Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions.

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Erratum: Hierarchy of Azimuthal Anisotropy Harmonics in Collisions of Small Systems from the Color Glass Condensate [Phys. Rev. Lett. 121, 052301 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.052301.

Hierarchy of Azimuthal Anisotropy Harmonics in Collisions of Small Systems from the Color Glass Condensate.

We demonstrate that the striking systematics of two-particle azimuthal Fourier harmonics v_{2} and v_{3} in ultrarelativistic collisions of protons, deuterons, and helium-3 ions off gold nuclei measured by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC) is reproduced in the color glass condensate effective field theory. This contradicts the claim in C. Aidala et al. (PHENIX Collaboration), arXiv:1805.02973, that their data rule out initial state-based explanations. The underlying systematics of the effect, as discussed previously in K. Dusling, M. Mace, R. Venugopalan, Phys. Rev. D 97, 016014 (2018)PRVDAQ2470-001010.1103/PhysRevD.97.016014; Phys. Rev. Lett. 120, 042002 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.042002; Proc. Sci., QCDEV2017 (2018) 039, arise from the differing structure of strong color correlations between gluon domains of size 1/Q_{S} at fine (p_{⊥}⪆Q_{S}) or coarser (p_{⊥}⪅Q_{S}) transverse momentum resolution. Further tests of the limits of validity of this framework can be carried out in light-heavy ion collisions at both RHIC and the Large Hadron Collider. Such measurements also offer novel opportunities for further exploration of the role of the surprisingly large short-range nuclear correlations measured at Jefferson Lab.

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.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram.

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. We demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Mass Ordering of Spectra from Fragmentation of Saturated Gluon States in High-Multiplicity Proton-Proton Collisions.

The mass ordering of mean transverse momentum ⟨p_{T}⟩ and of the Fourier harmonic coefficient v_{2}(p_{T}) of azimuthally anisotropic particle distributions in high energy hadron collisions is often interpreted as evidence for the hydrodynamic flow of the matter produced. We investigate an alternative initial state interpretation of this pattern in high-multiplicity proton-proton collisions at the LHC. The QCD Yang-Mills equations describing the dynamics of saturated gluons are solved numerically with initial conditions obtained from the color-glass-condensate-based impact-parameter-dependent glasma model. The gluons are subsequently fragmented into various hadron species employing the well established Lund string fragmentation algorithm of the pythia event generator. We find that this initial state approach reproduces characteristic features of bulk spectra, in particular, the particle mass dependence of ⟨p_{T}⟩ and v_{2}(p_{T}).

Comprehensive description of J/ψ production in proton-proton collisions at collider energies.

We employ a small x color glass condensate (CGC)+ nonrelativistic QCD (NRQCD) formalism to compute J/ψ production at low p(⊥) in proton-proton collisions at collider energies. Very good agreement is obtained for total cross sections, rapidity distributions, and low momentum p(⊥) distributions. Similar agreement is obtained for ψ' production. We observe an overlap region in p(⊥) where our results match smoothly to those obtained in a next-to-leading order collinearly factorized NRQCD formalism. The relative contribution of color singlet and color octet contributions can be quantified in the CGC+NRQCD framework, with the former contributing approximately 10% of the total cross section.

Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb, and Pb+Pb collisions.

We determine the transverse system size of the initial nonequilibrium Glasma state and of the hydrodynamically evolving fireball as a function of produced charged particles in p+p, p+Pb, and Pb+Pb collisions at the Large Hadron Collider. Our results show features similar to those of recent measurements of Hanbury Brown-Twiss (HBT) radii by the ALICE Collaboration. Azimuthal anisotropy coefficients vn generated by combining the early time Glasma dynamics with viscous fluid dynamics in Pb+Pb collisions are in excellent agreement with experimental data for a wide range of centralities. In particular, event-by-event distributions of the vn values agree with the experimental data out to fairly peripheral centrality bins. In striking contrast, our results for p+Pb collisions significantly underestimate the magnitude and do not reproduce the centrality dependence of data for v2 and v3 coefficients. We argue that the measured vn data and HBT radii strongly constrain the shapes of initial parton distributions across system sizes that would be compatible with a flow interpretation in p+Pb collisions. Alternately, additional sources of correlations may be required to describe the systematics of long-range rapidity correlations in p+p and p+Pb collisions.

Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics.

Anisotropic flow coefficients v(1)-v(5) in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated v(n) data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v(2), v(3) and v(4) measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

Fluctuating glasma initial conditions and flow in heavy ion collisions.

We compute initial conditions in heavy ion collisions within the color glass condensate framework by combining the impact parameter dependent saturation model with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this impact parameter dependent Glasma description includes quantum fluctuations of color charges on the length scale determined by the inverse nuclear saturation scale Q(s). The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity ε(3)/ε(2) is close to that in a model tuned to reproduce experimental flow data. We compare transverse momentum spectra and v(2,3,4)(p(T)) of pions from different models of initial conditions using relativistic viscous hydrodynamic evolution.

Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions.

The azimuthal collimation of dihadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the color glass condensate (CGC) effective theory [A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi, and R. Venugopalan, Phys. Lett. B 697, 21 (2011).] by N(c)(2) suppressed multiladder QCD diagrams that are enhanced α(S)(-8) due to gluon saturation in hadron wave functions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger dihadron yields and predict further systematics of these yields with varying trigger p(T) and charged hadron multiplicity. Radial flow generated by rescattering is strongly limited by the structure of the p+p dihadron correlations. In contrast, radial flow explains the systematics of identical measurements in heavy ion collisions.

Collective non-Abelian instabilities in a melting color glass condensate.

We present first results for (3 + 1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time tau as exp(gamma square root(g2 mu tau)), where g2 mu is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate gamma is set by a plasmon mass, defined as omega(pl) = kappa0 square root(g2 mu/tau)), generated dynamically in the collision. We compare the numerical ratio gamma/kappa0 to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.

Quantitative study of the violation of kperpendicular factorization in hadroproduction of quarks at collider energies.

We demonstrate the violation of kperpendicular factorization for quark production in high energy hadronic collisions. This violation is quantified in the color glass condensate framework and studied as a function of the quark mass, the quark transverse momentum, and the saturation scale Q(s), which is a measure of large parton densities. At x values where parton densities are large but leading twist shadowing effects are still small, violations of kperpendicularkfactorization can be significant--especially for lighter quarks. At very small x, where leading twist shadowing is large, we show that violations of kperpendicular factorization are relatively weaker.