CMS-HIN-15-010

CMS-HIN-15-010 ; CERN-EP-2017-133
Principal-component analysis of two-particle azimuthal correlations in PbPb and pPb collisions at CMS
CMS Collaboration
23 August 2017
Phys. Rev. C 96 (2017) 064902
Abstract: For the first time a principal-component analysis is used to separate out different orthogonal modes of the two-particle correlation matrix from heavy ion collisions. The analysis uses data from $\sqrt{s_{\mathrm{NN}}} =$ 2.76 TeV PbPb and $\sqrt{s_{\mathrm{NN}}} =$ 5.02 TeV pPb collisions collected by the CMS experiment at the LHC. Two-particle azimuthal correlations have been extensively used to study hydrodynamic flow in heavy ion collisions. Recently it has been shown that the expected factorization of two-particle results into a product of the constituent single-particle anisotropies is broken. The new information provided by these modes may shed light on the breakdown of flow factorization in heavy ion collisions. The first two modes ("leading" and "subleading") of two-particle correlations are presented for elliptical and triangular anisotropies in PbPb and pPb collisions as a function of $p_{\mathrm{T}}$ over a wide range of event activity. The leading mode is found to be essentially equivalent to the anisotropy harmonic previously extracted from two-particle correlation methods. The subleading mode represents a new experimental observable and is shown to account for a large fraction of the factorization breaking recently observed at high transverse momentum. The principal-component analysis technique has also been applied to multiplicity fluctuations. These also show a subleading mode. The connection of these new results to previous studies of factorization is discussed.
Links: e-print arXiv:1708.07113 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Leading ( $\alpha =$ 1) and subleading ( $\alpha =$ 2) modes for $n=$ 2 as a function of ${p_{\mathrm {T}}}$ , measured in a wide centrality range of PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV. The results for the leading mode ( $\alpha =$ 1) are compared to the standard elliptic flow magnitude measured by ALICE and CMS using the two-particle correlation method taken from Refs. [7,15], respectively. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 2: Leading ( $\alpha =$ 1) and subleading ( $\alpha =$ 2) modes for $n=$ 3 as a function of ${p_{\mathrm {T}}}$ , measured in a wide centrality range of PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV. The results for the leading mode ( $\alpha =$ 1) are compared to the standard triangular flow magnitude measured by ALICE and CMS using the two-particle correlation method taken from Refs. [7,15], respectively. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 3: Leading ( $\alpha =$ 1) and subleading ( $\alpha =$ 2) modes for $n=$ 2 as a function of ${p_{\mathrm {T}}}$ , measured in high-multiplicity pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV, for four classes of reconstructed track multiplicity $N^\text {offline}_{\text {trk}}$ . The results for the leading mode ( $\alpha =$ 1) are compared to the standard elliptic flow magnitude taken from Ref. [25]. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 4: Leading ( $\alpha =$ 1) and subleading ( $\alpha =$ 2) modes for $n=$ 3 as a function of ${p_{\mathrm {T}}}$ , measured in high-multiplicity pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV, for four classes of reconstructed track multiplicity $N^\text {offline}_{\text {trk}}$ . The results for the leading mode ( $\alpha =$ 1) are compared to the standard triangular flow magnitude taken from Ref. [25]. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 5: Comparison of the Pearson correlation coefficient $r_2$ reconstructed with harmonic decomposition using the leading and subleading modes and $r_2$ values from Ref. [19], as a function of ${p_{\mathrm {T}}} ^a- {p_{\mathrm {T}}} ^b$ in bin of ${p_{\mathrm {T}}} ^a$ for six centrality classes in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 6: Comparison of the Pearson correlation coefficient $r_3$ reconstructed with harmonic decomposition using the leading and subleading modes and $r_3$ values from Ref. [19], as a function of ${p_{\mathrm {T}}} ^a- {p_{\mathrm {T}}} ^b$ in bin of ${p_{\mathrm {T}}} ^a$ for six centrality classes in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV. The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 7: The ratio between values of the subleading and leading modes, taken for the highest ${p_{\mathrm {T}}}$ bin, as a function of centrality and of charged-particle multiplicity at midrapidity (double axis). The PCA flow results for PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV (filled blue squares) and for pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV (filled red circles). The error bars correspond to statistical uncertainties and boxes to systematic ones.
png pdf	Figure 8: Leading and subleading modes for $n=$ 0, i.e. fluctuations in the total multiplicity, spanning eight centralities in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 2.76 TeV. The error bars correspond to statistical uncertainties and boxes to systematic ones. The systematic uncertainties are strongly correlated bin-to-bin.

Tables
png pdf	Table 1: Summary of estimated systematic uncertainties relative to the given mode for the last ${p_{\mathrm {T}}}$ bin 2.5 $< {p_{\mathrm {T}}} <$ 3.0 GeV/ $c$ for PbPb and pPb data.

Summary

For the first time the leading and subleading modes of elliptic and triangular flow have been measured for 5.02 TeV pPb and 2.76 TeV PbPb collisions. For PbPb collisions the leading and subleading modes of multiplicity fluctuations have also been measured. Since the principal component analysis uses all the information encoded in the covariance matrix, it provides increased sensitivity to fluctuations. For a very wide range of

$p_{\mathrm{T}}$ and centrality, the leading modes of the elliptic and triangular flow are found to be essentially equal to the anisotropy coefficients measured using the standard two-particle correlation method. For both the elliptic and triangular cases the subleading modes are non-zero and increase with

$p_{\mathrm{T}}$ . This behavior reflects a breakdown of flow factorization at high

$p_{\mathrm{T}}$ in both the pPb and PbPb systems. For charged-particle multiplicity both the leading and subleading modes increase steadily from central to peripheral PbPb events. The leading mode depends only weakly upon

$p_{\mathrm{T}}$ while the subleading mode increases strongly with

$p_{\mathrm{T}}$ . This centrality and

$p_{\mathrm{T}}$ dependence is suggestive of the presence of fluctuations in the radial flow.

In summary the subleading modes of the principal-component analysis capture new information from the spectra of flow and multiplicity fluctuations and provide an efficient method to quantify the breakdown of factorization in two-particle correlations.

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