Next-to-leading order QCD predictions for dijet photoproduction in lepton-nucleus scattering at the future EIC and at possible LHeC, HE-LHeC, and FCC facilities
We calculate cross sections for inclusive dijet photoproduction in electron-nucleus scattering in the kinematics of the future EIC and the possible LHeC, HE-LHeC, and the FCC using next-to-leading order (NLO) perturbative QCD and nCTEQ15 and EPPS16 nuclear parton density functions (nPDFs). We make predictions for distributions in the dijet average transverse momentum ${\bar p}_T$, the average rapidity $\barη$, the observed nuclear momentum fraction $x_A^{\rm obs}$, and the observed photon momentum fraction $x_γ^{\rm obs}$. Comparing the kinematic reaches of the four colliders, we find that an increase of the collision energy from the EIC to the LHeC and beyond extends the coverage in all four considered variables. Notably, the LHeC and HE-LHeC will allow one to probe the dijet cross section down to $x_A^{\rm obs} \sim 10^{-4}$ (down to $x_A^{\rm obs} \sim 10^{-5}$ at the FCC). The ratio of the dijet cross sections on a nucleus and the proton, $σ_A/(Aσ_p)$, depends on $x_A^{\rm obs}$ in a similar way as the ratio of gluon densities, $g_A(x_A,μ^2)/[A g_p(x_A,μ^2)]$, for which current nPDFs predict a strong suppression due to nuclear shadowing in the region $x_A^{\rm obs} < 0.01$. Dijet photoproduction at future lepton-nucleus colliders can therefore be used to test this prediction and considerably reduce the current uncertainties of nPDFs.
We discuss the prospects of diffractive dijet photoproduction at the EIC to distinguish different fits of diffractive proton PDFs, different schemes of factorization breaking, to determine diffractive nuclear PDFs and pion PDFs from leading neutron 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…
Deeply-inelastic scattering (DIS) stands to enter a golden age with the prospect of precision programs at the Electron-Ion Collider (EIC) and Large Hadron-electron Collider (LHeC). While these programs will be of considerable importance to resolving longstanding issues in (non)perturbative QCD as well as hadronic and nuclear structure, they will also have valuable implications for a wider range of physics at the Energy and Intensity Frontiers, including at the High-Luminosity LHC (HL-LHC) and future $νA$ facilities. In this plenary contribution, we highlight a number of salient examples of the…
Leading neutron (LN) production in $ep$ collisions at high energies is investigated using the color dipole formalism and taking into account saturation effects. We update the treatment of absorptive effects and estimate the impact of these effects on LN spectra in the kinematical range that will be probed by the Electron Ion Collider (EIC) and by the Large Hadron electron Collider (LHeC). We demonstrate that Feynman scaling, associated to saturation, is not violated by the inclusion of absorptive effects. Moreover, our results indicate that the LN spectrum is strongly suppressed at small photo…
Based on the nonrelativistic QCD framework, we study the $Υ$ production in semi-inclusive deep inelastic electron-proton scattering (SIDIS) at HERA, EIC, and LHeC, with the main aim of assessing the viability of observing $Υ$ electroproduction at the three colliders. The color-octet (CO) contributions are found to have a crucial effect on both the integrated and differential cross sections, serving to further establish the significance of the CO mechanism. By setting the kinematic cuts to $p_{t,Υ}^{\star 2}>1~\textrm{GeV}^{2}$, $W>50$ GeV, $2<Q^2<100~\textrm{GeV}^2$, and $0.3<z<0.9$, only a fe…
We present a first, detailed study of diffractive dijet photoproduction at the recently approved electron-ion collider (EIC) at BNL. Apart from establishing the kinematic reaches for various beam types, energies and kinematic cuts, we make precise predictions at next-to-leading order (NLO) of QCD in the most important kinematic variables. We show that the EIC will provide new and more precise information on the diffractive parton density functions (PDFs) in the pomeron than previously obtained at HERA, illuminate the still disputed mechanism of global vs.\ only resolved-photon factorization br…
We study the potential of dijet photoproduction measurements at a future electron-ion collider (EIC) to better constrain our present knowledge of the nuclear parton distribution functions. Based on theoretical calculations at next-to-leading order and approximate next-to-next-to-leading order of perturbative QCD, we establish the kinematic reaches for three different EIC designs, the size of the parton density function modifications for four different light and heavy nuclei from He-4 over C-12 and Fe-56 to Pb-208 with respect to the free proton, and the improvement of EIC measurements with res…
