| Angular correlations between unidentified charged trigger ($t$) and associated ($a$) particles are measured by the ALICE experiment in \PbPb\ collisions at $\snn=2.76$ 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 $V_{n\Delta} \equiv <\cos(n\Delta\phi)>$ are extracted from the long-range azimuthal correlation functions. If the particle pair correlation arises dominantly from production mechanisms that distribute according to a common plane of symmetry, then the pair $\vnd$ coefficients are expected to factorize as the product of single-particle anisotropies $v_n (\pt)$, i.e. $V_{n\Delta}(p_{T}^t, p_{T}^a) = v_n(p_{T}^t) \, v_n(p_{T}^a)$. This expectation is tested for $1 \leq n \leq 5$ by applying a global fit of all $\vnd (p_{T}^t, p_{T}^a)$ to obtain the best values $\vngf (\pt)$. It is found that for $2 \leq n \leq 5$, the factorization holds for associated particle momenta up to $\pta \sim 3$-4 GeV/$c$, with a trend of increasing deviation between the data and the factorization hypothesis as $p_{T}^t$ and $p_{T}^a$ are increased or as collisions become more peripheral. $V_{1\Delta}$ does not factorize precisely at any $\pt$ or centrality, as indicated by the lack of a good global fit over the full $\ptt, \pta$ range. The $\vngf$ values for $2 \leq n \leq 5$ from the global fit are in close agreement with previous measurements. |
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