Fluctuations of harmonic and radial flow in heavy ion collisions with principal components

TL;DR

This paper uses principal component analysis on hydrodynamic simulations of heavy ion collisions to dissect the fluctuations and factorization breaking of harmonic flow coefficients, revealing the roles of radial excitation and nonlinear mixing.

Contribution

It introduces PCA to identify dominant flow components and their origins, highlighting nonlinear effects and radial flow contributions in flow fluctuations and factorization breaking.

Findings

Leading PCA components correspond to event plane flows.

Subleading components relate to radial excitation and nonlinear mixing.

Factorization breaking varies with collision centrality.

Abstract

We analyze the spectrum of harmonic flow, $v_n(p_T)$ for $n=0\text{--}5$, in event-by-event hydrodynamic simulations of Pb+Pb collisions at the CERN Large Hadron Collider ($\sqrt{s_{NN}}=2.76\,{\text{TeV}}$) with principal component analysis (PCA). The PCA procedure finds two dominant contributions to the two-particle correlation function. The leading component is identified with the event plane $v_n(p_T)$, while the subleading component is responsible for factorization breaking in hydrodynamics. For $v_0$, $v_1$, and $v_3$ the subleading flow is a response to the radial excitation of the corresponding eccentricity. By contrast, for $v_2$ the subleading flow in \emph{peripheral collisions} is dominated by the nonlinear mixing between the leading elliptic flow and radial flow fluctuations. In the $v_2$ case, the sub-sub-leading mode more closely reflects the response to the radial excitation of $\varepsilon_2$. A consequence of this picture is that the elliptic flow fluctuations and factorization breaking change rapidly with centrality, and in central collisions (where the leading $v_2$ is small and nonlinear effects can be neglected) the subsub-leading mode becomes important. Radial flow fluctuations and nonlinear mixing also play a significant role in the factorization breaking of $v_4$ and $v_5$. We construct good geometric predictors for the orientation and magnitudes of the leading and subleading flows based on a linear response to the geometry, and a quadratic mixing between the leading principal components. Finally, we suggest a set of measurements involving three point correlations which can experimentally corroborate the nonlinear mixing of radial and elliptic flow and its important contribution to factorization breaking as a function of centrality.