Azimuthal Anisotropy in U+U and Au+Au Collisions at RHIC

Imaging shapes of atomic nuclei in high-energy nuclear collisions

Atomic nuclei are self-organized, many-body quantum systems bound by strong nuclear forces within femtometre-scale space. These complex systems manifest a variety of shapes1-3, traditionally explored using non-invasive spectroscopic techniques at low energies4,5. However, at these energies, their instantaneous shapes are obscured by long-timescale quantum fluctuations, making direct observation challenging. Here we introduce the collective-flow-assisted nuclear shape-imaging method, which images the nuclear global shape by colliding them at ultrarelativistic speeds and analysing the collective response of outgoing debris. This technique captures a collision-specific snapshot of the spatial matter distribution within the nuclei, which, through the hydrodynamic expansion, imprints patterns on the particle momentum distribution observed in detectors6,7. We benchmark this method in collisions of ground-state uranium-238 nuclei, known for their elongated, axial-symmetric shape. Our findings show a large deformation with a slight deviation from axial symmetry in the nuclear ground state, aligning broadly with previous low-energy experiments. This approach offers a new method for imaging nuclear shapes, enhances our understanding of the initial conditions in high-energy collisions and addresses the important issue of nuclear structure evolution across energy scales.

Hexadecapole Deformation of ^{238}U from Relativistic Heavy-Ion Collisions Using a Nonlinear Response Coefficient

The hexadecapole deformation (β_{4}) of the ^{238}U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation (β_{2}) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic U+U collisions that is solely sensitive to β_{4} and insensitive to β_{2}. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the β_{4} of ^{238}U in heavy-ion data at the Relativistic Heavy Ion Collider.

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.

Collision-System and Beam-Energy Dependence of Anisotropic Flow Fluctuations

Elliptic flow measurements from two-, four-, and six-particle correlations are used to investigate flow fluctuations in collisions of U+U at sqrt[s_{NN}]=193  GeV, Cu+Au at sqrt[s_{NN}]=200  GeV and Au+Au spanning the range sqrt[s_{NN}]=11.5-200  GeV. The measurements show a strong dependence of the flow fluctuations on collision centrality, a modest dependence on system size, and very little if any, dependence on particle species and beam energy. The results, when compared to similar LHC measurements, viscous hydrodynamic calculations, and trento model eccentricities, indicate that initial-state-driven fluctuations predominate the flow fluctuations generated in the collisions studied.

Evidence of the Triaxial Structure of ^{129}Xe at the Large Hadron Collider

The interpretation of the emergent collective behavior of atomic nuclei in terms of deformed intrinsic shapes is at the heart of our understanding of the rich phenomenology of their structure, ranging from nuclear energy to astrophysical applications across a vast spectrum of energy scales. A new window into the deformation of nuclei has been recently opened with the realization that nuclear collision experiments performed at high-energy colliders, such as the CERN Large Hadron Collider (LHC), enable experimenters to identify the relative orientation of the colliding ions in a way that magnifies the manifestations of their intrinsic deformation. Here we apply this technique to LHC data on collisions of ^{129}Xe nuclei to exhibit the first evidence of nonaxiality in the ground state of ions collided at high energy. We predict that the low-energy structure of ^{129}Xe is triaxial (a spheroid with three unequal axes) and show that such deformation can be determined from high-energy data. This result demonstrates the unique capabilities of precision collider machines such as the LHC as new means to perform imaging of the collective structure of atomic nuclei.

Evidence of Quadrupole and Octupole Deformations in ^{96}Zr+^{96}Zr and ^{96}Ru+^{96}Ru Collisions at Ultrarelativistic Energies

In the hydrodynamic model description of heavy-ion collisions, the elliptic flow v_{2} and triangular flow v_{3} are sensitive to the quadrupole deformation β_{2} and octupole deformation β_{3} of the colliding nuclei. The relations between v_{n} and β_{n} have recently been clarified and were found to follow a simple parametric form. The STAR Collaboration has just published precision v_{n} data from isobaric ^{96}Ru+^{96}Ru and ^{96}Zr+^{96}Zr collisions, where they observe large differences in central collisions v_{2,Ru}>v_{2,Zr} and v_{3,Ru}<v_{3,Zr}. Using a transport model simulation, we show that these orderings are a natural consequence of β_{2,Ru}≫β_{2,Zr} and β_{3,Ru}≪β_{3,Zr}. We reproduce the centrality dependence of the v_{2} ratio qualitatively and v_{3} ratio quantitatively and extract values of β_{2} and β_{3} that are consistent with those measured at low-energy nuclear structure experiments. STAR data provide the first direct evidence of strong octupole correlations in the ground state of ^{96}Zr in heavy-ion collisions. Our analysis demonstrates that flow measurements in high-energy, heavy-ion collisions, especially using isobaric systems, are a new precision tool to study nuclear structure physics.

Impact of Nuclear Deformation on Relativistic Heavy-Ion Collisions: Assessing Consistency in Nuclear Physics across Energy Scales

In the hydrodynamic framework of heavy-ion collisions, elliptic flow v_{2} is sensitive to the quadrupole deformation β of the colliding ions. This enables one to test whether the established knowledge on the low-energy structure of nuclei is consistent with collider data from high-energy experiments. We derive a formula based on generic scaling laws of hydrodynamics to relate the difference in v_{2} measured between collision systems that are close in size to the value of β of the respective species. We validate our formula in simulations of ^{238}U+^{238}U and ^{197}Au+^{197}Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to experimental data. Using the deformation of ^{238}U from low-energy experiments, we find that RHIC v_{2} data implies 0.16≲|β|≲0.20 for ^{197}Au nuclei, i.e., significantly more deformed than reported in the literature, posing an interesting issue in nuclear phenomenology.

