Hard Dijet Research Articles

Incoherent diffractive production of jets in electron DIS off nuclei at high energy

We study incoherent diffractive production of two and three jets in electron-nucleus deep inelastic scattering (DIS) at small xBj using the color dipole picture and the effective theory of the color glass condensate (CGC). We consider color fluctuations in the CGC weight-function as the source of the nuclear break-up and the associated momentum transfer |t|. We focus on the regime in which the two jets are almost back-to-back in transverse space and have transverse momenta P⊥ much larger than both the momentum transfer and the saturation scale Qs. The cross section for producing such a hard dijet is parametrically dominated by large size fluctuations in the projectile wave-function that scatter strongly and for which a third, semihard, jet appears in the final state. The 2+1 jets cross section can be written in a factorized form in terms of incoherent quark and gluon diffractive transverse momentum distributions (DTMDs) when the third jet is explicit, or incoherent diffractive parton distribution functions (DPDFs) when the third jet is integrated over. We find that the DPDFs and the corresponding cross section saturate logarithmically when |t|≪Qs2, while they fall like 1/|t|2 in the regime Qs2≪|t|≪P⊥2. We further show that there is no angular correlation between the hard jet momentum and the momentum transfer. For typical EIC kinematics the 2 jets and 2+1 jets cross sections are of the same order. Published by the American Physical Society 2024

Revisiting azimuthal angular asymmetries in diffractive di-jet production

We explore the impact of initial state soft gluon radiations on the azimuthal angle asymmetries in photo-production of hard di-jet via coherent diffraction in ultraperipheral heavy ion collisions, as well as in electron-proton (ep) and electron-nucleus (eA) collisions. The primary production mechanism is identified as the diffractive production of two hard jets, accompanied by a collinear gluon emission along the beam direction. In contrast, the diffractive exclusive di-jet production, where the initial state radiation is absent, is suppressed due to color transparency. Our analysis shows that azimuthal asymmetries, traditionally attributed to final state gluon emissions, are reduced by the presence of initial state radiations. The sensitivity of azimuthal asymmetries to both initial and final state radiations suggests that they could provide novel insights into the mechanisms of di-jet production in diffractive processes.

Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions

We argue that semi-inclusive photo-production of a pair of hard jets via coherent diffraction in nucleus-nucleus ultra-peripheral collisions at high energy is a golden channel to study gluon saturation. The dominant contribution is the diffractive production of three jets in an asymmetric configuration. Two of the jets are hard and propagate at nearly central pseudo-rapidities. The third jet is semi-hard, with transverse momentum comparable to the nuclear saturation momentum, and is well separated in pseudo-rapidity from the hard dijets. The emission of the semi-hard jet allows for strong scattering, thus avoiding the “higher-twist” suppression of the exclusive dijet production due to colour transparency. We compute the trijet cross-section using the diffractive TMD factorisation which emerges from the CGC effective theory at high energy. The cross-section is controlled by gluon saturation, which leaves its imprints on the structure of the final state, notably on the rapidity distribution.

Probing Parton Saturation and the Gluon Dipole via Diffractive Jet Production at the Electron-Ion Collider.

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 factorized form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing the transverse momentum imbalance between the hard dijets. The dominant contribution comes from the black disk limit and leads to a dijet imbalance of the order of the target saturation momentum Q_{s} evaluated at the rapidity gap. Integrating out the dijet imbalance, we obtain a collinear factorization where the initial condition for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution is set by gluon saturation.

Measuring the Weizsäcker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries

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-sections with WW gluon distributions that solve the non-linear small-x QCD evolution equations. These configurations are fragmented to hadrons using PYTHIA, and final state jets are reconstructed. We report on background studies and on the effect of kinematic cuts introduced to remove beam jet remnants. We estimate that with an integrated luminosity of 20 fb^{-1}/A one can determine the distribution of linearly polarized gluons with a statistical accuracy of approximately 5%.

Merging weak and QCD showers with matrix elements

We present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell-Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton shower resummation into a single framework. The new merging strategy is implemented in the PYTHIA event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.

Multiple hard partonic collisions with correlations in proton-proton scattering

We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parameterizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.

Unitarity cutting rules for the nucleus excitation and topological cross sections in hard production off nuclei from nonlineark⊥-factorization

At the partonic level, a typical final state in small-x deep inelastic scattering off nuclei and hard proton-nucleus collisions can be characterized by the multiplicity of color-excited nucleons. Within the Reggeon field theory, each color-excited nucleon is associated with the unitarity cut of the Pomeron exchanged between the projectile and nucleus. In this communication we derive the unitarity rules for the multiplicity of excited nucleons, alias cut pomerons, alias topological cross sections, for typical hard dijet production processes. We demonstrate how the coupled-channel non-Abelian intranuclear evolution of color dipoles, inherent to pQCD, gives rise to the Reggeon field theory diagrams for final states in terms of the uncut, and two kinds of cut, Pomerons. Upon the proper identification of the uncut and cut-Pomeron exchanges, the topological cross sections for dijet production follow in a straightforward way from the earlier derived nonlinear k{sub perpendicular} factorization quadratures for the inclusive dijet cross sections. The concept of a coherent (collective) nuclear glue proves extremely useful for the formulation of the Reggeon field theory vertices of multi-Pomeron--cut and uncut--couplings to particles and between themselves. A departure of our unitarity cutting rules from the ones suggested by the pre-QCD Abramovsky-Kancheli-Gribov rules, stems from the coupled-channelmore » features of non-Abelian intranuclear pQCD. We propose a multiplicity resummation as a tool for the isolation of topological cross sections for single-jet production.« less

Nonuniversality Aspects of Nonlineark⊥Factorization for Hard Dijets

The origin of the breaking of conventional linear k_\perp-factorization for hard processes in a nuclear environment is by now well established. The realization of the nonlinear nuclear k_\perp-factorization which emerges instead was found to change from one jet observable to another. Here we demonstrate how the pattern of nonlinear k_\perp-factorization, and especially the role of diffractive interactions, in the production of dijets off nuclei depends on the color properties of the underlying pQCD subprocess.

Nonlineark⊥factorization for quark-gluon dijet production off nuclei

The breaking of conventional linear k_\perp-factorization for hard processes in a nuclear environment is by now well established. Here we report a detailed derivation of the nonlinear k_\perp-factorization relations for the production of quark-gluon dijets. This process is of direct relevance to dijets in the proton hemisphere of proton-nucleus collisions at energies of the Relativistic Heavy Ion Collider (RHIC). The major technical problem is a consistent description of the non-Abelian intranuclear evolution of multiparton systems of color dipoles. Following the technique developed in our early work [ N.N. Nikolaev, W. Sch\"afer, B.G. Zakharov and V.R. Zoller, J. Exp. Theor. Phys.\ {\bf 97} (2003) 441], we reduce the description of the intranuclear evolution of the $qgg\bar{q}$ state to the system of three coupled-channel equations in the space of color singlet 4-parton states $\ket{3\bar{3}}, \ket{6\bar{6}}$ and $\ket{15\bar{15}}$ (and their large-N_c generalizations). At large number of colors N_c, the eigenstate $(\ket{6\bar{6}}-\ket{15\bar{15}})/\sqrt{2}$ decouples from the initial state $\ket{3\bar{3}}$. The resulting nuclear distortions of the dijet spectrum exhibit much similarity to those found earlier for forward dijets in Deep Inelastic Scattering (DIS). Still there are certain distinctions regarding the contribution from color-triplet $qg$ final states and from coherent diffraction excitation of dijets. To the large-N_c approximation, we identify four universality classes of nonlinear k_\perp-factorization for hard dijet production.

Exclusive diffractive electroproduction of dijets in collinear factorization

Exclusive electroproduction of hard dijets can be described within the collinear factorization. This process has clear experimental signature and provides one with an interesting alternative venue to test QCD description of hard diffractive processes and extract information on generalized nucleon parton distributions. In this work we present detailed leading-order QCD calculations of the relevant cross sections, including longitudinal momentum fraction distribution of the dijets and their azimuthal angle dependence.

Probing s-Channel Unitarity With LRG Signatures

Hard diffractive di-jets with large rapidity gap (LRG) signatures are explored following the Tevatron and HERA observations that their production rates are considerably smaller than the pQCD estimates. It is argued that a consistent description of these data can be attained only after s -channel unitarity re-scattering screening corrections are incorporated. To this end a simple and very successful procedure is presented in which information derived from the measured soft total, elastic and diffractive cross sections simplifies the calculation and makes it parameter free. Consequently, we consider LRG hard diffraction an excellent probe to explore the role of s -channel unitarity in high energy soft scattering.

Fate of [formula omitted]-factorization for hard processes in nuclear environment

Large thickness of heavy nuclei brings in a new scale into the pQCD description of hard processes in nuclear environment. The familiar linear k ⊥ -factorization breaks down and must be replaced by a new concept of the nonlinear k ⊥ -factorization introduced in [N.N. Nikolaev, W. Schafer, B.G. Zakharov and V.R. Zoller, J. Exp. Theor. Phys. 97 (2003) 441]. I demonstrate the salient features of nonlinear k ⊥ -factorization on an example of hard dijet production in PIS off heavy nuclei. I also discuss briefly the non-linear BFKL evolution for gluon density of nuclei.

Why Breakup of Photons and Pions into Forward Dijets Is So Different: Predictions from Nonlinear Nuclear k[sub ⊥] Factorization

Based on an approach to non-Abelian propagation of color dipoles in a nuclear medium we formulate a nonlinear k_t-factorization for the breakup of photons and pions into forward hard dijets in terms of the collective Weizs\"acker-Williams (WW) glue of nuclei. We find quite distinct practical consequences of nonlinear nuclear k_t-factorization for interactions of pointlike photons and non-pointlike pions. In the former case the large transverse momentum p_t of jets comes from the intrinsic momentum of quarks and antiquarks in the photon and nuclear effects manifest themselves as an azimuthal decorrelation with an acoplanarity momentum of the order of the nuclear saturation momentum Q_A. In the breakup of pions off free nucleons to the leading order in pQCD the spectator parton has a small transverse momentum and the hard dijet cross section is suppressed. In the breakup of pions off heavy nuclei the forward hard jets are predicted to be entirely decorrelated. We comment on the sensitivity of the pionic dijet cross section to the pion distribution amplitude. The predicted distinction between the breakup of photons and pions can be tested by the sphericity and thrust analysis of the forward hadronic system in the COMPASS experiment at CERN.

3D parton imaging of the nucleon in high-energypp andpA collisions

We discuss several examples of how the transverse spatial distribution of partons in the nucleon, as well as multiparton correlations, can be probed by observing hard processes (dijets) in high-energy pp (pbar p) and pA (dA) collisions. Such studies can complement the information gained from measurements of hard exclusive processes in ep scattering. The transverse spatial distribution of partons determines the distribution over pp impact parameters of events with hard dijet production. Correlations in the transverse positions of partons can be studied in multiple dijet production. We find that the correlation cross section measured by the CDF Collaboration, sigma_eff = 14.5 +/- 1.7^{+ 1.7}_{-2.3} mb, can be explained by "constituent quark" type quark-gluon correlations with r_q ~ r_N / 3, as suggested by the instanton liquid model of the QCD vacuum. Longitudinal and transverse multiparton correlations can be separated in a model-independent way by comparing multiple dijet production in pp and pA collisions. Finally, we estimate the cross section for exclusive diffractive Higgs production in pp collisions at LHC (rapidity gap survival probability), by combining the impact parameter distribution implied by the hard partonic process with information about soft interactions gained in pp elastic scattering.

3D parton imaging of the nucleon in high‐energy pp and pA collisions*

AbstractWe discuss several examples of how the transverse spatial distribution of partons in the nucleon, as well as multiparton correlations, can be probed by observing hard processes (dijets) in high‐energy and pA (dA collisions. Such studies can complement the information gained from measurements of hard exclusive processes in ep scattering. The transverse spatial distribution of partons determines the distribution over pp impact parameters of events with hard dijet production. Correlations in the transverse positions of partons can be studied in multiple dijet production. We find that the correlation cross section measured by the CDF Collaboration, σeff = 14.5±1.7+ 1.7‐2.3 mb, can be explained by “constituent quark” type quark–gluon correlations with rq ≊ rN / 3, as suggested by the instanton liquid model of the QCD vacuum. Longitudinal and transverse multiparton correlations can be separated in a model‐independent way by comparing multiple dijet production in pp and pA collisions. Finally, we estimate the cross section for exclusive diffractive Higgs production in pp collisions at LHC (rapidity gap survival probability), by combining the impact parameter distribution implied by the hard partonic process with information about soft interactions gained in pp elastic scattering.

Dijet production as a centrality trigger forppcollisions at CERN LHC

We demonstrate that a trigger on hard dijet production at small rapidities allows us to establish a quantitative distinction between central and peripheral collisions in $\overline{p}p$ and pp collisions at Tevatron and LHC energies. Such a trigger strongly reduces the effective impact parameters as compared to minimum bias events. This happens because the transverse spatial distribution of hard partons $(x\ensuremath{\gtrsim}{10}^{\ensuremath{-}2})$ in the proton is considerably narrower than that of soft partons, whose collisions dominate the total cross section. In the central collisions selected by the trigger, most of the partons with $x\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}$ interact with a gluon field whose strength rapidly increases with energy. At LHC (and to some extent already at Tevatron) energies the strength of this interaction approaches the unitarity (``blackbody'') limit. This leads to specific modifications of the final state, such as a higher probability of multijet events at small rapidities, a strong increase of the transverse momenta and depletion of the longitudinal momenta at large rapidities, and the appearance of long-range correlations in rapidity between the forward or backward fragmentation regions. The same pattern is expected for events with production of new heavy particles (Higgs boson, SUSY). Studies of these phenomena would be feasible with the CMS-TOTEM detector setup, and would have considerable impact on the exploration of the physics of strong gluon fields in QCD, as well as the search for new particles at LHC.

Dijets with 2, 1 or 0 rapidity gap: factorization breaking at the Tevatron

Central production cross-sections of hard dijets with 2, 1 or 0 rapidity gap at Tevatron are analyzed in terms of diffractive (“a la Good–Walker”) and non-diffractive fluctuations of the incident particles. The observed large factorization breaking and the unexpected high value of the 2 to 1 gap cross-section ratio are explained in terms of scattering with and between the incident particles.

Nonlinear k ⊥-factorization for forward dijets in deep inelastic scattering off nuclei in the saturation regime

We develop the QCD description of the breakup of photons into forward dijets in small-x deep inelastic scattering off nuclei in the saturation regime. Based on the color dipole approach, we derive a multiple scattering expansion for intranuclear distortions of the jet-jet transverse momentum spectrum. A special attention is paid to the non-Abelian aspects of the propagation of color dipoles in a nuclear medium. We report a nonlinear $k_{\perp}$-factorization formula for the breakup of photons into dijets in terms of the collective Weizs\"acker-Williams (WW) glue of nuclei as defined in ref. \cite{Saturation,NSSdijet}. For hard dijets with the transverse momenta above the saturation scale the azimuthal decorrelation (acoplanarity) momentum is of the order of the nuclear saturation momentum QA. For minijets with the transverse momentum below the saturation scale the nonlinear kT-factorization predicts a complete disappearance of the jet-jet correlation. We comment on a possible relevance of the nuclear decorrelation of jets to the experimental data from the STAR-RHIC Collaboration.

Exclusive production of dijets in QCD

We study in a framework of QCD collinear factorization the processes of a pion and a photon diffraction dissociation into two jets. The structure of non-factorizable contributions is discussed. We argue that coherent production of hard dijets by linearly polarized real photons can provide direct evidence for chirality violation in hard processes, the first measurement of the magnetic susceptibility of the quark condensate and the photon distribution amplitude.