Relative flow fluctuations as a probe of initial state fluctuations

Elliptic flow, ${v}_{2}$, and triangular flow, ${v}_{3}$, are to a good approximation linearly proportional to the corresponding spatial anisotropies of the initial density profile, ${\ensuremath{\varepsilon}}_{2}$ and ${\ensuremath{\varepsilon}}_{3}$. Using event-by-event hydrodynamic simulations, we point out when deviations from this linear scaling are to be expected. When these deviations are negligible, relative ${v}_{n}$ fluctuations are equal to relative ${\ensuremath{\varepsilon}}_{n}$ fluctuations, and one can directly probe models of initial conditions using ratios of cumulants, for instance ${v}_{n}{4}/{v}_{n}{2}$. We argue that existing models of initial conditions tend to overestimate flow fluctuations in central Pb + Pb collisions, and to underestimate them in peripheral collisions. We make predictions for ${v}_{3}{6}$ in noncentral Pb + Pb collisions, and for ${v}_{3}{4}$ and ${v}_{3}{6}$ in high-multiplicity $p+\text{Pb}$ collisions.

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