The exclusive vector meson production in electron-ion collisions for the energies of the future colliders is investigated. We present predictions for the coherent and incoherent $ϕ$ and $J/ψ$ production in $eAu$ collisions considering the possible states of nucleon configurations in the nuclear wave function and taking into account of the non-linear corrections to the QCD dynamics. The cross sections and transverse momentum distributions are estimated assuming the energies of the Electron-Ion Collider (EIC), Large Hadron Electron Collider (LHeC) and Future Circular Collider (FCC-$eh$). Our res…
We discuss the measurement of gluon transverse momentum distribution (TMD) in dijet and heavy hadron pair (HHP) production in semi-inclusive deep inelastic scattering. The factorization of these processes in impact parameter space shows the appearance of a specific new soft factor matrix element on top of angular a complex valued anomalous dimensions. We show in detail how these features can be treated consistently and we discuss a scale prescription for the evolution kernel of the dijet soft function. As a result we obtain phenomenological predictions for unpolarized and angular modulated cro…
Particle and nuclear physics are moving toward a new generation of experiments to stress-test the Standard Model (SM), search for novel degrees of freedom, and comprehensively map the internal structure of hadrons. Due to the complex nature of QCD and wide array of past, present, and possible future experiments, measurements taken at these next-generation facilities will inhabit an expansive space of high-energy data. Maximizing the impact of each future collider program will depend on identifying its place within this sprawling landscape. As an initial exploration, we use the recently-develop…
In this paper we consider a small-$x$ model for gluon GTMDs that we fit to data on diffractive dijet production in electron-proton collisions obtained by HERA's H1 Collaboration. Assuming a small number of free parameters, each with a physical motivation, we are able to describe those data fairly well and with this model we obtain predictions for the EIC for both electroproduction and photoproduction which may allow to further test the underlying GTMD description. In the general discussion of the impact parameter dependence we recall some subtle issues related to localization of states, choice…
We propose a novel way of studying the gluon number density (the so-called Weizsäcker-Williams gluon distribution) using the planned Electron Ion Collider. Namely, with the help of the azimuthal correlations between the total transverse momentum of the dijet system and the scattered electron, we examine an interplay between the effect of the soft gluon emissions (the Sudakov form factor) and the gluon saturation effects. The kinematic cuts are chosen such that the dijet system is produced in the forward direction in the laboratory frame, which provides an upper bound on the probed longitudinal…
In this paper we investigate the impact of the higher - twist effects, resummed by the non - linear approaches for the QCD dynamics, on the inclusive observables that will be measured in future electron - ion colliders. We assume a phenomenological model for the dipole - nucleus scattering amplitude which takes into account the non - linear corrections and estimate the contribution of the different twists for $F_2^A(x,Q^2)$, $F_L^A(x,Q^2)$ and $\partial F_2^A /\partial ln Q^2$ considering different values of the Bjorken - $x$ variable, photon virtuality $Q^2$ and atomic number $A$. A compariso…
Quark-antiquark pair (or dijet) production at the electron-ion collider (EIC) has been argued to be one of most important processes that allowing to access the Weizsäcker-Williams (WW) gluon distributions at small $x$ limit. Within the framework of Color Glass Condensate (CGC) effective field theory (EFT), we calculated the dijet cross sections and the azimuthal correlations by including the Sudakov resummations, numerical results shown that the back-to-back correlations are significantly suppressed when the Sudakov resummations are taken into account. In addition, by using the solutions of ru…
We review our transverse momentum dependent factorization and resummation formalism for heavy flavor dijet production at the EIC. In this formalism, we have calculated the heavy flavor mass corrections in the collinear-soft and jet functions, and in the resummed expression for the cross section. By establishing this formalism, we then study the effects of the mass corrections by providing predictions at the EIC for the massive case and for the case where the mass is neglected. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.
