Color Glass Condensate Research Articles

Beyond Color Glass Condensate: particle production at both low and high transverse momenta

We propose a new formalism for particle production in high energy collisions including both gluon saturation and large x gluons in the target.

Ultracentral Collisions of Small and Deformed Systems at RHIC

We study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-pT “(semi)dilute-(semi)dilute” regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in 0–1% ultracentral symmetric collisions of small deformed ions and in 0–10% d197Au collisions. The collision systems we consider are 238U238U, d197Au, 9Be197Au, 9Be9Be, 3He3He, and 3He197Au.

The elliptic asymmetry of heavy quarkonia in pA collisions from the initial state

We compute the azimuthal angular correlation between a heavy quarkonium (or an open charm meson) and a charged light hadron produced in pA collisions in the color glass condensate framework. The obtained elliptic asymmetries (v2) of J/ψ and D0 mesons agree with the recent experimental data from the LHC quite well. Our calculation demonstrates that an initial state effect due to the interaction between the partons inside the projectile proton and the dense gluons inside the target nucleus can generate a sizable collectivity which can be measured at RHIC and the LHC. In this framework, we find the mass dependence for the heavy quarkonium v2 is quite weak, while that for the open meson v2 is rather strong. It will be very interesting to test our results regarding other heavy mesons in the future experimental measurements.

Comparison of improved TMD and CGC frameworks in forward quark dijet production

For studying small-x gluon saturation in forward dijet production in high-energy dilute-dense collisions, the improved TMD (ITMD) factorization formula was recently proposed. In the Color Glass Condensate (CGC) framework, it represents the leading term of an expansion in inverse powers of the hard scale. It contains the leading-twist TMD factorization formula relevant for small gluon’s transverse momentum kt, but also incorporates an all-order resummation of kinematical twists, resulting in a proper matching to high-energy factorization at large kt. In this paper, we evaluate the accuracy of the ITMD formula quantitatively, for the case of quark dijet production in high-energy proton-proton(p+p) and proton-nucleus (p+A) collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal angle ∆ϕ distribution to that obtained with the CGC formula. For a dijet with each quark momentum pt much larger than the target saturation scale, Qs, the ITMD formula is a good approximation to the CGC formula in a wide range of azimuthal angle. It becomes less accurate as the jet pt’s are lowered, as expected, due to the presence of genuine higher-twists contributions in the CGC framework, which represent multi-body scattering effects absent in the ITMD formula. We find that, as the hard jet momenta are lowered, the accuracy of ITMD start by deteriorating at small angles, in the high-energy-factorization regime, while in the TMD regime near ∆ϕ = π, very low values of pt are needed to see differences between the CGC and the ITMD formula. In addition, the genuine twists corrections to ITMD become visible for higher values of pt in p + A collisions, compared to p+p collisions, signaling that they are enhanced by the target saturation scale.

Model comparison for initial density fluctuations in high-energy heavy-ion collisions

Four models for the initial conditions of a fluid dynamic description of high energy heavy ion collisions are analysed and compared. We study expectation values and event-by-event fluctuations in the initial transverse energy density profiles from Pb-Pb collisions. Specifically, introducing a Fourier-Bessel mode expansion for fluctuations, we determine expectation values and two-mode correlation functions of the expansion coefficients. The analytically solveable independent point-sources model is compared to an initial state model based on Glauber theory and two models based on the Color Glass Condensate framework. We find that the large wavelength modes of all investigated models show universal properties for central collisions and also discuss to which extent general properties of initial conditions can be understood analytically.

Measurement of inclusive J/ψ polarization in p+p collisions at s=200 GeV by the STAR experiment

We report on new measurements of inclusive J/$\psi$ polarization at mid-rapidity in p+p collisions at $\sqrt{s}$ = 200 GeV by the STAR experiment at RHIC. The polarization parameters, $\lambda_\theta$, $\lambda_\phi$, and $\lambda_{\theta\phi}$, are measured as a function of transverse momentum ($p_T$) in both the Helicity and Collins-Soper (CS) reference frames within $p_T< 10$ GeV/$C$. Except for $\lambda_\theta$ in the CS frame at the highest measured $p_T$, all three polarization parameters are consistent with 0 in both reference frames without any strong $p_T$ dependence. Several model calculations are compared with data, and the one using the Color Glass Condensate effective field theory coupled with non-relativistic QCD gives the best overall description of the experimental results, even though other models cannot be ruled out due to experimental uncertainties.

Observable Signatures of Initial State Momentum Anisotropies in Nuclear Collisions.

