Searching for small droplets of hydrodynamic fluid in proton–proton collisions at the LHC

In this paper, we investigate the hydrodynamic collectivity in proton-proton collisions at $\sqrt{s}=$ 13 TeV, using iEBE-VISHNU with three different initial conditions, namely, HIJING, super-MC and TRENTo. With properly tuned parameters, hydrodynamics gives reasonable descriptions of the measured two-particle correlations, including the integrated and $p_\mathrm{T}$-differential flow. However, the hydrodynamic simulations fail to describe the negative four-particle cumulant $c_2^v\{4\}$ as measured in experiments. The four-particle cumulant $c_2^v\{4\}$ is always positive after hydrodynamic evolutions. Further investigations show that the non-linear response between the final $v_2$ and the initial $\varepsilon _2$ becomes significant in p-p systems. This leads to a large deviation from linear eccentricity scaling and generates additional flow fluctuations, which results in a positive $c_2^v\{4\}$ even with a negative $c_2^\varepsilon \{4\}$ from the initial state. We also presented the first hydrodynamic calculations of mixed harmonic azimuthal correlations in p-p collisions. Although many qualitative features are reproduced by the hydrodynamic simulations, the measured negative normalized Symmetric-Cumulant $nsc_{2,3}\{4\}$ cannot be reproduced. Obviously hydrodynamic calculations have a general difficulty to describe the data. It triggers that whether hydrodynamics with a new initial state could solve this puzzle, or hydrodynamics itself is not the appreciated mechanism of the observed collectivity, and the non-hydrodynamic modes become important in p-p collisions at the LHC.