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Register a new userPrincipal Component Analysis of collective flow in Relativistic Heavy-Ion Collisions
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In this paper, we implement Principal Component Analysis (PCA) to study the single particle distributions generated from thousands of {tt VISH2+1} hydrodynamic simulations with an aim to explore if a machine could directly discover flow from the huge amount of data without explicit instructions from human-beings. We found that the obtained PCA eigenvectors are similar to but not identical with the traditional Fourier bases. Correspondingly, the PCA defined flow harmonics $v_n^prime$ are also similar to the traditional $v_n$ for $n=2$ and 3, but largely deviated from the Fourier ones for $ngeq 4$. A further study on the symmetric cumulants and the Pearson coefficients indicates that mode-coupling effects are reduced for these flow harmonics defined by PCA.
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The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy ion collisions. Using simulated data from AMPT and HIJING models, we show that the PCA modes are not fixed, but depend on the choice of the particle weight and the $p_T$ range. Furthermore, the shape of the leading mode is affected by the presence of non-flow correlations, and fake subleading mode may arise from the mixing of non-flow correlations with leading flow mode with a magnitude that could be larger than the genuine subleading flow mode. Therefore, the meaning of PCA modes and their relations to physical leading and subleading flow modes associated initial state eccentricities need to be further clarified/validated in realistic model simulations.
The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb+Pb collisions at $sqrt{s}=2760$GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of $v_2^2$ and $v_4$, of $v_2v_3$ and $v_5$, or of $v_2^3$, $v_3^3$, and $v_6$. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.
A systematic analysis of correlations between different orders of $p_T$-differential flow is presented, including mode coupling effects in flow vectors, correlations between flow angles (a.k.a. event-plane correlations), and correlations between flow magnitudes, all of which were previously studied with integrated flows. We find that the mode coupling effects among differential flows largely mirror those among the corresponding integrated flows, except at small transverse momenta where mode coupling contributions are small. For the fourth- and fifth-order flow vectors $V_4$ and $V_5$ we argue that the event plane correlations can be understood as the ratio between the mode coupling contributions to these flows and and the flow magnitudes. We also find that for $V_4$ and $V_5$ the linear response contribution scales linearly with the corresponding cumulant-defined eccentricities but not with the standard eccentricities.
In high-energy heavy-ion collisions, structures in the initial collision zone are a matter of intense investigation, both from theory and experimental points of view. A large number of models have been developed to represent the initial state of the collision including Glauber model, Colour Glass Condensate (CGC) among others. Another important aspect of the study is to investigate proper observables that will be sensitive to the initial collision zone. In this work, we have discussed a formalism to implement the spatial clusters at the partonic level in the string melting version of the AMPT model for PbPb collisions at $sqrt{s_{NN}}$ = 200 GeV. These clusters are then propagated through the AMPT hadronization scheme. The Principal Component Analysis (PCA) has been used on the $eta$, $phi$ and $p_T$ distributions of the produced charged particles and the eigenvalues have been compared before and after the implementation of the clustering. It is found that for all these three different distributions, all the prominent PCA modes have shown sensitivity to the clustering. A centrality dependent study has also been performed on those eigenvalues.
Radial flow can be directly extracted from the azimuthal distribution of mean transverse rapidity. We apply the event-plane method and the two-particle correlation method to estimate the anisotropic Fourier coefficient of the azimuthal distribution of mean transverse rapidity. Using the event sample generated by a multiphase transport model with string melting, we show that both methods are effective. For the two-particle correlation method to be reliable, the mean number of particles in an azimuthal bin must be above a certain threshold. Using these two methods, anisotropic radial flow can be estimated in a model-independent way in relativistic heavy-ion collisions.
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