Sensitivity of observables to coarse-graining size in heavy-ion collisions

An open question in the field of heavy-ion collisions is to what extent the size of initial inhomogeneities in the system affects measured observables. Here we present a method to smooth out these inhomogeneities with minimal effect on global properties, to quantify the effect of short-range features of the initial state. We show a comparison of hydrodynamic predictions with original and smoothened initial conditions for four models of initial conditions and various observables. Integrated observables (integrated $v_n$, scaled $v_n$ distributions, normalized symmetric cumulants, event-plane correlations) as well as most differential observables $\left[v_n\left(p_T\right)\right]$ show little dependence on the inhomogeneity sizes and instead are sensitive only to the largest-scale geometric structure. However, other differential observables such as the flow factorization ratio and subleading principal components are more sensitive to the granularity and could be a good tool to probe the short-scale dynamics of the initial stages of a heavy-ion collision, which are not currently well understood.

Figure 1

Top: NeXus initial energy density in a midrapidity transverse plane without modification and modified by a cubic spline filter with $\lambda =0.3$ and 1 fm. This corresponds to a central Pb-Pb collision at $\sqrt{s_{\text{NN}}}=2.76$ TeV. Bottom: MC-KLN initial energy density in a midrapidity transverse plane without modification and modified by a cubic spline filter with $\lambda =0.3$ and 1 fm. This corresponds to a noncentral Pb-Pb collision at $\sqrt{s_{\text{NN}}}=2.76$ TeV.

Figure 2

Cumulants $W_{n,m}$ as a function of smoothing parameter $\lambda$ for NeXus events in the 20–25% centrality bin. Each cumulant is normalized by its value without smoothing $W_{n,m}\left(0\right)$.

Figure 3

Top: $\langle {\epsilon }_n\rangle$ as a function of smoothing parameter $\lambda$ for NeXus events in the 20–25% centrality bin. Each $\langle {\epsilon }_n\rangle$ is normalized by its value without smoothing $\langle {\epsilon }_n\left(0\right)\rangle$. Bottom: Similar plots for $\langle r^n\rangle$.

Figure 4

Comparison of original and filtered eccentricity scaled flow harmonics $\langle v_n\rangle /\langle {\varepsilon }_n\rangle$ for the 20–25% centrality window.

Figure 5

Comparison of original and filtered scaled ${\epsilon }_n$ probability distributions for NeXus initial condition in the 20–30% windows.

Figure 6

Comparison of original and filtered scaled ${\epsilon }_n$ probability distributions for various models of initial conditions in the 20–30% windows. In the legend, lines 1, 3, and 6 indicate the symbols for the original initial conditions and lines 2, 4, and 6 for their respective filtered $\lambda =1fm$ versions.

Figure 7

Comparison of original and filtered scaled $v_2$ probability distributions for MC-KLN initial conditions.

Figure 8

Comparison of NSC(2,4) for NeXus and MC-KLN original and smoothed initial conditions.

Figure 9

Flow factorization ratio for NeXus original and smoothed initial conditions in the 20–25% centrality window and $2.5\text{GeV}<p_T^b<3.0\text{GeV}$.

Figure 10

Flow factorization ratio for MC-KLN original and smoothed initial conditions in the 20–30% centrality window and $p_T^b=3.0\text{GeV}$.

Figure 11

Leading and subleading components for NeXus original and smoothed initial conditions in the 25–30% centrality class for $n=2–4$.