Flow analysis with cumulants: direct calculations (1010.0233v2)

Abstract: Anisotropic flow measurements in heavy-ion collisions provide important information on the properties of hot and dense matter. These measurements are based on analysis of azimuthal correlations and might be biased by contributions from correlations that are not related to the initial geometry, so called non-flow. To improve anisotropic flow measurements advanced methods based on multi-particle correlations (cumulants) have been developed to suppress non-flow contribution. These multi-particle correlations can be calculated by looping over all possible multiplets, however this quickly becomes prohibitively CPU intensive. Therefore, the most used technique for cumulant calculations is based on generating functions. This method involves approximations, and has its own biases, which complicates the interpretation of the results. In this paper we present a new exact method for direct calculations of multi-particle cumulants using moments of the flow vectors.

• The paper introduces a direct cumulant approach that exactly computes multi-particle correlations to yield unbiased anisotropic flow estimates.
• The method maintains linear scaling with event multiplicity and compensates for detector non-uniformities to optimize reference and differential flow calculations.
• Simulations demonstrate that the technique effectively suppresses non-flow contributions, offering a robust alternative to traditional generating function approaches.

Flow Analysis with Cumulants: Direct Calculations

The paper by Bilandzic, Snellings, and Voloshin presents a novel method for precise estimation of anisotropic flow in heavy-ion collisions through direct calculations of multi-particle cumulants using flow vectors moments. Anisotropic flow, characterized by the coefficient $v_n$ in the Fourier expansion of particle azimuthal distributions, is a key observable in understanding the properties of the quark-gluon plasma. However, its measurement can be biased by non-flow correlations unrelated to the initial collision geometry. Traditional cumulant methods, which leverage multi-particle correlations to suppress non-flow contributions, often rely on generating function approximations and can suffer from biases and computational inefficiencies.

Methodology and Contributions

The authors propose an alternative approach that computes multi-particle cumulants directly from flow vectors, avoiding the approximations typical of generating function methods while maintaining computational efficiency. This direct cumulant approach involves:

• Exact Computation: The method provides exact calculations without resorting to approximations, thus offering unbiased estimates of flow harmonics that do not suffer from interference between different harmonics.
• Operational Efficiency: The computational complexity remains linear with multiplicity, $M$, making it feasible for high-multiplicity environments typical in heavy-ion collisions.
• Reference and Differential Flow: The method distinguishes between reference flow (integrated over some momentum window) and differential flow (specific to particles of interest), providing a robust framework for flow analysis.
• Weighted Calculations: The framework accounts for particle weightings, allowing optimization of reference flow calculations for enhanced precision.
• Non-uniform Acceptance: Comprehensive accommodation for detector non-uniformities ensures applicability across experimental settings.

Results and Implications

The paper showcases the effectiveness of the proposed method through simulations and comparison with existing methodologies. Key findings include:

• Suppression of Non-flow Contributions: Multi-order cumulants effectively reduce contributions from non-flow correlations. The higher-order cumulants, in particular, provide robust anisotropic flow estimates that are resilient against non-flow interferences, as demonstrated in the paper.
• Handling of Detector Artifacts: The approach accommodates detectors with significant acceptance imperfections, achieving corrections to a degree comparable or superior to existing methods.
• Independence from Harmonic Interference: Unlike other techniques, the proposed calculations are inherently resistant to biases introduced by multiple harmonics presences, ensuring accurate extraction of anisotropic flow coefficients.

The introduction of direct cumulants as proposed by Bilandzic and collaborators represents an advancement in the measurement of anisotropic flow in heavy-ion collisions. The method's exactness, efficiency, and versatility make it a valuable tool in the continued exploration of quantum chromodynamics under extreme conditions. Future developments could involve further optimizations for even higher multiplicity scenarios and integration with experimental data analysis workflows in major particle physics experiments, such as those undertaken by the STAR and ALICE Collaborations at RHIC and LHC, respectively. This research underlines the potential for advancing our understanding of collective phenomena in heavy-ion collisions, supporting a closer examination of the quark-gluon plasma's near-perfect fluid behavior.