Eccentricities, fluctuations and A-dependence of elliptic and triangular flows in heavy-ion collisions

Abstract

A simple geometrical model with event-by-event fluctuations is suggested to study elliptical and triangular eccentricities in the initial state of relativistic heavy-ion collisions. This model describes rather well the ALICE and ATLAS data for Pb+Pb collisions at center-of-mass energy $\sqrt{s_{NN}}=5.02$~TeV per nucleon pair, assuming that the second, $v_2$, and third, $v_3$, harmonics of the anisotropic flow are simply linearly proportional to the eccentricities ${\epsilon }_2$ and ${\epsilon }_3$, respectively. We show that the eccentricity ${\epsilon }_3$ has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity ${\epsilon }_2$ is mainly related to the average collision geometry. Elliptic flow, therefore, is weakly dependent on the event-by-event fluctuations everywhere except of the very central collisions 0--2%, whereas triangular flow is mostly determined by the fluctuations. The scaling dependence of the magnitude of the flow harmonics on atomic number, $v_n\propto A^{-1/3}$, is predicted for this centrality interval.

Comments: Further development and extension of ideas discussed in arXiv:2007.04850. Accepted for publication in J. of Physics G: Nucl. and Part. Physics