We show that the correlation between the elliptic momentum anisotropy v_{2} and the average transverse momentum [p_{T}] at fixed multiplicity in small system nuclear collisions carries information on the origin of the observed momentum anisotropy. A calculation using a hybrid IP-Glasma+music+UrQMD model that includes contributions from final state response to the initial geometry as well as initial state momentum anisotropies of the color glass condensate predicts a characteristic sign change of the correlator ρ[over ^](v_{2}^{2},[p_{T}]) as a function of charged particle multiplicity in p+Au and d+Au collisions at sqrt[s]=200 GeV, and p+Pb collisions at sqrt[s]=5.02 TeV. This sign change is absent in calculations without initial state momentum anisotropies. The model further predicts a qualitative difference between the centrality dependence of ρ[over ^](v_{2}^{2},[p_{T}]) in Au+Au collisions at sqrt[s]=200 GeV and Pb+Pb collisions at sqrt[s]=5.02 TeV, with only the latter showing a sign change in peripheral events. Predictions for O+O collisions at different collision energy show a similar behavior. Experimental observation of these distinct qualitative features of ρ[over ^](v_{2}^{2},[p_{T}]) in small and large systems would constitute strong evidence for the presence and importance of initial state momentum anisotropies predicted by the color glass condensate effective theory.

Color glass condensate at next-to-leading order meets HERA data

We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation to massive quarks.

Jet momentum broadening in the pre-equilibrium Glasma

Jets are important probes of heavy ion collisions as they can provide information on the interaction of a highly energetic parton with the medium it traverses. In the hydrodynamic stage of dense, strongly interacting matter, these interactions can be explained in terms of scattering processes, soft gluon emission and collinear parton splittings. However, jets originate even before the hydrodynamic stage. Here we report on the first numerical simulation of transverse momentum broadening of jets stemming from the interaction of partons with boost-invariantly expanding Glasma flux tubes. The Glasma stage is a pre-hydrodynamic stage based on the Color Glass Condensate framework. Our calculation shows strong time-dependence and an intrinsic anisotropy of momentum broadening in the directions transverse to the jet propagation direction.

Collectivity of heavy mesons in proton-nucleus collisions

Using a model based on the Color Glass Condensate framework and the dilute-dense factorization, we systematically study the azimuthal angular correlations between a heavy flavor meson and a light reference particle in proton-nucleus collisions. The obtained second harmonic coefficients (also known as the elliptic flows) for $J/\psi$ and $D^0$ agree with recent experimental data from the LHC. We also provide predictions for the elliptic flows of $\Upsilon$ and $B$ meson, which can be measured in the near future at the LHC. This work can shed light on the physics origin of the collectivity phenomenon in the collisions of small systems.

Deeply inelastic scattering structure functions on a hybrid quantum computer

We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical path integral over 0+1-dimensional fermionic and bosonic worldlines. The proper time evolution of these worldlines can be determined on a quantum computer. While extremely challenging in general, the problem simplifies in the Regge limit of QCD, where the interaction of the worldlines with gauge fields is strongly localized in proper time and the corresponding quantum circuits can be written down. As a first application, we employ the Color Glass Condensate effective theory to construct the quantum algorithm for a simple dipole model of the $F_2$ structure function. We outline further how this computation scales up in complexity and extends in scope to other real-time correlation functions.

Photoproduction of three jets in the CGC: gluon TMDs and dilute limit

We study the process γA → qoverline{q}g + X in the Color Glass Condensate (CGC) effective theory. After obtaining the cross section, we consider two kinematic limits which are encompassed in our result. In the so-called correlation limit, the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta; the cross section then simplifies considerably and can be written in a factorized form, sensitive to both the unpolarized and linearly-polarized Weizsäcker-Williams transverse momentum dependent gluon distribution function (gluon TMD). The second limit of the CGC cross section that we consider is the dilute limit, which we obtain after performing a weak-field expansion; we recover a typical linear-regime expression, involving a single unintegrated gluon distribution function. Using numerical simulations of the small-x QCD evolution of the TMDs, we investigate the rapidity dependence of the cross section in the correlation limit.

From small to large x: toward a unified description of high energy collisions

Inclusive particle production at high pt (equivalently intermediate to large x) in high energy hadronic collisions is successfully described by perturbative QCD, using the collinear-factorization formalism. On the other hand at very high energies and not so high pt the Color Glass Condensate (CGC) formalism has been quite successful in describing particle production at small Bjorken x. Here we propose a way to unify the two approaches which enables one to apply it to particle production at all x (all pt ).

Exclusive photoproduction of vector meson at next-to-leading order from color glass condensate * * Supported by the National Natural Science Foundation of China (11765005, 11947119, 11305040, 11847152, 11775097), the Fund of Science and Technology Department of Guizhou Province ([2018]1023, [2019]5653), the Education Department of Guizhou Province (KY[2017]004), Qian Kehe Platform Talents ([2017]5736-027), the National key research and development program of

The exclusive photoproduction of vector mesons ( and ) is investigated by considering the next-to-leading order corrections in the framework of the color glass condensate. We compare the next-to-leading order modified dipole amplitude with the HERA data, finding a good agreement. Our studies show that the from the leading order, running coupling, and collinearly improved next-to-leading order dipole amplitudes are 2.159, 1.097, and 0.932 for the elastic cross-section, and 2.056, 1.449, and 1.357 for the differential cross-section, respectively. The results indicate that the higher-order corrections contribute significantly to the vector meson productions, and the description of the experimental data is dramatically improved once the higher order corrections are included. We extend the next-to-leading order exclusive vector meson production model to LHC energies using the same parameters obtained from HERA. We find that our model provides a rather good description of the and data in proton-proton collisions at 7 TeV and 13 TeV in LHCb experiments.

