[Paper Review] Observation of the collective flow in proton-proton collisions

Piotr Bożek|arXiv (Cornell University)|Nov 12, 2009

High-Energy Particle Collisions Research7 references3 citations

TL;DR

This paper proposes that collective flow in proton-proton collisions at LHC energies can be detected through multiplicity-dependent elliptic flow ($v_2$) in high-multiplicity events, where two flux tubes create an initial azimuthal asymmetry. Hydrodynamic simulations show that such asymmetric sources generate measurable $v_2$ that departs from statistical fluctuations, with $\sqrt{N}v_2 \approx 0.95$ in one-string events and saturation at high multiplicities due to two-string dominance.

ABSTRACT

The scenario of a collective expansion of matter created in proton-proton (p-p) collisions at the CERN Large Hadron Collider (LHC) is discussed. Assuming a small transverse size and a formation time of 0.1fm/c of the source we observe the build up of a substantial transverse flow in relativistic hydrodynamic simulations. In order to demonstrate the collectivity in p-p collisions we propose to look at the multiplicity dependence of the elliptic flow coefficient. If high multiplicity events originate from azimuthally asymmetric events containing two flux tubes, an observable signal above the statistical fluctuations in the measured elliptic flow could appear.

Motivation & Objective

• To identify a clear signature of collectivity in p-p collisions, where traditional hydrodynamic models are questionable due to small system size.
• To address the challenge of distinguishing true collective flow from statistical fluctuations in low-multiplicity p-p events.
• To investigate whether initial-state azimuthal asymmetry from two flux tubes can generate observable elliptic flow in high-multiplicity p-p collisions.
• To demonstrate that $v_2$ deviates from the $1/\sqrt{N}$ dependence expected for uncorrelated emission, providing a testable signature of collectivity.
• To validate the hydrodynamic model's predictions against HBT radii and $v_2$ measurements, showing consistency with experimental trends.

Proposed method

• Uses ideal relativistic hydrodynamics with Bjorken scaling in the longitudinal direction and a Gaussian transverse energy density profile $\epsilon_{FT}(x,y) = \epsilon_0 \exp\left(-\frac{x^2 + y^2}{2\sigma^2}\right)$, with $\sigma = 0.5$ fm.
• Models the initial state as a single flux tube (azimuthally symmetric) or two flux tubes (asymmetric), with energy density $\epsilon_{FT}(x,y) = \epsilon_{FT}(x,y - d/2) + \epsilon_{FT}(x,y + d/2)$ for $d = 0.7$–$0.9$ fm.
• Sets initial time $\tau_0 = 0.1$ fm/c and freeze-out temperature $T_{\text{fo}} = 140$ MeV, using THERMINATOR for particle emission and resonance decays.
• Calculates the elliptic flow coefficient $v_2 = \frac{1}{N} \sum_{i=1}^N \cos(2(\phi_i - \Psi))$, where $\Psi$ is the event-wise reaction plane angle to maximize $v_2$.
• Estimates the contribution of statistical fluctuations via $v_2 \approx \sqrt{\pi}/(2\sqrt{N}) \approx 0.866/\sqrt{N}$, used as a baseline for comparison.
• Computes HBT interferometry radii from Gaussian fits to correlation functions, accounting for finite lifetime effects.

Experimental results

Research questions

• RQ1 Can collective flow in p-p collisions be distinguished from statistical fluctuations in particle emission?
• RQ2 Does the presence of two flux tubes in high-multiplicity p-p events lead to an initial eccentricity that generates measurable elliptic flow?
• RQ3 How does the elliptic flow $v_2$ depend on total charged particle multiplicity $N$ in p-p collisions at LHC energies?
• RQ4 To what extent does hydrodynamic expansion of a small, short-lived fireball produce observable transverse flow and modified HBT radii?
• RQ5 Can the multiplicity dependence of $\sqrt{N}v_2$ serve as a signature to distinguish collective effects from uncorrelated emission?

Key findings

• Hydrodynamic simulations show that a p-p fireball with a lifetime of ~2 fm/c and initial time $\tau_0 = 0.1$ fm/c develops significant transverse flow, reaching ~0.5c at freeze-out.
• The HBT radii increase to ~1.5 fm due to finite lifetime effects, consistent with experimental data from STAR at RHIC.
• For one-string events, $\sqrt{N}v_2 \approx 0.95$, exceeding the statistical fluctuation baseline $\approx 0.866/\sqrt{N}$, indicating non-trivial correlations.
• In high-multiplicity events dominated by two-string configurations, $v_2$ saturates instead of decreasing as $1/\sqrt{N}$, signaling a departure from statistical fluctuations.
• The elliptic flow from primordial particles follows the statistical fluctuation formula, while the full $v_2$ includes contributions from resonance decays and collective dynamics.
• The model predicts that after subtracting statistical fluctuations, a non-zero signal in $v_2$ at high multiplicity would confirm the presence of collective flow in p-p collisions.