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.

Observing the Deformation of Nuclei with Relativistic Nuclear Collisions

I show that particle collider experiments on relativistic nuclear collisions can serve as direct probes of the deformation of the colliding nuclear species. I argue that collision events presenting very large multiplicities of particles and very small values of the average transverse momentum of the emitted hadrons probe collision geometries in which the nuclear ellipsoids fully overlap along their longer side. By looking at these events one selects interaction regions whose elliptic anisotropy is determined by the deformed nuclear shape, which becomes accessible experimentally through the measurement of the elliptic flow of outgoing hadrons.

Correlations in the Initial Conditions of Heavy-Ion Collisions

Ultracentral collisions of heavy nuclei, in which the impact parameter is nearly zero, are especially sensitive to the details of the initial state model and the microscopic mechanism for collective flow. In a hydrodynamic “flow” picture, the final state momentum correlations are a direct response to the fluctuating initial geometry, although models of the initial geometry differ widely. Alternatively, dynamical mechanisms based in the color glass condensate (CGC) formalism can naturally lead to many-body correlations with very different systematics. Here we present a calculation of event-by-event elliptic flow in both the hydrodynamic and CGC paradigms and show that they can be qualitatively distinguished in ultracentral collisions of deformed nuclei. Specifically, the multiplicity dependence in such collisions is qualitatively opposite, with the CGC correlations increasing with multiplicity while the hydrodynamic correlations decrease. The consistency of the latter with experimental data on UU collisions appears to rule out a CGC-mediated explanation. We find that these qualitative features also persist in small deformed systems and can therefore be a valuable test of the microscopic physics in that regime.

The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

Azimuthal Harmonics in Small and Large Collision Systems at RHIC Top Energies

The first (v_{1}^{fluc}), second (v_{2}), and third (v_{3}) harmonic coefficients of the azimuthal particle distribution at midrapidity are extracted for charged hadrons and studied as a function of transverse momentum (p_{T}) and mean charged particle multiplicity density ⟨N_{ch}⟩ in U+U (sqrt[s_{NN}]=193  GeV), Au+Au, Cu+Au, Cu+Cu, d+Au, and p+Au collisions at sqrt[s_{NN}]=200  GeV with the STAR detector. For the same ⟨N_{ch}⟩, the v_{1}^{fluc} and v_{3} coefficients are observed to be independent of the collision system, while v_{2} exhibits such a scaling only when normalized by the initial-state eccentricity (ϵ_{2}). The data also show that ln(v_{2}/ϵ_{2}) scales linearly with ⟨N_{ch}⟩^{-1/3}. These measurements provide insight into initial-geometry fluctuations and the role of viscous hydrodynamic attenuation on v_{n} from small to large collision systems.

Pseudorapidity Dependence of Particle Production and Elliptic Flow in Asymmetric Nuclear Collisions of p+Al, p+Au, d+Au, and ^{3}He+Au at sqrt[s_{NN}]=200 GeV

Asymmetric nuclear collisions of p+Al, p+Au, d+Au, and ^{3}He+Au at sqrt[s_{NN}]=200  GeV provide an excellent laboratory for understanding particle production, as well as exploring interactions among these particles after their initial creation in the collision. We present measurements of charged hadron production dN_{ch}/dη in all such collision systems over a broad pseudorapidity range and as a function of collision multiplicity. A simple wounded quark model is remarkably successful at describing the full data set. We also measure the elliptic flow v_{2} over a similarly broad pseudorapidity range. These measurements provide key constraints on models of particle emission and their translation into flow.

Phenomenology of anomalous chiral transports in heavy-ion collisions

High-energy Heavy-ion collisions can generate extremely hot quark-gluon matter and also extremely strong magnetic fields and fluid vorticity. Once coupled to chiral anomaly, the magnetic fields and fluid vorticity can induce a variety of novel transport phenomena, including the chiral magnetic effect, chiral vortical effect, etc. Some of them require the environmental violation of parity and thus provide a means to test the possible parity violation in hot strongly interacting matter. We will discuss the underlying mechanism and implications of these anomalous chiral transports in heavy-ion collisions.

Correlated Event-by-Event Fluctuations of Flow Harmonics in Pb-Pb Collisions at sqrt[s_{NN}]=2.76 TeV

We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus-nucleus collisions, obtained for the first time using a new analysis method based on multiparticle cumulants in mixed harmonics. This novel method is robust against systematic biases originating from nonflow effects and by construction any dependence on symmetry planes is eliminated. We demonstrate that correlations of flow harmonics exhibit a better sensitivity to medium properties than the individual flow harmonics. The new measurements are performed in Pb-Pb collisions at the center-of-mass energy per nucleon pair of sqrt[s_{NN}]=2.76  TeV by the ALICE experiment at the Large Hadron Collider. The centrality dependence of correlation between event-by-event fluctuations of the elliptic v_{2} and quadrangular v_{4} flow harmonics, as well as of anticorrelation between v_{2} and triangular v_{3} flow harmonics are presented. The results cover two different regimes of the initial state configurations: geometry dominated (in midcentral collisions) and fluctuation dominated (in the most central collisions). Comparisons are made to predictions from Monte Carlo Glauber, viscous hydrodynamics, ampt, and hijing models. Together with the existing measurements of the individual flow harmonics the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions.