Forward quark jets from protons shattering the color glass condensate

Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions

With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future electron-ion collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy quantum chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in pp and pA collisions, especially in the high p_{T} region, and obtain reliable descriptions of all existing data measured at RHIC and the LHC across all p_{T} regions. Consequently, this technique can pave the way for the precision studies of the CGC next-to-leading-order predictions by confronting them with a large amount of precise data.

Mining for Gluon Saturation at Colliders

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 recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.

Elliptic Flow of Heavy Quarkonia in pA Collisions

Using the dilute-dense factorization in the color glass condensate framework, we investigate the azimuthal angular correlation between a heavy quarkonium and a charged light hadron in proton-nucleus collisions. We extract the second harmonic v_{2}, commonly known as the elliptic flow, with the light hadron as the reference. This particular azimuthal angular correlation between a heavy meson and a light hadron was first measured at the LHC recently. The experimental results indicate that the elliptic flows for heavy flavor mesons (J/ψ and D^{0}) are almost as large as those for light hadrons. Our calculation demonstrates that this result can be naturally interpreted as an initial state effect due to the interaction between the incoming partons from the proton and the dense gluons inside the target nucleus. Since the heavy quarkonium v_{2} exhibits a weak mass dependence according to our calculation, we predict that the heavy quarkonium ϒ should have a similar elliptic flow as compared to that of the J/ψ, which can be tested in future measurements.

Multiparticle Collectivity from Initial State Correlations in High Energy Proton-Nucleus Collisions

Qualitative features of multiparticle correlations in light-heavy ion (p+A) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include (i) the ordering of the magnitudes of the azimuthal angle nth Fourier harmonics of two-particle correlations v_{n}{2}, (ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic v_{2}{4}, and (iii) the energy dependence of four-particle symmetric cumulants measuring correlations between different Fourier harmonics. Similar patterns are seen in an Abelian version of the model, where we observe v_{2}{2}>v_{2}{4}≈v_{2}{6}≈v_{2}{8} of two, four, six, and eight particle correlations. While such patterns are often interpreted as signatures of collectivity arising from hydrodynamic flow, our results provide an alternative description of the multiparticle correlations seen in p+A collisions.

Azimuthal Angular correlations in high energy processes in QCD

Angular (azimuthal or polar) correlations between produced particles in high energy hadronic/nuclear collisions carry a wealth of information on the dynamics of the strong interactions in the novel regime where parton densities of the target hadron or nucleus are high. As such they probe a relatively unexplored region of QCD kinematic phase space. Here we consider azimuthal angular correlations between three jets produced in Deep Inelastic Scattering in the kinematics region corresponding to low xBjorken of the target and show that high gluon density effects in the target lead to a disappearance of the away-side peaks.

High gluon densities in heavy ion collisions

The early stages of heavy ion collisions are dominated by high density systems of gluons that carry each a small fraction x of the momenta of the colliding nucleons. A distinguishing feature of such systems is the phenomenon of 'saturation' which tames the expected growth of the gluon density as the energy of the collision increases. The onset of saturation occurs at a particular transverse momentum scale, the 'saturation momentum', that emerges dynamically and that marks the onset of non-linear gluon interactions. At high energy, and for large nuclei, the saturation momentum is large compared to the typical hadronic scale, making high density gluons amenable to a description with weak coupling techniques. This paper reviews some of the challenges faced in the study of such dense systems of small x gluons, and of the progress made in addressing them. The focus is on conceptual issues, and the presentation is both pedagogical, and critical. Examples where high gluon density could play a visible role in heavy ion collisions are briefly discussed at the end, for illustration purpose.

Next-to-leading-order forward hadron production in the small-x regime: the role of rapidity factorization

Single inclusive hadron production at forward rapidity in high energy p+A collisions is an important probe of the high gluon density regime of QCD and the associated small-x formalism. We revisit an earlier one-loop calculation to illustrate the significance of the "rapidity factorization" approach in this regime. Such factorization separates the very small-x unintegrated gluon density evolution and leads to a new correction term to the physical cross section at one-loop level. Importantly, this rapidity factorization formalism remedies the previous unphysical negative next-to-leading-order contribution to the cross section. It is much more stable with respect to "rapidity" variation when compared to the leading-order calculation and provides improved agreement between theory and experiment in the forward rapidity region.

