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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

Heavy ion collisions at ultrarelativistic energies, such as currently studied at the top energy ranges of the Large Hadron Collider (LHC) at CERN, can typically generate more than 20 000 charged particles in each central collision

In Ref.

In this paper we present such a study of the angular power spectrum based on the analysis of public heavy-ion data from Pb-Pb collisions at

Charged particles produced in ultrarelativistic heavy ion collisions at the LHC can be described in terms of their azimuthal angle

The software HEALPix (Hierarchical Equal Area isoLatitude Pixelation)

Maps of all available events (top) and a single heavy ion event divided by it,

The polar angle relates to pseudorapidity

In order to correct for detector efficiency, we have chosen the following approach: first, all events corresponding to a certain centrality were added and thus mapped onto the same Mollweide projection (top of Fig.

The fixed value

Angular power spectra of the event in Fig.

In order to test these important edge effects on the power spectrum, we have generated 8000 distributions that are isotropic on the surface of a unit sphere and have the same multiplicities as the 0–5 % centrality. We then computed

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

Comparison between averaged power spectra of isotropic distributions for different

It is striking that the isotropic distributions shown in Fig.

Since gross features of the angular power spectrum are so well reproduced by simulations, it is straightforward to conclude that the suppression of modes with

For isotropic distributions,

Comparison between averaged odd modes of heavy ion data and isotropic power spectra for 0–5% centrality; data is fit to

Parameter

The limitation imposed by the acceptance of the TPC leads us to explore a new strategy that corrects the data from artificial suppressions of those even-

Averaged power spectra for

Averaged power spectra for

Matter produced in heavy ion collisions exhibits strikingly what is known as collective flow

Given our observed enhancement of low-

Solving for

Increased sparsity of particles leads to higher

The extraction of leading flow coefficients

Comparison between

The angular power spectrum is simply the two-point correlation function in Fourier space. In that case, computing

In regards to correlations arising from jets and resonance decays, it escapes the range of this paper to answer how the angular power spectrum responds to such effects. Having said that, it must be emphasized that the scale structure of a jet, for instance, is quite small in comparison to elliptic eccentricity. Therefore, jets are expected to mainly influence higher

We have explored some of the powerful methods of cosmic microwave background analyses when applied to the study of heavy ion collisions with very large particle multiplicities. We have shown that it is crucial to take into account the limitations of detector coverage as compared with the (almost) full-sky coverage of the cosmic microwave background. Detector limitations introduce artificial structures in the angular power spectrum

Finally, we have demonstrated that the angular power spectrum can be used to compute flow coefficients

These results show that analyzing heavy ion collisions by means of the angular power spectrum is a promising new avenue. As a measure of two-point correlations between

M.M. is most grateful to Ante Bilandzic for crucial help in the first part of this project. We thank Pavel Naselsky, Hao Liu, and You Zhou for illuminating discussions. This work was supported in part by the Danish National Research Foundation (DNRF). The research of M.M. is supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).