Collective dynamics of the high-energy proton-nucleus collisions (1304.3044v1)

Abstract: We analyze the proton-lead collisions at the LHC energy of 5.02TeV in the three-stage approach, previously used to successfully describe the relativistic A-A collisions. The approach consists of the early phase, modeled with the Glauber model, the event-by-event viscous 3+1 dimensional (3+1 D) relativistic hydrodynamics, and the statistical hadronization at freeze-out. We show that features typical of collective dynamics, such as the harmonic flow and the ridge structures in the two-particle correlations in relative azimuth and pseudorapidity, may be naturally explained in our framework. In the proton-nucleus system the harmonic flow is generated from an initially event-by-event deformed system and is entirely due to these initial fluctuations. Notably, fluctuations of strength of the initial Glauber sources which yield the observed distribution of hadron multiplicities and, at the same time, lead to correct values of the elliptic flow coefficients both from the two- and four-particle cumulant method, as measured by the ATLAS collaboration. The azimuthally asymmetric flow is not modified significantly when changing the viscosity coefficient, the initial time for the collective expansion, or the initial size of the fireball. The results present an estimate of the collective component in the two-particle correlations measured experimentally. We demonstrate that the harmonic flow coefficients can be experimentally measured with methods based on large rapidity gaps which reduce some of the other sources of correlations.

• The paper introduces a three-stage model (Glauber, hydrodynamics, hadronization) that captures collective flow in p-Pb collisions at √sNN = 5.02 TeV.
• The paper demonstrates that fluctuations in Glauber sources produce harmonic flow patterns consistent with ATLAS and CMS observations.
• The paper reveals that variations in hydrodynamic parameters, such as viscosity and start time, directly influence the emergence of ridge structures.

Analyzing Collective Dynamics in High-Energy Proton-Nucleus Collisions

The study conducted by Piotr Bożek and Wojciech Broniowski explores the intricate processes governing proton-lead (p-Pb) collisions at the Large Hadron Collider (LHC) at an energy level of $\sqrt{s_{NN}} = 5.02$ TeV. By employing a three-stage model, this research aims to capture the essence of collective dynamics, particularly focusing on harmonic flow and ridge structures observed in experimental data.

Methodological Framework

The paper's methodological structure involves a comprehensive three-stage approach:

1. Initial Phase Modeling: The authors employ the Glauber model to simulate initial conditions. This involves generating energy deposits at location points in the transverse plane and spatial rapidity. Given the complexity of events, a fluctuating weight is assigned to each source in this model, reflecting the variable deposition of energy in events.
2. Event-by-Event Hydrodynamics: Utilizing a 3+1 dimensional viscous relativistic hydrodynamical model, the researchers capture the dynamics post-initialization. This phase accounts for fluctuations and incorporates parameters for shear and bulk viscosity, examining variations in starting times and viscosity to assess their impact on flow.
3. Statistical Hadronization: THERMINATOR, a Monte Carlo event generator, is used for statistical hadronization, considering resonance decays and kinematic constraints that align precisely with experimental conditions.

Key Findings

• Harmonic Flow and Ridge Structures: The research provides insights into the harmonic flow characteristics such as elliptic and triangular flow coefficients, derived from the initial conditions’ fluctuation-dependent nature. Observations are performance-driven, derived using methods like the two- and four-particle cumulant method, with comparisons made against ATLAS and CMS experimental data.
• Fluctuations from Glauber Sources: The results elucidate that significant fluctuations in initial conditions originate from strength variations in Glauber sources. This insight is bolstered by measurements showing elliptic flow coefficients consistent with those observed experimentally by ATLAS.
• Two-Particle Correlations: By exploring these correlations, the authors find that collective behaviors such as ridge structures emerge naturally from the collective flow model. The ridge-like correlation patterns align with the azimuthal correlation across pseudorapidity, further supporting the study's collective dynamic interpretation.
• Effects of Hydrodynamic Parameters: Variability in hydrodynamic parameters, like starting time and viscosity, directly influences the characteristics of flow coefficients, offering a nuanced understanding of the collision dynamics.

Implications and Future Directions

The implications of this study notably span both theoretical and practical spheres in high-energy nuclear physics. Outstandingly, the confirmation of flow-driven collective behavior in small systems like p-Pb collisions challenges and refines the understanding of quark-gluon plasma and its formation in these environments. The ability of the model to account for experimental observations reaffirms the robustness of hydrodynamic treatment in describing such systems.

Looking forward, this research paves the way for more refined models that could include a broader scope of initial condition variances or alternative non-equilibrium models for early-stage dynamics. Furthermore, longitudinal studies contrasting p-Pb with proton-proton and nucleus-nucleus collisions could drastically enhance the understanding of collective dynamics’ emergence in varying system sizes.

In conclusion, this work profoundly contributes to the discourse on proton-nucleus collision modeling, setting a benchmark for future explorations in collective dynamics at collider facilities like the LHC.