Creating small circular, elliptical, and triangular droplets of quark-gluon plasma (1805.02973v2)

Abstract: The experimental study of the collisions of heavy nuclei at relativistic energies has established the properties of the quark-gluon plasma (QGP), a state of hot, dense nuclear matter in which quarks and gluons are not bound into hadrons. In this state, matter behaves as a nearly inviscid fluid that efficiently translates initial spatial anisotropies into correlated momentum anisotropies among the produced particles, producing a common velocity field pattern known as collective flow. In recent years, comparable momentum anisotropies have been measured in small-system proton-proton ($p$$+$$p$) and proton-nucleus ($p$$+$$A$) collisions, despite expectations that the volume and lifetime of the medium produced would be too small to form a QGP. Here, we report on the observation of elliptic and triangular flow patterns of charged particles produced in proton-gold ($p$$+$Au), deuteron-gold ($d$$+$Au), and helium-gold ($^3$He$+$Au) collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_{_{NN}}}$~=~200 GeV. The unique combination of three distinct initial geometries and two flow patterns provides unprecedented model discrimination. Hydrodynamical models, which include the formation of a short-lived QGP droplet, provide a simultaneous description of these measurements.

• The paper demonstrates that QGP droplets with circular, elliptical, and triangular shapes form in p+Au, d+Au, and 3He+Au collisions.
• It applies precise Fourier analysis of azimuthal anisotropies (v2 and v3) by selecting high-multiplicity events to reveal flow patterns.
• Results strongly favor hydrodynamic models, with high statistical p-values confirming the role of initial geometry in driving QGP behavior.

Analysis of Quark-Gluon Plasma Droplets in Small-System Collisions

The paper focuses on the experimental observation and analysis of quark-gluon plasma (QGP) droplets formed in small-system collisions, specifically proton-gold ($p$+Au), deuteron-gold ($d$+Au), and helium-gold ($^3$He+Au) at the Relativistic Heavy Ion Collider (RHIC). In these studies, the researchers aim to understand the properties and behavior of QGP, which is characterized by quarks and gluons existing in a deconfined state, functioning as an almost perfect fluid. This state is revealed through pronounced momentum anisotropies represented by elliptic and triangular flow patterns, quantified by the Fourier coefficients $v_2$ and $v_3$ respectively.

Experimental Methodology

To investigate the formation and properties of QGP in small systems, the study utilizes precision azimuthal anisotropy measurements of final-state particles. The azimuthal distribution of these particles is handled through a Fourier series expansion, where the significant coefficients $v_2$ and $v_3$ correspond to elliptic and triangular flow. Noteworthy is the methodology to derive these coefficients, which apply the event plane method to assess the directional flow of emitted particles. The analysis is performed on events selected from the top 5% with the highest multiplicity, thereby maximizing detection of the pertinent flow patterns.

The researchers designed a systematic study using different geometrical configurations: $p$+Au (circular geometry), $d$+Au (elliptical geometry), and $^3$He+Au (triangular geometry). This layout enables a robust test of their hypothesized hydrodynamic model. Such a model expects that anisotropies in the initial geometry would translate into corresponding anisotropies in momentum space, observable as varied $v_2$ and $v_3$ in the resultant droplet of QGP.

Models and Comparisons

The results from the experiments are juxtaposed against both hydrodynamic and initial-state momentum correlation models. In comparison to initial-state models where differences in $v_n$ should predominantly arise from momentum correlations set early during the collision, hydrodynamic models suggest the observance of flow-based phenomena linked to the initial geometry.

Foundational to the study is the cone of possible explanations for the observed anisotropies. Hydrodynamic models, such as iEBE-VISHNU, which apply relativistic viscous hydrodynamics to transition the initial spatial configurations into observable momentum distributions, convey a successful match with empirical $v_2$ and $v_3$ data. The $p$-values obtained — specifically, a combined $p$-value of 0.96 for one of the models — affirm the substantial alignment of this model with experimental data across all systems.

Conversely, models premising significant contributions from initial-state momentum correlations are less congruent, largely failing to describe the differential flow patterns across the varied small-system configurations.

Implications and Future Prospects

The findings corroborate the dominance of hydrodynamic behavior in small system collisions, aligning with the broader corpus of heavy-ion collision studies that suggest QGP formation. This is pivotal as it offers insight into the behavior of QCD matter under extreme conditions similar to those of the early universe. The results provide a comprehensive understanding of QGP that surpasses previous studies, drawing connections across differing collision systems and expanding the potential applicability of these models in future research.

Subsequent inquiries may build on these foundations, examining the finer structural properties of QGP or expanding the study to other collision energies and configurations. Understanding these phenomena on such a reduced scale could eventually translate to intricate insights into the initial conditions of our universe shortly after the Big Bang. The study sets a new baseline for experimental examination and theoretical modeling of QGP in small-system configurations, thus enhancing the empirical and conceptual toolkit available for high-energy nuclear physics.