Single inclusive jet photoproduction at very forward rapidities in pp and pPb collisions at the LHC

The particle production at very forward rapidities is expected to be sensitive to the non-linear effects in the QCD dynamics at high energies. In this paper we present, for the first time, the predictions of the Color Dipole formalism for the single inclusive jet photoproduction in pp and pPb collisions considering the very forward rapidities probed by the CMS-CASTOR calorimeter, which will be characterized by a jet in the rapidity range of 5.2 le Y le 6.6, a rapidity gap in the rapidity range probed by the central CMS detector and one of the incident hadrons remaining intact in the final state. The transverse momentum distributions and energy spectra are estimated considering the more recent phenomenological models for the dipole-proton scattering amplitude, which are based on the Color Glass Condensate formalism and are able to describe the inclusive and exclusive ep HERA data. Our results indicate that a future experimental analysis of this process is, in principle, feasible and useful to constrain the description of the QCD dynamics at high energies.

Saturation corrections to dilute-dense particle production and azimuthal correlations in the Color Glass Condensate

We perform a numerical study of higher order saturation corrections to the dilute-dense approximation for multi-particle production in high-energy hadronic collisions in the framework of the Color Glass Condensate. We compare semi-analytical results obtained by performing a leading order expansion in the dilute field of the projectile with numerical simulations of the full Classical Yang-Mills dynamics for a number of phenomenologically relevant observables. By varying the saturation momentum of the target and the projectile, we establish the regime of validity of the dilute-dense approximation and assess the magnitude and basic features of higher order saturation corrections. In particular, we find that dilute-dense approximation faithfully reproduces dense-dense results if restricted to the range of its validity.

JIMWLK evolution, Lindblad equation and quantum-classical correspondence

In the Color Glass Condensate (CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane. Averaging over the valence degrees of freedom is effected by integrating over classical color charges with some quasi probability weight functional W [j] whose evolution with rapidity is governed by the JIMWLK equation. In this paper, we reformulate this setup in terms of effective quantum field theory on valence Hilbert space governed by the reduced density matrix hat{rho} for hard gluons, which is obtained after properly integrating out the soft gluon “environment”. We show that the evolution of this density matrix with rapidity in the dense and dilute limits has the form of Lindblad equation. The quasi probability distribution (weight) functional W is directly related to the reduced density matrix hat{rho} through the generalization of the Wigner-Weyl quantum-classical correspondence, which reformulates quantum dynamics on Hilbert space in terms of classical dynamics on the phase space. In the present case the phase space is non Abelian and is spanned by the components of transverse color charge density j. The same correspondence maps the Lindblad equation for hat{rho} into the JIMWLK evolution equation for W .

Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering

We highlight the principal results of a computation in the Color Glass Condensate effective field theory (CGC EFT) of the next-to-leading order (NLO) impact factor for inclusive photon+dijet production at Bjorken $x_{\rm Bj} \ll 1$ in deeply inelastic electron-nucleus (e+A DIS) collisions. When combined with extant results for next-to-leading log $x_{\rm Bj}$ JIMWLK renormalization group (RG) evolution of gauge invariant two-point ("dipole") and four-point ("quadrupole") correlators of light-like Wilson lines, the inclusive photon+dijet e+A DIS cross-section can be determined to $\sim 10$\% accuracy. Our computation simultaneously provides the ingredients to compute fully inclusive DIS, inclusive photon, inclusive dijet and inclusive photon+jet channels to the same accuracy. This makes feasible quantitative extraction of many-body correlators of saturated gluons and precise determination of the saturation scale $Q_{S,A}(x_{\rm Bj})$ at a future Electron-Ion Collider. An interesting feature of our NLO result is the structure of the violation of the soft gluon theorem in the Regge limit. Another is the appearance in gluon emission of time-like non-global logs which also satisfy JIMWLK RG evolution.

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_\perp$, and it deviates from the perturbative calculation at small $p_\perp$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_\perp$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider.

We study inclusive and diffractive dijet production in electron-proton and electron-nucleus collisions within the color glass condensate effective field theory. We compute dijet cross sections differentially in both mean dijet transverse momentum P and recoil momentum Δ, as well as the anisotropy in the relative angle between P and Δ. Our results cover a much larger kinematic range than accessible in previous computations performed in the correlation limit approximation, where it is assumed that |P|≫|Δ|. We validate this approximation in its range of applicability and quantify its failure for |P|≲|Δ|. We also predict significant target-dependent deviations from the correlation limit approximation for |P|>|Δ| and |P|≲Q_{s}, which offers a straightforward test of gluon saturation and access to multigluon distributions at a future Electron-Ion Collider.