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.

Viscosities of the Baryon-Rich Quark-Gluon Plasma from Beam Energy Scan Data.

This work presents the first Bayesian inference study of the (3+1)D dynamics of relativistic heavy-ion collisions and quark-gluon plasma viscosities using an event-by-event (3+1)D hydrodynamics+hadronic transport theoretical framework and data from the Relativistic Heavy Ion Collider Beam energy scan program. Robust constraints on initial state nuclear stopping and the baryon chemical potential-dependent shear viscosity of the produced quantum chromodynamic (QCD) matter are obtained. The specific bulk viscosity of the QCD matter is found to exhibit a preferred maximum around sqrt[s_{NN}]=19.6 GeV. This result allows for the alternative interpretation of a reduction (and/or increase) of the speed of sound relative to that of the employed lattice-QCD based equation of state for net baryon chemical potential µ_{B}∼0.2(0.4) GeV.

Multiscale Imaging of Nuclear Deformation at the Electron-Ion Collider.

We show within the color glass condensate framework that exclusive vector meson production at high energy is very sensitive to the geometric deformation of the target nucleus at multiple length scales. We show that different multipole deformation parameters affect different regions of transverse momentum transfer. These results have two important consequences: (1) Deformations of nuclear targets need to be taken into account when making predictions for and interpreting certain observables at the EIC. (2) Differential diffractive vector meson production has the potential to become a powerful tool, enabling the most direct measurements of nuclear structure at different length scales, ranging from large scale nuclear deformation at low transverse momentum transfer to fluctuations on nucleon- and subnucleon-size scales at higher transverse momentum transfer.

Evidence of Hexadecapole Deformation in Uranium-238 at the Relativistic Heavy Ion Collider.

State-of-the-art hydrodynamic simulations of the quark-gluon plasma are unable to reproduce the elliptic flow of particles observed at the BNL Relativistic Heavy Ion Collider (RHIC) in relativistic ^{238}U+^{238}U collisions when they rely on information obtained from low-energy experiments for the implementation of deformation in the colliding ^{238}U ions. We show that this is due to an inappropriate treatment of well-deformed nuclei in the modeling of the initial conditions of the quark-gluon plasma. Past studies have identified the deformation of the nuclear surface with that of the nuclear volume, though these are different concepts. In particular, a volume quadrupole moment can be generated by both a surface hexadecapole and a surface quadrupole moment. This feature was so far neglected in the modeling of heavy-ion collisions, and is particularly relevant for nuclei like ^{238}U, which is both quadrupole deformed and hexadecapole deformed. With rigorous input from Skyrme density functional calculations, we show that correcting for such effects in the implementation of nuclear deformations in hydrodynamic simulations restores agreement with BNL RHIC data. This brings consistency to the results of nuclear experiments across energy scales, and demonstrates the impact of the hexadecapole deformation of ^{238}U on high-energy collisions.

Constraining the Nucleon Size with Relativistic Nuclear Collisions.

The notion of the "size" of nucleons and their constituents plays a pivotal role in the current paradigm of the formation and the fluctuations of the quark-gluon plasma produced in high-energy nuclear collision experiments. We report on state-of-the-art hydrodynamic results showing that the correlation between anisotropic flow v_{n}^{2} and the mean transverse momentum of hadrons [p_{t}] possesses a unique sensitivity to the nucleon size in off-central heavy-ion collisions. We argue that existing experimental measurements of this observable support a picture where the relevant length scale characterizing the colliding nucleons is of order 0.5 fm or smaller, and we discuss the broad implications of this finding for future global Bayesian analyses aimed at extracting initial-state and medium properties from nucleus-nucleus collision data, including v_{n}^{2}-[p_{t}] correlations. Determinations of the nucleon size in heavy-ion collisions will provide a solid independent constraint on the initial state of small system collisions and will establish a deep connection between collective flow data in nucleus-nucleus experiments and data on deep inelastic scattering on protons and nuclei.

Collectivity in Ultraperipheral Pb+Pb Collisions at the Large Hadron Collider.

We present the first full (3+1)D dynamical simulations of ultraperipheral Pb+Pb collisions at the Large Hadron Collider. Extrapolating from p+Pb collisions, we explore whether a quasireal photon γ^{*} interacting with the lead nucleus in an ultraperipheral collision can create a many-body system exhibiting fluid behavior. Assuming strong final-state interactions, we provide model results for charged hadron multiplicity, identified particle mean transverse momenta, and charged hadron anisotropic flow coefficients, and compare them with experimental data from the ALICE and ATLAS Collaborations. The elliptic flow hierarchy between p+Pb and γ^{*}+Pb collisions is dominated by the difference in longitudinal flow decorrelations and reproduces the experimental data well. We have demonstrated that our theoretical framework provides a quantitative tool to study particle production and collectivity for all system sizes, ranging from central heavy-ion collisions to small asymmetric collision systems at the Relativistic Heavy-Ion Collider and the Large Hadron Collider and even at the future Electron-Ion Collider.

The smallest fluid on Earth.

High energy heavy ion collisions create quark gluon plasmas that behave like almost perfect fluids. Very similar features to those that led to this insight have also been observed in experimental data from collisions of small systems, involving protons or other light nuclei. We describe recent developments aimed at understanding whether, and if so how, systems that produce relatively few particles (orders of magnitude less than in typical heavy ion collisions) and are only one to a few times the size of a proton, can behave like fluids. This involves a deeper understanding of fluid dynamics and its applicability, improvements of our understanding of the initial geometry of the collisions by considering fluctuations of the proton shape, as well as advancements in the calculation of initial state effects within an effective theory of quantum chromodynamics, which can affect the observables that are used to study fluid behavior. We further address open questions and discuss future directions.

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.

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.

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}).

Evidence of Strong Proton Shape Fluctuations from Incoherent Diffraction.

We show within the saturation framework that measurements of exclusive vector meson production at high energy provide evidence for strong geometric fluctuations of the proton. In comparison, the effect of saturation scale and color charge fluctuations is weak. This knowledge will allow detailed future measurements of the incoherent cross section to tightly constrain the fluctuating geometry of the proton as a function of the parton momentum fraction x.

Moving Forward to Constrain the Shear Viscosity of QCD Matter.

We demonstrate that measurements of rapidity differential anisotropic flow in heavy-ion collisions can constrain the temperature dependence of the shear viscosity to entropy density ratio η/s of QCD matter. Comparing results from hydrodynamic calculations with experimental data from the RHIC, we find evidence for a small η/s≈0.04 in the QCD crossover region and a strong temperature dependence in the hadronic phase. A temperature independent η/s is disfavored by the data. We further show that measurements of the event-by-event flow as a function of rapidity can be used to independently constrain the initial state fluctuations in three dimensions and the temperature dependent transport properties of QCD matter.

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.

Elliptic and triangular flow in event-by-event D=3+1 viscous hydrodynamics.

We present results for the elliptic and triangular flow coefficients v(2) and v(3) in Au+Au collisions at √s=200 AGeV using event-by-event D=3+1 viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v(2) and v(3) as functions of transverse momentum and pseudorapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v(2) and v(3) can determine η/s more precisely.

Dilepton yields from brown-rho scaled vector mesons including memory effects.

Scenarios with dropping vector meson masses, motivated by the work of Brown and Rho, have been strongly discussed after recent NA60 Collaboration data were presented. In this Letter they are investigated within a nonequilibrium field theoretical description that includes quantum mechanical memory. Dimuon yields are calculated by application of a model for the fireball, and strong modifications are found in the comparison to quasiequilibrium calculations, which assume instantaneous adjustment of all meson properties to the surrounding medium. In addition, results for the situation of very broad excitations are presented.