The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsaecker-Williams (WW) Transverse Momentum Dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross-section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an Electron-Ion Collider. We introduce the MCDijet Monte-Carlo generator to sample quark-antiquark dijet configurations based on leading order parton level cross-…
Asymmetries in heavy quark pair and dijet production in electron-proton collisions allow studies of gluon TMDs in close analogy to studies of quark TMDs in semi-inclusive DIS. Here we present expressions for azimuthal asymmetries for both unpolarized and transversely polarized proton cases and consider the maximal asymmetries allowed. The latter are found to be rather sizeable, except in certain kinematic limits which are pointed out. In addition, we consider the small-x limit and expectations from a McLerran-Venugopalan model for unpolarized and linearly polarized gluons and from a perturbati…
In the framework of collinear factorization and next-to-leading order (NLO) perturbative QCD, we make predictions for inclusive and diffractive dijet photoproduction in electron-proton and electron-nucleus scattering in the EIC kinematics. We establish kinematic ranges in the ${\bar p}_T$, ${\bar η}$, $x_A^{\rm obs}$ and $x_γ^{\rm obs}$ variables, quantify sensitivity to small-$x$ nuclear PDFs, and analyze various scenarios of factorization breaking in the case of diffractive scattering.
We study the diffractive jet production in electron-ion collisions in the kinematical region where the mass $M_X$ of the diffractive final state is larger than $Q^2$. Based on parton saturation framework predictions are done for the kinematics of future or possible $eA$ machines as the EIC, LHeC, HE-LHeC and FCC-eA. We analyze the differential cross section as a function of jet (gluon) transverse momentum and from the experimental point of view this observable could be used to extract the saturation scale as a function of $x_{I\!\!P}$.
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.
In this work, we present an overview of experimental considerations relevant to the utilization of jets at a future Electron-Ion Collider (EIC), a subject which has been largely overlooked up to this point. A comparison of jet-finding algorithms and resolution parameters is presented along with a detailed analysis of basic jet quantities, such as multiplicities and kinematic distributions. A characterization of the energy in the event not associated with a jet is also made. In addition, detector requirements and the effects of realistic detector resolutions are discussed. Finally, an example a…
We calculate the fully differential Next-to-Leading Order (NLO) corrections to (longitudinally) polarized dijet production in deep inelastic scattering, featuring both neutral current and charged current processes. We also analyze their phenomenological impact in the Electron-Ion Collider (EIC) kinematics.
Large angle gluon radiations induced by multiple parton scatterings contribute to dijet production in deeply inelastic scattering off a large nucleus at the Electron-Ion Collider. Within the generalized high-twist approach to multiple parton scattering, such contributions at the leading order in perturbative QCD and large Bjorken momentum fraction $x_B$ can be expressed as a convolution of the multiple parton scattering amplitudes and the transverse momentum dependent (TMD) two-parton correlation matrix elements. We study this medium-induced dijet spectrum and its azimuthal angle correlation u…
In this paper we study the electroproduction of open heavy flavor $D$- and $B$-mesons in the kinematics of future $ep$ colliders, such as the Electron Ion Collider (EIC), the Large Hadron electron Collider (LHeC) and the Future Circular Collider (FCC-he). We study in detail the dependence of the cross-sections on multiplicity of co-produced hadrons, in view of its possible sensitivity to contributions from multipomeron contributions, and discuss different observables which might be used for its study. According to our theoretical expectations, in $ep$ collisions the multipomeron contributions …
We propose to investigate the properties of nuclear matter by measuring the elastic scattering of J/ψon nuclei with high precision. The J/ψmesons are produced from the photons emitted in high energy electron-proton or electron-nucleus scattering in the low-x region. The measurement could be performed at the future ENC, EIC or LHeC facilities.
