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

Abstract: In this paper, we investigate the hydrodynamic collectivity in high-multiplicity events of proton-proton collisions at $\sqrt{s}=$ 13 TeV, using iEBE-VISHNU hybrid model with three different initial conditions, namely, HIJING, super-MC and TRENTo. With properly tuned parameters, hydrodynamic simulations with each initial model give reasonable descriptions of the measured two-particle correlations, including the integrated and $p_{\rm T}$-differential flow for all charged and identified hadrons. However, the hydrodynamic simulations fail to describe the negative value of the four-particle cumulant $c_2^v{4}$ as measured in experiments. Further investigations show that the non-linear response between the elliptic flow $v_2$ and the initial eccentricity $\varepsilon_2$ becomes significant in the small 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 multi-particle mixed harmonic azimuthal correlations in p-p collisions, such as normalized asymmetric cumulant $nac_n{3}$, normalized Symmetric-Cumulant, $nsc_{2,3}{4}$ and $nsc_{2,4}{4}$. Although many qualitative features are reproduced by the hydrodynamic simulations with chosen parameters, the measured negative $nsc_{2,3}{4}$ cannot be reproduced. The failure of the description of negative $c_2{4}$ and $nsc_{2,3}{4}$ triggers the question on whether hydrodynamics with a fundamentally new initial state model could solve this puzzle, or hydrodynamics itself might not be the appreciated mechanism of the observed collectivity in p-p collisions at the LHC.