3D glasma initial state for relativistic heavy ion collisions

We extend the impact-parameter-dependent Glasma model to three dimensions using explicit small-$x$ evolution of the two incoming nuclear gluon distributions. We compute rapidity distributions of produced gluons and the early-time energy momentum tensor as a function of space-time rapidity and transverse coordinates. We study rapidity correlations and fluctuations of the initial geometry and multiplicity distributions and make comparisons to existing models for the three-dimensional initial state.

Figure 1

Computation scheme for single inclusive observables (left) at midrapidity and (right) forward or backward rapidity. Starting from the IP-Glasma parametrization of gluon distributions at an initial rapidity scale, JIMWLK rapidity evolution is applied to both nuclei to resum leading logarithmic corrections to inclusive observables. While the same amount of rapidity evolution, $\mathrm{\Delta }{y}_{1/2}=\mathrm{\Delta }{y}_0$, is applied to both nuclei to compute observables at midrapidity $\left(y_{\mathrm{obs}}=0\right)$, the amount of evolution in the two nuclei is different, $\mathrm{\Delta }{y}_{1/2}=\mathrm{\Delta }{y}_0\pm y_{\mathrm{obs}}$, when computing observables at forward or backward rapidities $\left(y_{\mathrm{obs}}\ne 0\right)$.

Figure 2

JIMWLK evolution of the gluon fields in one nucleus for $m=0.4$ GeV and ${\alpha }_s=0.3$. Shown is $1-\mathrm{Re}\left[\mathrm{tr}\left(V_{\mathbf{x}}\right)\right]/N_c$ in the transverse plane at rapidities $Y=-2.4 \left(x\approx 2\times {10}^{-3}\right)$ (a), $Y=0 \left(x\approx 2\times {10}^{-4}\right)$ (b), and $Y=2.4 \left(x\approx 1.6\times {10}^{-5}\right)$ (c) to illustrate the change of the typical transverse length scale with decreasing $x$. The global geometry clearly remains correlated over the entire range in rapidity.

Figure 3

View of the three-dimensional distribution of $T^{\tau \tau }$ in a single event from different angles, covering the entire transverse plane and 4.8 units in rapidity.

Figure 4

(a) Gluon multiplicity relative to its value at $Y=0$ for ${\alpha }_s=0.15,{\alpha }_s=0.225$, and ${\alpha }_s=0.3$ using $m=0.4$ GeV. The various dashed lines show results from three single events for each value of the coupling constant. The green dash-dot-dotted line is a Gaussian fit to the charged hadron $d{N}_{\mathrm{ch}}/dY$ data from the ALICE Collaboration [67]. (b) The same results plotted vs ${\alpha }_{s}Y$.

Figure 5

The correlation function $C_N(Y_1,Y_2)$ for $m=0.4$ GeV and ${\alpha }_s=0.15$ (a) and ${\alpha }_s=0.3$ (b).

Figure 6

Legendre coefficients $\sqrt{|a_{n,m}|}$ labeled by $(n,m)$ of the gluon multiplicity correlator for different values of ${\alpha }_s$ and $m$.

Figure 7

Change of the eccentricity relative to its value at $\eta =0$ [panels (a)–(c)] and the corresponding variation in angle quantified by $sin\left\{n[{\varphi }_n\left(\eta \right)-{\varphi }_n\left(0\right)]\right\}$ [panels (d)–(f)] in three single configurations. Simulations used ${\alpha }_s=0.3$ and $m=0.4$ GeV.

Figure 8

Decorrelation of the initial spatial eccentricity $r_2({\eta }_a,{\eta }_b)$ for ${\eta }_b=2.4$ in central events ($b=0$ fm) using three different values of ${\alpha }_s$. We compare to experimental data from the CMS Collaboration [65].

Figure 9

Decorrelation of the initial spatial eccentricity $r_3({\eta }_a,{\eta }_b)$ for ${\eta }_b=2.4$ in central events ($b=0$ fm) using three different values of ${\alpha }_s$. We compare to experimental data from the CMS Collaboration [65].

Figure 10

Decorrelation of the initial spatial eccentricity $r_2({\eta }_a,{\eta }_b)$ for ${\eta }_b=2.4$ in central events ($b=0$ fm) with ${\alpha }_s=0.225$, compared to results from the torque model [77], the AMPT model [76], and the 3DMCG model [15]. We compare to experimental data from the CMS Collaboration [65].

Figure 11

Decorrelation of the initial spatial eccentricity $r_3({\eta }_a,{\eta }_b)$ for ${\eta }_b=2.4$ in central events ($b=0$ fm) with ${\alpha }_s=0.225$, compared to results from the torque model [77], the AMPT model [76], and the 3DMCG model [15]. We compare to experimental data from the CMS Collaboration [65].

Figure 12

The deviation in percent of ${\epsilon }_n\left({\eta }_a\right)$ from ${\epsilon }_n\left(0\right)$ given by $\mathrm{\Delta }{\epsilon }_n({\eta }_a,0)$ for $n=2$ (a) and $n=3$ (b) with $m=0.4$ GeV.

Figure 13

Change in angle ${\varphi }_n\left({\eta }_a\right)$ relative to ${\varphi }_n\left(0\right)$ quantified by $〈cos\left\{n[{\varphi }_n\left({\eta }_a\right)-{\varphi }_n\left(0\right)]\right\}〉$ for $n=2$ (a) and $n=3$ (b) with $m=0.4$ GeV.

Figure 14

Legendre coefficients of the expansion of the eccentricity-vector correlator, characterizing fluctuations of the transverse geometry in rapidity.