Initial-state geometry and the role of hydrodynamics in proton-proton, proton-nucleus, and deuteron-nucleus collisions

We apply the successful Monte Carlo Glauber and IP-Glasma initial-state models of heavy-ion collisions to the much smaller size systems produced in proton-proton, proton-nucleus, and deuteron-nucleus collisions. We observe a significantly greater sensitivity of the initial-state geometry to details of multiparticle production in these models compared to nucleus-nucleus collisions. In particular, we find that the size of the system produced in $p+A$ collisions is very similar to the one produced in $p+p$ collisions and predict comparable Hanbury-Brown-Twiss radii in the absence of flow in both systems. Differences in the eccentricities computed in the models are large, while differences among the generated flow coefficients $v_2$ and $v_3$ are smaller. For a large number of participants in proton-lead collisions, the $v_2$ generated in the IP-Glasma model is comparable to the value obtained in proton-proton collisions. Viscous corrections to flow are large over characteristic lifetimes in the smaller size systems. In contrast, viscous contributions are significantly diminished over the longer space-time evolution of a heavy-ion collision.

Figure 1

Various models of the energy density deposition (denoted by red dots) in nucleon-nucleon collisions. In the left plot (a) the energy density is produced at the center of the colliding nucleons even for grazing collisions. The center and right plots (b) and (c) correspond to different eccentricities depending on the matter distribution in the nucleon overlap region. For the configuration depicted on the left eccentricity ${\varepsilon }_2\approx 1$, whereas for the configuration in the center ${\varepsilon }_2=0$.

Figure 2

System size in $p+p$ and $p+\text{Pb}$ collisions as a function of the number of gluons to the power of $1/3$, ${(dN/dy)}^{1/3}$, computed in the IP-Glasma model. $r_{\max }$ is the maximal radius for which the energy density of the Yang-Mills fields are above a minimal value of ${\varepsilon }_{\min }=\alpha {\Lambda }_{\mathrm{QCD}}^4$, with $\alpha =1$ (solid symbols) and $\alpha =10$ (open symbols). Note different energies for $p+p$ and $p+\text{Pb}$.

Figure 3

Eccentricities ${\varepsilon }_2$ and ${\varepsilon }_3$ as a function of $dN/dy$ in the IP-Glasma model for $p+\text{Pb}$ (solid symbols) and $p+p$ (open symbols) collisions.

Figure 4

Eccentricities ${\varepsilon }_2$ (a) and ${\varepsilon }_3$ (b) as a function of the number of wounded nucleons $N_{\mathrm{part}}$. In the MC-Glauber (participant centers) model the energy density is deposited in the centers of wounded nucleons (without smearing). Smearing energy densities with the Gaussian distribution (${\sigma }_0=0.4\mathrm{fm}$) results in the MC-Glauber 1 model. In the MC-Glauber 2 model the energy density is smeared about the midpoint between colliding nucleons.

Figure 5

Initial energy density distribution (arbitrary units, increasing from blue to red) in the transverse plane in a $d+\text{Au}$ collision in (a) the MC-Glauber model and (b) the IP-Glasma approach. The nucleon positions (open circles for the deuteron, solid circles for gold) are exactly the same in the two cases.

Figure 6

Integrated ${\langle v_2^2\rangle }^{1/2}$ and ${\langle v_3^2\rangle }^{1/2}$ for charged hadrons in $p+\text{Pb}$ collisions at different $N_{\mathrm{part}}$ in the MC-Glauber 1 and IP-Glasma model for $p_T>0.5\mathrm{GeV}$ and $\eta /s=0.08$. $v_2$ decreases with $N_{\mathrm{part}}$. Results for $p+p$ collisions are for $b=0\mathrm{fm}$.

Figure 7

Integrated ${\langle v_2^2\rangle }^{1/2}$ and ${\langle v_3^2\rangle }^{1/2}$ for charged hadrons in $d+\text{Au}$ collisions at different $N_{\mathrm{part}}$ in the MC-Glauber 1 and IP-Glasma model for $p_T>0.5\mathrm{GeV}$ and $\eta /s=0.08$. $v_2$ increases with $N_{\mathrm{part}}$.

Figure 8

$v_2\left(p_T\right)$ for charged hadrons in $p+\text{Pb}$ collisions at fixed $N_{\mathrm{part}}=7$ (thin lines) and 20 (thick lines) in the MC-Glauber (dashed lines) and IP-Glasma (solid lines) model.

Figure 9

$v_3\left(p_T\right)$ for charged hadrons in $p+\text{Pb}$ collisions at fixed $N_{\mathrm{part}}=7$ (thin lines) and 20 (thick lines) in the MC-Glauber (dashed lines) and IP-Glasma (solid lines) model.

Figure 10

$v_2\left(p_T\right)$ for charged hadrons in $d+\text{Au}$ collisions at fixed $N_{\mathrm{part}}=10$ (thin lines) and 30 (thick lines) in the MC-Glauber (dashed lines) and IP-Glasma (solid lines) model.

Figure 11

$v_3\left(p_T\right)$ for charged hadrons in $d+\text{Au}$ collisions at fixed $N_{\mathrm{part}}=10$ (thin lines) and 30 (thick lines) in the MC-Glauber (dashed lines) and IP-Glasma (solid lines) model.

Figure 12

Fraction of all cells within the freeze-out surface that have a viscous correction of at least 25$\%$ of the ideal $T^{\mu \nu }$. Initialization with ${\pi }_0^{\mu \nu }=0$.

Figure 13

Fraction of all cells within the freeze-out surface that have a viscous correction of at least 25$\%$ of the ideal $T^{\mu \nu }$. Initialization with the Navier-Stokes value for ${\pi }_0^{\mu \nu }$.

Figure 14

Fraction of all cells within the freeze-out surface that have a viscous correction of at least 50$\%$ of the ideal $T^{\mu \nu }$. Initialization with the Navier-Stokes value for ${\pi }_0^{\mu \nu }$.