Smallest QCD droplet and multiparticle correlations in $p\text{−}p$ collisions

The collective evolution of produced matter in heavy-ion collisions is effectively described by hydrodynamics from time scales greater than the inverse of the temperature, $\tau \gtrsim 1/T$. In the context of the Gubser solution, I show that the hydrodynamization condition $\tau T\gtrsim 1$ is translated into an allowed domain in the spatial system size and the final multiplicity for hydrodynamics applicability. It turns out that the flow measurements in $p\text{−}p$ collisions are inside the domain of validity. I predict that by approaching the boundaries of the allowed domain the hydrodynamic response to the initial ellipticity changes its sign. I follow a rather model-independent approach for the initial state where, instead of modeling the initial energy density of individual events, the initial system size and ellipticity event-by-event fluctuation are modeled. The model, initial state $\mathrm{fluctuation}+\mathrm{Gubser}$ solution$+$Cooper-Frye freeze-out, describes the multiplicity and transverse momentum dependence of two-point and four-point correlation functions ($c_2\left\{2\right\}$ and $c_2\left\{4\right\}$) in an accurate agreement with $p\text{−}p$ collision experimental measurements. In particular, the sign of the four-point correlation function is the same as the observation, which failed to be described correctly in previous studies. I also predict a signal for the sign change in the hydrodynamic response that can be inspected in future experimental measurements of two-point and four-point correlation functions at lower multiplicities.

Figure 1

The initiation of hydrodynamic evolution at $\tau ={\tau }_{\text{hyd}}$ (left) and $\rho ={\rho }_{\text{hyd}}$ (right).

Figure 2

Freeze-out surfaces for systems of three different sizes where $r_{\text{crit}}=0.1\mathrm{fm}$, ${\tau }_{\text{hyd}}=0.62\mathrm{fm}$/c, $C_0=11$.

Figure 3

Domain of hydrodynamics validity in the $(n_{\text{tot}},r_{\text{rms}})$ phase space. The gubshyd output for $k_2(n_{\text{tot}},r_{\text{rms}})$ ($0.3<p_T<3.0\text{GeV}$) is shown as a contour plot ($n_{\text{tot}}\equiv dN/d{y}_p$).

Figure 4

Two- and four-particle correlations ($v_2\left\{2\right\}$ and $v_2\left\{4\right\}$) from mc-glauber$+$vish2$+$1 and mc-glauber$+$gubshyd.

Figure 5

Comparing gubshyd predictions with CMS and ATLAS measurements published in Refs. [3, 5].

Figure 6

Differential anisotropic flow $v_2\left\{2\right\}$ and $v_2\left\{4\right\}$ from mc-glauber$+$vish2$+$1 and mc-glauber$+$gubshyd.

Figure 7

Charged pions $p_T$ spectrum and centrality dependence of the charged pions multiplicity from mc-glauber$+$vish2$+$1 and mc-glauber$+$gubshyd.