Principle Component Analysis of two-particle correlations in PbPb and pPb collisions at CMS

A Principle Component Analysis (PCA) of two-particle azimuthal correlations as a function of transverse momentum ($p_T$) is presented in PbPb collisions at 2.76 TeV and high-multiplicity pPb collisions at 5.02 TeV. The data were recorded using the CMS detector at the LHC. It was shown that factorization breaking of two-particle azimuthal correlations can be attributed to the effect of initial-state fluctuations. Using a PCA approach, Fourier coefficients of observed two-particle azimuthal correlations as a function of both particles $p_T$ are characterized into leading and sub-leading mode terms. The leading modes are essentially equivalent to anisotropy harmonics ($v_n$) previously extracted from two-particle correlation methods as a function of $p_T$. The sub-leading modes represent the largest sources of factorization breaking. In the context of hydrodynamic models, they are a direct consequence of initial-state fluctuations. The results are presented over a wide range of centrality and event multiplicity. The results are connected to the measurement of $p_T$-dependent flow factorization breaking