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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 TeV PbPb and sqrt(s[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 pt 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 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.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 0-0.2% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 0-5% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 0-10% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 10-20% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 20-30% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 30-40% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 40-50% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ in 50-60% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 0-0.2% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 0-5% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 0-10% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 10-20% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 20-30% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 30-40% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 40-50% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ in 50-60% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ for multiplicity class $220 \leq N^{offline}_{trk}<260$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ for multiplicity class $185 \leq N^{offline}_{trk}<220$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ for multiplicity class $150 \leq N^{offline}_{trk}<185$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) elliptic flow, $v^{(\alpha)}_2$, as a function of $p_T$ $120 \leq N^{offline}_{trk}<150$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ for multiplicity class $220 \leq N^{offline}_{trk}<260$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ for multiplicity class $185 \leq N^{offline}_{trk}<220$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ for multiplicity class $150 \leq N^{offline}_{trk}<185$ in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) triangular flow, $v^{(\alpha)}_3$, as a function of $p_T$ for multiplicity class $120 \leq N^{offline}_{trk}<150$ in pPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 0-0.2% in PbPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 0-5% in PbPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 10-20% in PbPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 20-30% in PbPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 30-40% in PbPb collisions.
Pearson correlation coefficients $r_2$ and $r_3$ reconstructed using the leading and subleading flows as a function of $p^{a}_{T} - p^{b}_{T}$ in bin $p^{a}_{T}$ for centrality class 40-50% in PbPb collisions.
Elliptic and triangular ratios of subleading and leading flow as a function of multiplicity for the highest bin 2.5 < $p_T$ < 3.0 GeV in PbPb collisions.
Elliptic and triangular ratios of subleading and leading flow as a function of multiplicity for the highest bin 2.5 < $p_T$ < 3.0 GeV in pPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 0-0.2% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 0-5% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 0-10% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 10-20% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 20-30% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 30-40% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 40-50% centrality PbPb collisions.
Leading ($\alpha$ = 1) and subleading ($\alpha$ = 2) multiplicity modes, $v^{(\alpha)}_0$, as a function of $p_T$ in 50-60% centrality PbPb collisions.
Differential measurements of charged particle azimuthal anisotropy are presented for lead-lead collisions at sqrt(s_NN) = 2.76 TeV with the ATLAS detector at the LHC, based on an integrated luminosity of approximately 8 mb^-1. This anisotropy is characterized via a Fourier expansion of the distribution of charged particles in azimuthal angle (phi), with the coefficients v_n denoting the magnitude of the anisotropy. Significant v_2-v_6 values are obtained as a function of transverse momentum (0.5<pT<20 GeV), pseudorapidity (|eta|<2.5) and centrality using an event plane method. The v_n values for n>=3 are found to vary weakly with both eta and centrality, and their pT dependencies are found to follow an approximate scaling relation, v_n^{1/n}(pT) \propto v_2^{1/2}(pT). A Fourier analysis of the charged particle pair distribution in relative azimuthal angle (Dphi=phi_a-phi_b) is performed to extract the coefficients v_{n,n}=<cos (n Dphi)>. For pairs of charged particles with a large pseudorapidity gap (|Deta=eta_a-eta_b|>2) and one particle with pT<3 GeV, the v_{2,2}-v_{6,6} values are found to factorize as v_{n,n}(pT^a,pT^b) ~ v_n(pT^a)v_n(pT^b) in central and mid-central events. Such factorization suggests that these values of v_{2,2}-v_{6,6} are primarily due to the response of the created matter to the fluctuations in the geometry of the initial state. A detailed study shows that the v_{1,1}(pT^a,pT^b) data are consistent with the combined contributions from a rapidity-even v_1 and global momentum conservation. A two-component fit is used to extract the v_1 contribution. The extracted v_1 is observed to cross zero at pT\sim1.0 GeV, reaches a maximum at 4-5 GeV with a value comparable to that for v_3, and decreases at higher pT.
The EP Resolution Factor vs. Centrality for n values from2 to 6.
The Chi Reolution Factor vs. Centrality for n values from 2 to 6.
The one-dimensional Delta(PHI) correlation function vs Delta(PHI) for |DETARAP| in the range 2 to 5 summed over all n values from 1 to 6.
The Fourier coefficient V_n,n vs. |Delta(ETARAP)| for individual n values.
