Measurement of the distributions of event-by-event flow harmonics in Pb-Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}}$=2.76 TeV

The event-by-event distributions of harmonic flow coefficients $v_n$ for $n$=2--4 are measured in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV, using charged particles with $p_T> 0.5$ GeV and in the pseudorapidity range $|\eta|<2.5$. These distributions are obtained by unfolding the raw $v_n$ distributions with a response function that accounts for the smearing of the $v_n$ due to finite number of tracks in the detector acceptance. The shape of the unfolded distributions is found to be consistent with a 2-D Gaussian for the underlying flow vector in central collisions for $v_2$ and over the full centrality range for $v_3$ and $v_4$; When these distributions are rescaled to the same $\langle v_n\rangle$, the resulting shapes are found to be nearly the same between $p_T<1$~GeV and $p_T>1$ GeV. The $v_n$ distributions are compared with the eccentricity distributions from two initial geometry models: a Glauber model and a model that includes corrections to the initial geometry due to gluon saturation effects. Both models fail to describe the experimental data consistently across the full centrality range. These results may shed light on the nature of the fluctuation of the created matter in the initial state as well as the subsequent hydrodynamic evolution.