Exploring new small system geometries in heavy ion collisions

Relativistic heavy ion collisions produce nuclei-sized droplets of quark-gluon plasma whose expansion is well described by viscous hydrodynamic calculations. Over the past half decade, this formalism was also found to apply to smaller droplets closer to the size of individual nucleons, as produced in $p+p$ and $p+A$ collisions. The hydrodynamic paradigm was further tested with a variety of collision species, including $p+\mathrm{Au},d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ producing droplets with different geometries. Nevertheless, questions remain regarding the importance of pre-hydrodynamic evolution and the exact medium properties during the hydrodynamic evolution phase, as well as the applicability of alternative theories that argue the agreement with hydrodynamics is accidental. In this work we explore options for new collision geometries including $p+\mathrm{O}$ and $\mathrm{O}+\mathrm{O}$ proposed for running at the Large Hadron Collider, as well as ${}^4\mathrm{He}+\mathrm{Au},\mathrm{C}+\mathrm{Au},\mathrm{O}+\mathrm{Au}$, and ${}^{7,9}\mathrm{Be}+\mathrm{Au}$ at the Relativistic Heavy Ion Collider.

Figure 1

Mean eccentricity $\left(\langle {\varepsilon }_2\rangle ,\langle {\varepsilon }_3\rangle ,\langle {\varepsilon }_4\rangle \right)$ as a function of impact parameter in $p$+O and O+O collisions at $\sqrt{s_{{}_{NN}}}=7\mathrm{TeV}$.

Figure 2

$d{N}_{\mathrm{ch}}/d\eta$ at midrapidity from sonic in unbiased (0%–100%) $p$+O and O+O collisions at $\sqrt{s_{{}_{NN}}}=7\mathrm{TeV}$, and the shaded region is corresponding to 5% events of highest $d{N}_{\mathrm{ch}}/d\eta$.

Figure 3

An example of time evolution of a O+O event from sonic; the color scale indicates the local temperature.

Figure 4

Comparison of $v_n$ and $v_n/\langle {\varepsilon }_n\rangle$ as a function of $p_T$ in 0%–5% of three collision systems, $p$+O and O+O collisions at $\sqrt{s_{{}_{NN}}}=7\mathrm{TeV}$ and $p$+Pb collisions at $\sqrt{s_{{}_{NN}}}=8.16\mathrm{TeV}$.

Figure 5

Comparison of $v_n$ and $v_n/\langle {\varepsilon }_n\rangle$ as a function of $p_T$ in a 5% centrality range of collisions showing a similar $\langle d{N}_{\mathrm{ch}}/d\eta \rangle$.

Figure 6

Comparison of the mean eccentricity as a function of impact parameter in O+O collisions between MC Glauber and IP-Jazma initial conditions.

Figure 7

Comparison of $d{N}_{ch}/d\eta ,v_n$, and $v_n/\langle {\varepsilon }_n\rangle$ in O+O collisions at $\sqrt{s_{{}_{NN}}}=7$ TeV from sonic between MC Glauber and IP-Jazma initial conditions.

Figure 8

Mean eccentricity $\left(\langle {\varepsilon }_2\rangle ,\langle {\varepsilon }_3\rangle ,\langle {\varepsilon }_4\rangle \right)$ as a function of impact parameter in ${}^3\mathrm{He}+\mathrm{Au}$ and ${}^4\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200\mathrm{GeV}$.

Figure 9

An example of time evolution of a ${}^4\mathrm{He}+\mathrm{Au}$ event from sonic; the color scale indicates the local temperature.

Figure 10

Comparison of $v_n$ and $v_n/\langle {\varepsilon }_n\rangle$ from sonic as a function of $p_T$ in 0%–5% of ${}^3\mathrm{He}+\mathrm{Au}$ and ${}^4\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200\mathrm{GeV}$.

Figure 11

Comparison of $v_n$ and $v_n/\langle {\varepsilon }_n\rangle$ from sonic as a function of $p_T$ in 0%–5% of ${}^3\mathrm{He}+\mathrm{Au}$ and 5%–10% of ${}^4\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200\mathrm{GeV}$.

Figure 12

Spatial triangularity $\langle {\varepsilon }_3\rangle$ is shown as a function of number of nucleon participants for C+Au (left) and O+Au (right) collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. Results are shown utilizing the full 12- and 16-nucleon configurations (black), the reshuffled nucleon configurations with no correlations (red), and with the toy geometry model involving simple triangles and tetrahedra (blue).

Figure 13

Number of participating nucleons in minimum bias $p$+O (left) and O+O (right) collisions from Monte Calro Glauber calculations. Shown are the results of two oxygen cases, one with the full 16-nucleon configurations and one with the simple $\alpha$-cluster tetrahedron configuration.

Figure 14

An example of time evolution of a ${}^9\mathrm{Be}+\mathrm{Au}$ event from sonic, and the color scale indicates the local temperature. In this event, one can see the distinct hot spots from the two $\alpha$ clusters and the extra neutron from the ${}^9\mathrm{Be}$ projectile.

Figure 15

Mean charged particle production per pair participant $\left(\langle d{N}_{\mathrm{ch}}/d\eta \rangle /(N_{\mathrm{part}}/2)\right)$ for $p$+Pb, Pb+Pb, and O+O collisions in ampt at $\sqrt{s_{NN}}=5.02$ TeV with the same Lund string fragmentation function parameters $\left(a=0.3,b=0.15\right)$. Measurements by the ALICE collaboration in Pb+Pb collisions [47] are shown for comparison.

Figure 16

Flow coefficients $v_n$ as a function of $p_T$ in the highest 0%–5% centrality class in $p$+O (a)–(c) and O+O (d)–(f) collisions at $\sqrt{s_{{}_{NN}}}=7$ TeV, as calculated with the ampt model. Two calculations are presented, namely the true flow $v_n\left\{\text{PP}\right\}$ relative to the parton participant plane, and the two-particle correlation flow $v_n\left\{\text{2PC}\right\}$.