Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions

We introduce a new parametric initial-condition model for high-energy nuclear collisions based on eikonal entropy deposition via a “reduced-thickness” function. The model simultaneously describes experimental proton-proton, proton-nucleus, and nucleus-nucleus multiplicity distributions and generates nucleus-nucleus eccentricity harmonics consistent with experimental flow constraints. In addition, the model is compatible with ultracentral uranium-uranium data unlike existing models that include binary collision terms.

Figure 1

Reduced thickness of a pair of nucleon participants. The nucleons collide with a nonzero impact parameter along the $x$ direction as shown in the upper right. The gray short-dashed lines are one-dimensional cross sections of the participant nucleon thickness functions $T_A,T_B$, and the colored lines are the reduced thickness $T_R$ for $p=1,0,-1$ (green dashed, blue solid, orange dash-dotted curves).

Figure 2

Multiplicity distributions for proton-proton, proton-lead, and lead-lead collisions. The histograms are ${\mathrm{T}}_{\mathrm{R}}\mathrm{ENTo}$ results for reduced thickness parameter $p=-1$ (top, orange), $p=0$ (middle, blue), and $p=1$ (bottom, green), with approximate best-fit fluctuation parameters $k$ and normalizations given in Table 1. The shaded bands show the sensitivity from varying $k$ by $\pm 30\%$. Data points (triangles, squares, circles) are experimental distributions from ALICE [34, 35] offset by powers of ten for comparison with the model.

Figure 3

Left and middle panels show eccentricity harmonics ${\varepsilon }_2$ and ${\varepsilon }_3$ as a function of centrality for reduced-thickness parameters $p=1,0,-1$ (green dashed, blue solid, orange dash-dotted curves). The shaded bands show the sensitivity from varying $k$ by $\pm 30\%$ from the values in Table 1. Right panel shows ratio of the root-mean-square eccentricities ${\left[{(\langle {\varepsilon }_2^2\rangle /\langle {\varepsilon }_3^2\rangle )}^{1/2}\right]}^{0.6}$ against the allowed region (gray band) and the ratio computed by IP-Glasma (circles) [17]. Note that the axes have different ranges in the ratio plot.

Figure 4

Comparison of tip-tip and side-side uranium-uranium collisions. Schematics are shown from a side view and looking down the beam axis, and the following quantities are compared: ellipticity ${\varepsilon }_2$, number of participating nucleons, $N_{\text{part}}$, and number of binary nucleon-nucleon collisions, $N_{\text{coll}}$.

Figure 5

Ellipticity ${\varepsilon }_2$ as a function of normalized charged-particle multiplicity $N_{\text{ch}}/\langle N_{\text{ch}}\rangle$ in ultracentral uranium-uranium and gold-gold collisions at RHIC. The top and bottom plots show the top 0.1% and 1% of collisions selected by number of spectators to mimic STAR's experimental zero-degree calorimeter (ZDC) selection [29]. Blue points with error bars are binned ${\mathrm{T}}_{\mathrm{R}}\mathrm{ENTo}$ results with reduced-thickness parameter $p=0$ and best-fit fluctuation parameter $k=1.4$. Blue lines are linear fits within $0.9<N_{\text{ch}}/\langle N_{\text{ch}}\rangle <1.1$. Gray dashed lines represent the analogous $\text{Glauber}+\text{NBD}$ (negative binomial distribution) slopes calculated in Ref. [29].