The Fourier coefficient V_n vs. |Delta(ETARAP)| from the 2PC anaysis for individual n values from 2 to n.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 0 TO 5%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 5 TO 10%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 10 TO 20%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 20 TO 30%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 30 TO 40%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 40 TO 50%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 50 TO 60%.
The Fourier coefiiciant V_n vs eta for PT 0.5 TO 1 GeV and centrality 60 TO 70%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 0 TO 5%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 5 TO 10%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 10 TO 20%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 20 TO 30%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 30 TO 40%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 40 TO 50%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 50 TO 60%.
The Fourier coefiiciant V_n vs eta for PT 1 TO 2 GeV and centrality 60 TO 70%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 0 TO 5%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 5 TO 10%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 10 TO 20%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 20 TO 30%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 30 TO 40%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 40 TO 50%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 50 TO 60%.
The Fourier coefiiciant V_n vs eta for PT 2 TO 3 GeV and centrality 60 TO 70%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 0 TO 5%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 5 TO 10%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 10 TO 20%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 20 TO 30%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 30 TO 40%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 40 TO 50%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 50 TO 60%.
The Fourier coefiiciant V_n vs eta for PT 3 TO 4 GeV and centrality 60 TO 70%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 0 TO 5%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 5 TO 10%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 10 TO 20%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 20 TO 30%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 30 TO 40%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 40 TO 50%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 50 TO 60%.
The Fourier coefiiciant V_n vs eta for PT 4 TO 8 GeV and centrality 60 TO 70%.
V_n vs PT for centrality 0 TO 5%.
V_n vs PT for centrality 5 TO 10%.
V_n vs PT for centrality 10 TO 20%.
V_n vs PT for centrality 20 TO 30%.
V_n vs PT for centrality 30 TO 40%.
V_n vs PT for centrality 40 TO 50%.
V_n vs PT for centrality 50 TO 60%.
V_n vs PT for centrality 60 TO 70%.
V_n vs Centrality for PT 1 TO 2 GeV.
V_n vs Centrality for PT 2 TO 3 GeV.
V_n vs Centrality for PT 3 TO 4 GeV.
V_n vs Centrality for PT 4 TO 8 GeV.
V_n vs Centrality for PT 8 TO 12 GeV.
V_n vs Centrality for PT 12 TO 20 GeV.
2PC.V_n vs n for Centrality 0 TO 1 %.
2PC.V_n vs n for Centrality 0 TO 5 %.
2PC.V_n vs n for Centrality 5 TO 10 %.
2PC.V_n vs n for Centrality 0 TO 10 %.
2PC.V_n vs n for Centrality 10 TO 20 %.
2PC.V_n vs n for Centrality 20 TO 30 %.
2PC.V_n vs n for Centrality 30 TO 40 %.
2PC.V_n vs n for Centrality 40 TO 50 %.
2PC.V_n vs n for Centrality 50 TO 60 %.
2PC.V_n vs n for Centrality 60 TO 70 %.
2PC.V_n vs n for Centrality 70 TO 80 %.
V_nn vs n for Centrality 0 TO 1 %.
V_nn vs n for Centrality 0 TO 5 %.
V_nn vs n for Centrality 5 TO 10 %.
V_nn vs n for Centrality 0 TO 10 %.
V_nn vs n for Centrality 10 TO 20 %.
V_nn vs n for Centrality 20 TO 30 %.
V_nn vs n for Centrality 30 TO 40 %.
V_nn vs n for Centrality 40 TO 50 %.
V_nn vs n for Centrality 50 TO 60 %.
V_nn vs n for Centrality 60 TO 70 %.
V_nn vs n for Centrality 70 TO 80 %.
correlation funcitons in various pT bins.
correlation funcitons in various pT bins.
correlation funcitons in various pT bins.
correlation funcitons in various pT bins.
v_{1,1} vs eta for different combinations of pTa and pTb. Figure 18.
v_{1,1} vs eta for different combinations of pTa and pTb. Figure 18.
v_{1,1} vs eta for different combinations of pTa and pTb. Figure 18.
v_{1,1} vs eta for different combinations of pTa and pTb. Figure 18.
v_{1} vs pT for different centrality selections, Figure 21.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_n extracted from 2PC method utilizing the factorization relation.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
v_ vs pta for various centrality pta combinations.
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