Angular power spectrum of heavy ion collisions

Particles produced in heavy ion collisions carry information about anisotropies present already in the early state of the system and play a crucial role in understanding the quark gluon plasma and its evolution. We explore the angular power spectrum of particle multiplicities in such heavy ion collisions to extract fluctuations in particle multiplicities on the surface a sphere. Results are presented for Pb-Pb data at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$, extracted from the ALICE open data portal. We find that odd modes of the power spectrum display a power-law behavior with corresponding index $\beta$, which is found to be close to unity. We also demonstrate that the angular power spectrum allows us to extract accurately the flow coefficients of noncentral collisions.

Figure 1

Maps of all available events (top) and a single heavy ion event divided by it, $f(\theta ,\varphi )/F^{\mathrm{all}}(\theta ,\varphi )$, (bottom) for 0–5 % centrality at energy $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ within $\left|\eta \right|<0.9$.

Figure 2

Angular power spectra of the event in Fig. 1 (diamonds) and of a 8000-event average (circles).

Figure 3

Comparison between averaged power spectra of heavy ion data and isotropic distributions for 0–5% centrality.

Figure 4

Comparison between averaged power spectra of isotropic distributions for different $\eta$ range values.

Figure 5

Comparison between averaged odd modes of heavy ion data and isotropic power spectra for 0–5% centrality; data is fit to $C\left(l\right)$.

Figure 6

Parameter $\beta$ resultant of fit to $C\left(l\right)$ as a function of centrality.

Figure 7

Averaged power spectra for $m\ne 0$ at 0–5% centrality. Real data are represented by the circles, while isotropic distributions are the stars.

Figure 8

Averaged power spectra for $m\ne 0$ at all centralities.

Figure 9

Comparison between $v_1$ (a), $v_2$ (b), and $v_3$ (c) calculated with the power spectrum approach and the $Q$ cumulants on real ALICE data [8].