Collective flow in high-multiplicity proton-proton collisions

We present evidence of strong radial flow in high-multiplicity $pp$ collisions. We analyze the CMS Collaboration data on the inclusive spectra of the charged pions, kaons and protons in the Large Hadron Collider $\sqrt{s}=7$ TeV collisions. For $\langle N_{\mathrm{tracks}}\rangle \gtrsim 75$ we demonstrate the consistency of the hydrodynamic description with the (idealized) Gubser flow. Using a one-parameter fit of the model to experimental data, we obtain the initial fireball size to be of the order of 1 fm. At smaller multiplicities, the fit cannot be performed, which shows a limitation of the hydrodynamic approach and provides us with falsifiability of our theory.

Figure 1

Profiles of the freezeout surfaces (upper plot) and the corresponding velocities (lower plot) for three different initial system sizes: at ${\epsilon }_0=10$ and $1/q=0.7\mathrm{fm}$ (upper blue), $1/q=1\mathrm{fm}$ (middle orange), $1/q=2\mathrm{fm}$ (lower red).

Figure 2

Normalized spectra of pions (squares), kaons (triangles) and protons (discs) at different multiplicities. Open symbols correspond to the CMS data [15] for $\left|\eta \right|<2.4$ and $\sqrt{s}=7$ TeV, while the solid ones are obtained from the best one-parameter fit of the Gubser flow.

Figure 3

Profiles of the freezeout surfaces (upper plot) and velocities (lower plot) for the Gubser solutions at various values of the parameters $(1/q\left[\mathrm{fm}\right],{\epsilon }_0)$ used in our calculations. Upper red – (1.05, 12.7), middle blue – (1.0, 8.6), lower orange – (1.0, 6.0).