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.
The measurement of two-particle angular correlations is a powerful tool to study jet quenching in a $p_{\mathrm{T}}$ region inaccessible by direct jet identification. In these measurements pseudorapidity ($\Delta\eta$) and azimuthal ($\Delta\varphi$) differences are used to extract the shape of the near-side peak formed by particles associated to a higher $p_{\mathrm{T}}$ trigger particle ($1 < p_{\mathrm{T, trig}} <$ 8 GeV/c). A combined fit of the near-side peak and long-range correlations is applied to the data allowing the extraction of the centrality evolution of the peak shape in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. A significant broadening of the peak in the $\Delta\eta$ direction at low $p_{\mathrm{T}}$ is found from peripheral to central collisions, which vanishes above 4 GeV/c, while in the $\Delta\varphi$ direction the peak is almost independent of centrality. For the 10% most central collisions and $1 < p_{\mathrm{T, assoc}} <$ 2 GeV/c, $1 < p_{\mathrm{T, trig}} <$ 3 GeV/c a novel feature is observed: a depletion develops around the centre of the peak. The results are compared to pp collisions at the same centre of mass energy and to AMPT model simulations. The comparison to the investigated models suggests that the broadening and the development of the depletion is connected to the strength of radial and longitudinal flow.
Variance of the near-side jet peak from a generalized Gaussian fit.
Variance of the near-side jet peak from a generalized Gaussian fit.
Variance of near-side peak in the 0-10% centrality bin divided by the variance of the near-side peak in the 50-80% centrality bin.
In two-particle angular correlation measurements, jets give rise to a near-side peak, formed by particles associated to a higher $p_{\mathrm{T}}$ trigger particle. Measurements of these correlations as a function of pseudorapidity ($\Delta\eta$) and azimuthal ($\Delta\varphi$) differences are used to extract the centrality and $p_{\mathrm{T}}$ dependence of the shape of the near-side peak in the $p_{\mathrm{T}}$ range $1 < p_{\mathrm{T}} <$ 8 GeV/c in Pb-Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. A combined fit of the near-side peak and long-range correlations is applied to the data and the peak shape is quantified by the variance of the distributions. While the width of the peak in the $\Delta\varphi$ direction is almost independent of centrality, a significant broadening in the $\Delta\eta$ direction is found from peripheral to central collisions. This feature is prominent for the low $p_{\mathrm{T}}$ region and vanishes above 4 GeV/c. The widths measured in peripheral collisions are equal to those in pp in the $\Delta\varphi$ direction and above 3 GeV/c in the $\Delta\eta$ direction. Furthermore, for the 10\% most central collisions and $1 < p_{\mathrm{T, assoc}} <$ 2 GeV/c, $1 < p_{\mathrm{T, trig}} <$ 3 GeV/c a departure from a Gaussian shape is found: a depletion develops around the centre of the peak. The results are compared to AMPT model simulations as well as other theoretical calculations indicating that the broadening and the development of the depletion is connected to the strength of radial and longitudinal flow.
Variance of the near-side jet peak from a generalized Gaussian fit.
Variance of the near-side jet peak from a generalized Gaussian fit.
Variance of near-side peak in the 0-10% centrality bin divided by the variance of the near-side peak in the 50-80% centrality bin.
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.
Angular correlations between unidentified charged trigger ($t$) and associated ($a$) particles are measured by the ALICE experiment in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV for transverse momenta $0.25 < p_{T}^{t,\, a} < 15$ GeV/$c$, where $p_{T}^t > p_{T}^a$. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval $|\eta| < 1.0$. Distributions in relative azimuth $\Delta\phi \equiv \phi^t - \phi^a$ are analyzed for $|\Delta\eta| \equiv |\eta^t - \eta^a| > 0.8$, and are referred to as "long-range correlations". Fourier components $V_{n\Delta} \equiv \langle \cos(n\Delta\phi)\rangle$ are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy $V_{n\Delta}(p_{T}^t, p_{T}^a)$ is fully described in terms of single-particle anisotropies $v_n (p_{T})$ as $V_{n\Delta}(p_{T}^t, p_{T}^a) = v_n(p_{T}^t) \, v_n(p_{T}^a)$. This expectation is tested for $1 \leq n \leq 5$ by applying a global fit of all $V_{n\Delta} (p_{T}^t, p_{T}^a)$ to obtain the best values $v_{n}\{GF\} (p_{T})$. It is found that for $2 \leq n \leq 5$, the fit agrees well with data up to $p_T^a \sim 3$-4 GeV/$c$, with a trend of increasing deviation as $p_{T}^t$ and $p_{T}^a$ are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full $0.25 < p_{T} < 15$ GeV/$c$ range using a single $v_n(p_T)$ curve; such a description is however approximately possible for $2 \leq n \leq 5$ when $p_T^a < 4$ GeV/$c$. For the $n=1$ harmonic, however, a single $v_1(p_T$ curve is not obtained even within the reduced range $p_T^a < 4$ GeV/$c$.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for two centrality classes 0-2% and 2-10%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for three centrality classes 10-20%, 20-30% and 40-50%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 8-15 GeV and associated particles in the range 6-8 GeV for two centrality classes 40-50% and 0-20%. Note that in the paper the data are plotted multiplied by 100.
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