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

We study the initial conditions for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ 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 them to the multiplicity data of $p+\mathrm{Pb}$ and $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02$ and $2.76$ TeV, respectively. We then compute the centrality dependence of the eccentricities up to 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 the 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 CERN Large Hadron Collider.

Figure 1

(a) The probability distribution of $d{N}_{\mathrm{ch}}/d\eta$ for $p+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02$ TeV compared among data [23], the MCGM, and the shMCGM. (b) The centrality dependence of $d{N}_{\mathrm{ch}}/d\eta$ for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV compared among data [18], the MCGM, and the shMCGM.

Figure 2

The centrality dependence of eccentricities compared between the IP-Glasma model, the MCGM, and the shMCGM.

Figure 3

The centrality dependence of the ratio of rms ${\varepsilon }_2$ to ${\varepsilon }_3$ compared between the MCGM and the shMCGM. Also shown is the band as proposed in Ref. [27] that is required to explain the correlation of $v_2\text{−}{v}_3$ in data assuming the linear hydrodynamic response.

Figure 4

The E/E distribution of ${\varepsilon }_2$ compared among data [19, 20], the IP-Glasma model, the MCGM, and the shMCGM.

Figure 5

The E/E distribution of ${\varepsilon }_3$ compared among data [19, 20], the IP-Glasma model, the MCGM, and the shMCGM.

Figure 6

The E/E distribution of ${\varepsilon }_4$ compared between data [19, 20], IP-Glasma, MCGM and shMCGM.

Figure 7

The comparison between E/E distributions of ${\varepsilon }_{1,2}$ and ${\varepsilon }_2$ obtained in the shMCGM with the data of $v_2$ [19, 20].

Figure 8

The centrality dependence of the normalized standard deviation of the eccentricities compared among data [20], the MCGM, and the shMCGM.

Figure 9

The centrality dependence of $F$ of the eccentricities compared among data [21], the MCGM, and the shMCGM.