Gluon TMDs can be accessed through the analysis of azimuthal asymmetries for heavy quark pair and dijet production in electron-proton collisions, similarly to the way quark TMDs are commonly extracted from semi-inclusive deep-inelastic scattering data. We calculate the upper bounds for these observables, showing in which kinematic regions they are large enough to be measured in future experiments at an Electron-Ion Collider. Moreover, we study their behavior in the small-$x$ region, adopting a McLerran-Venugopalan model for unpolarized and linearly polarized gluon distributions. By comparison …
We review a broad range of phenomena in diffraction in the context of hadron-hadron, hadron-nucleus collisions and deep inelastic lepton-proton/nucleus scattering focusing on the interplay between the perturbative QCD and non-perturbative models. We discuss inclusive diffraction in DIS, phenomenology of dipole models, resummation and parton saturation at low $x$, hard diffractive production of vector mesons, inelastic diffraction in hadron-hadron scattering, formalism of color fluctuations, inclusive coherent and incoherent diffraction as well as soft and hard diffraction phenomena in hadron-h…
The photoproduction of bottomonium-like states $Z_{b}(10610)$ and $Z_{b}(10650)$ via $γp$ scattering is studied within an effectiv Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of $Z_{b}$ states via $t$-channel with $π$ exchange.The numerical results show that the values of the total cross-sections of $Z_{b}(10610)$ and $Z_{b}(10650)$ can reach 0.09 nb and 0.02 nb, respectively, near the center of mass energy of 22 GeV. The experimental measurements and studies on the photoproduction of $Z_{b}$ states near energy region a…
Ultra-peripheral collisions (UPCs) of relativistic ions are an important tool for studying photoproduction at high energies. Vector meson photoproduction is an important tool for nuclear structure measurements and other applications. A future electron-ion collider (EIC) will allow additional studies, using virtual photons with a wide range of $Q^2$. We propose a significant expansion of the UPC and EIC photoproduction physics programs to include charged final states which may be produced via Reggeon exchange. We consider two examples: $a_2^+(1320)$, which is a conventional $q\overline q$ meson…
The diverse community of scientists involved in Deep Inelastic Scattering includes about 2000 experimental and theoretical physicists worldwide and envisages projects such as the EIC, LHeC, FCC-eh and VHEeP as future lepton-hadron scattering facilities. The proposed facilities will address fundamental questions in strong interaction / QCD physics, including a first-ever tomographic mapping of the hadrons' internal structure, a solution to the proton mass and spin problems, understanding of the high-energy structure of hadronic matter and insight into connections between gravity and the strong …
We perform the calculation of the fully differential single-jet production in longitudinally polarized deep inelastic scattering (DIS) at the next-to-next-to-leading order (NNLO) accuracy, featuring both neutral current and charged current processes. The computation is done with the projection-to-Born method (P2B), using the next-to-leading order (NLO) dijet calculation and the NNLO DIS structure functions as its main ingredients. We also analyze its phenomenological consequences in the kinematics of the future Electron-Ion Collider (EIC).
Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinati…
We propose the development and construction of a novel muon-ion collider (MuIC) at Brookhaven National Laboratory (BNL) in the USA as an upgrade to succeed the electron-ion collider (EIC) that is scheduled to commence in the early 2030s, by a joint effort of the nuclear and particle physics communities. The BNL facility could accommodate a muon storage beam with an energy up to about 1~TeV with existing magnet technology. When collided with a 275~GeV hadron beam, the MuIC center-of-mass energy of about 1~TeV will extend the kinematic coverage of deep inelastic scattering physics at the EIC (wi…
We propose the use of 1-jettiness, a global event shape, for exclusive single jet production in lepton-nucleus deep inelastic scattering (DIS). We derive a factorization formula, using the Soft-Collinear Effective Theory, differential in the transverse momentum and rapidity of the jet and the 1-jettiness event shape. It provides a quantitative measure of the shape of the final-state QCD radiation in the presence of the hard jet, providing a useful powerful probe of QCD and nuclear physics. For example, one expects differences in the observed pattern of QCD radiation between large and small nuc…
We present and discuss the theory and phenomenology of the leading twist theory of nuclear shadowing which is based on the combination of the generalization of the Gribov-Glauber theory, QCD factorization theorems, and the HERA QCD analysis of diffraction in lepton-proton deep inelastic scattering (DIS). We apply this technique for the analysis of a wide range of hard processes with nuclei---inclusive DIS on deuterons, medium-range and heavy nuclei, coherent and incoherent diffractive DIS with nuclei, and hard diffraction in proton-nucleus scattering---and make predictions for the effect of nu…
We present results for the complete NNLL+NLO (~ α_s) 1-jettiness (τ_1) event shape distribution for single jet (J) production in electron-nucleus (N_A) collisions e^- + N_A \to e^- + J + X, in the deep inelastic scattering (DIS) region where the hard scale is set by the jet transverse momentum P_{J_T}. These results cover the entire τ_1-spectrum including the resummation (τ_1<<P_{J_T}) and fixed-order (τ_1~ P_{J_T}) perturbative QCD regions. They incorporate non-perturbative soft radiation effects, the anti-k_T jet algorithm in the fixed-order calculation, and a smooth matching between the res…
We compute the differential cross-section for inclusive prompt photon$+$quark production in deeply inelastic scattering of electrons off nuclei at small $x$ ($e+A$ DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling $α_{\mathrm{s}}$) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale $Q_{s,A}(x)$. We perform a numerical study of this process for the kinematics of the Electron-Ion C…
After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky- Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (E…
