the spin polarization between the initial proton and produced Lambda_c^+, we found that the process is quite effective for testing both hard-scattering factorization and models of the polarized gluon distribution in the proton.
We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal …
In this work, we perform a comparison of the employ of distinct gluon propagators with the experimental data in diffractive processes, $pp$ elastic scattering and light meson photo-production. The gluon propagators are calculated through non-perturbative methods, being justified their use in this class of events, due to the smallness of the momentum transfer. Our results are not able to select the best choice for the modified gluon propagator among the analyzed ones, showing that the application of this procedure in this class of high energy processes, although giving a reasonable fit to the e…
High-mass diffractive production of protons on the deuteron target is studied in the next-to-leading order (NLO) of the perturbative QCD in the BFKL approach. The non-trivial part of the NLO contributions coming from the triple interactions of the exchanged reggeons is considered. Analytic formulas are presented and shown to be infrared free and so ready for practical calculation.
Diffractive production of $J/Ψ$ particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importa…
We consider the dependencies of spin asymmetries in the diffractive $J/Ψ$ and $Q \bar Q$ leptoproduction at HERA energies on the structure of the pomeron-proton coupling. It is shown that it is difficult to study the spin structure of the pomeron coupling with the proton from the $A_{ll}$ asymmetry. The $A_{lT}$ asymmetry is an appropriate object for this investigation.
We use the color-octet mechanism combined with the two gluon exchange model for the diffractive $J/ψ$ production in resolved photon processes. In the leading logarithmic approximation in QCD, we find that the diffractive $J/ψ$ production cross section is related to the off-diagonal gluon density of the proton, the gluon density of the photon and to the nonperturbative color-octet $^3 S_{1}^{(8)}$ matrix element of $J/ψ$. The cross section is found to be very sensitive to the gluon density of the photon. As a result, this process may provide a wide window for testing the two-gluon exchange mode…
Diffractive production of J/Psi particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importa…
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…
We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($γ^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector $\r$ and the dipole impact parameter $\b$. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $γ^{(*)}$-h collisi…
LPS provides access to new fundamental observables: the diffraction cone and azimuthal asymmetries. Diffraction cone has a unique rise of $B_T$ from the exclusive limit to excitation of continuum $M^2 \approx Q^2$ which is in striking contrast to experience with real photoproduction and hadronic diffraction. Azimuthal asymmetry is large and pQCD calculable at large $β$ and can be measured with LPS. It allows testing of the pQCD prediction of $L/T >> 1$.
We examine the origins of azimuthal correlations observed in high energy proton-nucleus collisions by considering the simple example of the scattering of uncorrelated partons off color fields in a large nucleus. We demonstrate how the physics of fluctuating color fields in the color glass condensate (CGC) effective theory generates these azimuthal multiparticle correlations and compute the corresponding Fourier coefficients v_n within different CGC approximation schemes. We discuss in detail the qualitative and quantitative differences between the different schemes. We will show how a recently…
The large transverse momentum muon pair and W boson productions in the quark initiated coherent diffractive processes at hadron colliders are discussed under the framework of the two-gluon exchange parametrization of the Pomeron model. In this approach, the production cross sections are related to the small-x off-diagonal gluon distribution and the large-x quark distribution in the proton (antiproton). By approximating the off-diagonal gluon distribution by the usual gluon distribution function, we estimate the production rates of these processes at the Fermilab Tevatron.
We consider the production of charm by real and virtual photons. Special attention is paid to diffractive charm production, which provides information on the gluonic content of the Pomeron. Our calculations are based on the gluon distributions of the CKMT-model, which is shown to lead to agreement with the data on open charm production in deep inelastic scattering. We compare predictions for diffractive charm production of different models for the distribution of gluons in the Pomeron. Experiments at HERA should be able to discriminate between them. Predictions for beauty production in diffrac…
The distribution of a suitably defined azimuthal angle in diffractive deep inelastic scattering contains information on the polarisation of the exchanged photon. In particular it allows one to constrain the longitudinal diffractive structure function. We investigate the potential of such bounds in general and for particular diffractive final states.
We calculate the inclusive gluon correlation function for arbitrary number of gluons with full rapidity and transverse momentum dependence for the initial glasma state of the p-p, p-A and A-A collisions. The formula we derive via superdiagrams generates cumulants for any number of gluons. Higher order cumulants contain information on correlations between multiple gluons, and they are necessary for calculations of higher dimensional ridges as well as flow coefficients from multi-particle correlations.
Within the colour dipole picture for deep inelastic scattering at small Bjorken $x$, we study the production of a pair of relatively hard jets via coherent diffraction. By "relatively hard" we mean that the transverse momenta of the two jets -- the quark ($q$) and the antiquark ($\bar{q}$) generated by the decay of the virtual photon -- are much larger than the target saturation momentum $Q_s(Y_{\mathbb{P}})$ evaluated at the rapidity gap $Y_{\mathbb{P}}$. We argue that the typical final-state configurations are such that the hard $q\bar q$ dijets are accompanied by a semi-hard gluon jet, with…
