Initial conditions from the shadowed Glauber model for Pb+Pb at $\sqrt{s_{\rm NN}}=2.76$ TeV

We study the initial conditions for Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV using the two component Monte-Carlo Glauber model with shadowing of the nucleons in the interior by the leading ones. The model parameters are fixed by comparing to the multiplicity data of p+Pb and Pb+Pb at $\sqrt{s_{\rm NN}}=5.02$ and $2.76$ TeV respectively. We then compute the centrality dependence of the eccentricities upto the fourth order as well as their event by event distributions. The inclusion of shadowing brings the Monte-Carlo Glauber model predictions in agreement with data as well as with results from other dynamical models of initial conditions based on gluon saturation at high energy nuclear collisions. Further, we find that the shadowed Glauber model provides the desired relative magnitude between the ellipticity and triangularity of the initial energy distribution required to explain the data on the even and odd flow harmonics $v_2$ and $v_3$ respectively at the LHC.