Towards the test of saturation physics beyond leading logarithm

We present results from the first next-to-leading-order (NLO) numerical analysis of forward hadron production in pA and dA collisions in the small-x saturation formalism. Using parton distributions and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. In the large p⊥ region beyond the saturation scale, we find that the NLO correction becomes dominant and negative, which indicates that other physics beyond NLO becomes important and should also be taken into account. Furthermore, we make predictions for forward hadron production in pPb collisions at the LHC. This analysis not only incorporates the important NLO corrections for all partonic channels, but also reduces the renormalization scale dependence and helps to significantly reduce the theoretical uncertainties. It therefore provides a precise test of saturation physics beyond the leading logarithmic approximation.

One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.

Forward neutral pion production in p + p and d + Au collisions at square root sNN=200 GeV

Measurements of the production of forward pi0 mesons from p + p and d + Au collisions at square root sNN=200 GeV are reported. The p + p yield generally agrees with next-to-leading order perturbative QCD calculations. The d + Au yield per binary collision is suppressed as eta increases, decreasing to approximately 30% of the p + p yield at eta =4.00, well below shadowing expectations. Exploratory measurements of azimuthal correlations of the forward pi0 with charged hadrons at eta approximately 0 show a recoil peak in p + p that is suppressed in d + Au at low pion energy. These observations are qualitatively consistent with a saturation picture of the low-x gluon structure of heavy nuclei.

High-density QCD and cosmic-ray air showers

We discuss particle production in the high-energy, small-x limit of QCD where the gluon density of hadrons is expected to become nonperturbatively large. Strong modifications of the phase-space distribution of produced particles as compared to leading-twist models are predicted, which reflect in the properties of cosmic-ray induced air showers in the atmosphere. Assuming hadronic primaries, our results suggest a light composition near Greisen-Zatsepin-Kuzmin cutoff energies. We also show that cosmic-ray data are sensitive to various QCD evolution scenarios for the rate of increase of the gluon density at small x, such as fixed-coupling and running-coupling Balitsky-Fadin-Kuraev-Lipatov evolution. There are clear indications for a slower growth of the gluon density as compared to RHIC and HERA, due, e.g., to running-coupling effects.

Evolution of the nuclear modification factors with rapidity and centrality in d + Au collisions at (sqrt)[N(S)N]=200 GeV

We report on a study of the transverse momentum dependence of nuclear modification factors R(dAu) for charged hadrons produced in deuteron + gold collisions at sqrt[s(NN)]=200 GeV, as a function of collision centrality and of the pseudorapidity (eta=0, 1, 2.2, 3.2) of the produced hadrons. We find a significant and systematic decrease of R(dAu) with increasing rapidity. The midrapidity enhancement and the forward rapidity suppression are more pronounced in central collisions relative to peripheral collisions. These results are relevant to the study of the possible onset of gluon saturation at energies reached at BNL RHIC.

Ion-induced quark-gluon implosion

We investigate nuclear fragmentation in the central proton-nucleus and nucleus-nucleus collisions at the energies of CERN LHC. Within the semiclassical approximation we argue that because of the fast increase with energy of the cross sections of soft and hard interactions each nucleon is stripped in the average process off "soft" partons and fragments into a collection of leading quarks and gluons with large p(t). Valence quarks and gluons are streaming in the opposite directions when viewed in the c.m. of the produced system. The resulting pattern of the fragmentation of the colliding nuclei leads to an implosion of the quark and gluon constituents of the nuclei. The nonequilibrium state produced at the initial stage in the nucleus fragmentation region is estimated to have densities >/=50 GeV/fm(3) at the LHC energies and probably >/=10 GeV/fm(3) at BNL RHIC.

Proton breakup in high-energy pA collisions from perturbative QCD

We argue that the distribution of hadrons near the longitudinal light cone in central high-energy pA collisions is computable in weak coupling QCD. This is because the density of gluons per unit transverse area in the dense target at saturation provides an intrinsic semihard momentum scale, Q(s). We predict that the longitudinal distribution of (anti)baryons and mesons steepens with increasing energy and atomic number of the target and that the transverse momentum distribution broadens. We show that the evolution of high moments of the longitudinal net baryon distribution with Q(s) is determined by the anomalous dimension gamma(qq).