McDIPPER: A novel saturation-based $3+1\mathrm{D}$ initial-state model for heavy ion collisions

We present a new three-dimensional resolved model for the initial state of ultrarelativistic heavy-ion collisions, based on the $k_{\perp }$-factorized color glass condensate (CGC) hybrid approach. The McDipper framework responds to the need for a rapidity-resolved initial-state Monte Carlo event generator which can deposit the relevant conserved charges (energy, charge, and baryon densities) both in the midrapidity and forward (backward) regions of the collision. This event-by-event generator computes the gluon and (anti-) quark phase-space densities using the IP-Sat model, from where the relevant conserved charges can be computed directly. In the present work we have included the leading-order contributions to the light flavor parton densities. As a feature, the model can be systematically improved in the future by adding next-to-leading-order calculations (in the CGC hybrid framework) and extending to lower energies by including subeikonal corrections to the channels included. We present relevant observables, such as the eccentricities and flow decorrelation, as tests of this new approach.

Figure 1

Diagrammatic representation for the leading-order processes included in the McDipper framework. (Left) Single gluon production of a gluon with transverse moment $\mathbf{p}$ and rapidity $y$ from the interaction of two CGCs with gluon distributions ${\mathrm{\Phi }}_1(x_1,\mathbf{q})$ and ${\mathrm{\Phi }}_2(x_2,\mathbf{k})$. (Right) Deposition of a single quark with transverse momentum $\mathbf{p}$ an rapidity $y$ from the stopping of a collinear quark from the incoming projectile with momentum fraction $x$ and virtuality ${\mathbf{p}}^2$.

Figure 2

Energy (upper panels) and electric and baryon charge deposition (lower panels) as a function of space rapidity ${\eta }_s$ for three different collisional energies, $\sqrt{s_{NN}}=0.2,2.76,5.02$ TeV, computed using the IP-Sat model with the CT18NNLO PDF set. The results here shown are presented for two different sets of fixed thickness, $T_{1,p}=T_{2,p}=2{\mathrm{fm}}^{-2}$ (left panels) and $T_{1,p}=1{\mathrm{fm}}^{-2}$, $T_{2,p}=4{\mathrm{fm}}^{-2}$ (right panels). The neutron density is fixed to zero for both projectiles for this representation, meaning $T_{1,n}=T_{2,n}=0$.

Figure 3

Energy (upper panels) and electric and baryon charge deposition (lower panels) as a function of space rapidity ${\eta }_s$ for $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, computed using both the IP-Sat and GBW model with the CT18NNLO PDF set. The results shown are presented for two different sets of fixed thickness, $T_{1,p}=T_{2,p}=2{\mathrm{fm}}^{-2}$ (left panels) and $T_{1,p}=1{\mathrm{fm}}^{-2}$, $T_{2,p}=4{\mathrm{fm}}^{-2}$ (right panels). The neutron density is fixed to zero for both projectiles for this representation, meaning $T_{1,n}=T_{2,n}=0$.

Figure 4

Energy (upper panels) and electric and baryon charge deposition (lower panels) as a function of the proton thickness $T_{2,p}$ for fixed $T_{1,p}=2{\mathrm{fm}}^{-2}$ and collisional energy $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, computed using both the IP-Sat and GBW model with the CT18NNLO PDF set. The results here shown are presented for two different sets of fixed space-time rapidity, ${\eta }_s=0$ (left panels) and ${\eta }_s=3$ (right panels).

Figure 5

Comparison of the energy density (top), electric charge density $Q$ (middle), and baryon charge-density $B$ (bottom) deposition when using different PDFs. Here are pictured the conserved charges when using the CT18NLO, CT18NLO, and CT14NNLO sets. As the reader can easily see, while the energy density changes around the fragmentation region, $Q$ and $B$ do not change, as expected. The former is due to differences in the parametrization of the sea-quark PDFs.

Figure 6

Charged particle yield as a function of centrality for $\sqrt{s_{\mathrm{NN}}}=200$ GeV (top), $\sqrt{s_{\mathrm{NN}}}=2.76$ GeV (center), and $\sqrt{s_{\mathrm{NN}}}=5.02$ GeV (bottom). Experimental data shown in the figure for Au-Au at $\sqrt{s_{\mathrm{NN}}}=200$ GeV is from Ref. [64], Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV from Refs. [65, 66], and $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV from Refs. [67, 68]. The bands represent the uncertainties in $\eta /s$ and $C_{\infty }$ for the estimates presented here, where they correspond to variations of $C_{\infty }=0.8-1.15$ and $\eta /s=0.08-0.24$.

Figure 7

Eccentricities in the IP-Sat (full symbols) and GBW (empty symbols) models as a function of centrality, ${\eta }_s$. We show here the $n=2,3,4$ harmonics (blue squares, red circles, and yellow diamonds, respectively) for Pb-Pb collisions at 2.76 TeV at midrapidity ${\eta }_s=0$. Included is a comparison to ${\mathrm{T}}_{\mathrm{R}}\mathrm{ENTo}$ [10, 63] and IP-Glasma [69] models.

Figure 8

Energy (a) and charge (b) profiles for different rapidity windows in a single 5.02-TeV $\mathrm{Pb}+\mathrm{Pb}$ event in the $0\%-5\%$ centrality class. The energy profiles are given for gluon energy deposition ($a$, upper panels) and quark energy density ($a$, lower panels). The rapidity windows are chosen for $\eta =0$ (left panels) and $\eta =4$ (left panels). In (b) the deposited electric ($b$, upper panels) and baryon ($b$, lower panels) charges are shown for the same rapidity windows.

Figure 9

Transverse deposition of energy (top panels), electric charge (central panels), and baryon charge (lower panels). Results are presented for Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV (left panels) and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV (right panels) for different centrality classes. The computation is performed using the IP-Sat model with the CT18NNLO PDF set.

Figure 10

Eccentricities in the IP-Sat (full symbols) and GBW (empty symbols) models as a function of space-time rapidity, ${\eta }_s$. We show here the $n=2,3,4$ harmonics (in descending order) for Pb-Pb collisions at 2.76 TeV and three centrality classes, $0\%-5\%$, $10\%-20\%$, and $30\%-40\%$.

Figure 11

Flow decorrelation of initial spatial eccentricities $r_n$ in Au-Au collisions $\sqrt{s}=200$ GeV for the GBW and IP-Sat models. In this figure we present the results for the harmonics $n=2,3,4$, (left), (center), and (right) panels, respectively, and a reference rapidity of ${\eta }_b=2.5\text{–}4.7$ [5].

Figure 12

Comparison of the decorrelation of initial spatial eccentricities $r_n$ of Pb-Pb collisions $\sqrt{s}=2.76$ TeV for the GBW and IP-Sat models. In this figure we present the results for the harmonics $n=2,3,4$ and a reference rapidity of ${\eta }_b=4.4\text{–}5.0$. The black squares correspond to experimental data from the CMS Collaboration [6].