Principal-component analysis of two-particle azimuthal correlations in PbPb and $p\text{Pb}$ collisions at CMS

For the first time a principle-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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$ PbPb and $\sqrt{s_{{}_{NN}}}=5.02\text{TeV}$ $p\text{Pb}$ collisions collected by the CMS experiment at the CERN Large Hadron Collider. Two-particle azimuthal correlations have been extensively used to study hydrodynamic flow in heavy ion collisions. Recently it was 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 $p\text{Pb}$ 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 principle-component analysis technique was also applied to multiplicity fluctuations. These also show a subleading mode. The connection of these new results to previous studies of factorization is discussed.

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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$. 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.

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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$. 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.

Figure 3

Leading $(\alpha =1)$ and subleading $(\alpha =2)$ modes for $n=2$ as a function of $p_{\mathrm{T}}$, measured in high-multiplicity $p\text{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}=5.02\text{TeV}$, for four classes of reconstructed track multiplicity $N_{\text{trk}}^{\text{offline}}$. 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.

Figure 4

Leading $(\alpha =1)$ and subleading $(\alpha =2)$ modes for $n=3$ as a function of $p_{\mathrm{T}}$, measured in high-multiplicity $p\text{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}=5.02\text{TeV}$, for four classes of reconstructed track multiplicity $N_{\text{trk}}^{\text{offline}}$. 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.

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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$. The error bars correspond to statistical uncertainties and boxes to systematic ones.

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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$. The error bars correspond to statistical uncertainties and boxes to systematic ones.

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 $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$ (solid blue squares) and for $p\text{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}=5.02\text{TeV}$ (solid red circles). The error bars correspond to statistical uncertainties and boxes to systematic ones.

Figure 8

Leading and subleading modes for $n=0$, i.e., fluctuations in the total multiplicity, spanning eight centralities in PbPb collisions at $\sqrt{s_{{}_{NN}}}=2.76\text{TeV}$. The error bars correspond to statistical uncertainties and boxes to systematic ones. The systematic uncertainties are strongly correlated bin to bin.