Searching for small droplets of hydrodynamic fluid in proton\u2013proton collisions at the LHC

Abstract

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.