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

Abstract

AbstractIn this paper, we investigate the hydrodynamic collectivity in proton-proton collisions at $$\sqrt{s}=$$ s = 13 TeV, using with three different initial conditions, namely, , and . With properly tuned parameters, hydrodynamics gives reasonable descriptions of the measured two-particle correlations, including the integrated and $$p_\mathrm{T}$$ p T -differential flow. However, the hydrodynamic simulations fail to describe the negative four-particle cumulant $$c_2^v\{4\}$$ c 2 v { 4 } as measured in experiments. The four-particle cumulant $$c_2^v\{4\}$$ c 2 v { 4 } is always positive after hydrodynamic evolutions. Further investigations show that the non-linear response between the final $$v_2$$ v 2 and the initial $$\varepsilon _2$$ ε 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 $$c_2^v\{4\}$$ c 2 v { 4 } even with a negative $$c_2^\varepsilon \{4\}$$ c 2 ε { 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 $$nsc_{2,3}\{4\}$$ n s c 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.