# Smallest QCD Droplet and Multiparticle Correlations in pp Collisions

## TL;DR

This paper investigates the applicability of hydrodynamics in proton-proton collisions, using the Gubser solution to model initial state fluctuations and predict multiparticle correlations, aligning well with experimental data and suggesting future tests at lower multiplicities.

## Contribution

It introduces a model-independent approach combining initial state fluctuations with the Gubser solution to accurately describe multiparticle correlations in pp collisions.

## Key findings

- Hydrodynamics is valid in certain pp collision regimes.
- The model reproduces the sign and magnitude of multiparticle correlations.
- Predicted sign change in correlations at lower multiplicities.

## Abstract

The collective evolution of produced matter in heavy-ion collisions is effectively described by hydrodynamics from time scales greater than the inverse of the temperature, $\tau \gtrsim 1/T$. In the context of the Gubser solution, I show that the hydrodynamization condition $\tau \, T \gtrsim 1$ is translated into an allowed domain in the spatial system size and the final multiplicity for hydrodynamics applicability. It turns out that the flow measurements in pp collisions are inside the domain of validity. I predict that by approaching the boundaries of the allowed domain the hydrodynamic response to the initial ellipticity changes its sign. I follow a rather model-independent approach for the initial state where, instead of modeling the initial energy density of individual events, the initial system size and ellipticity event-by-event fluctuation are modeled. The model, initial state fluctuation+Gubser solution+Cooper-Frye freeze-out, describes the multiplicity and transverse momentum dependence of two-point and four-point correlation functions ($c_2\{2\}$ and $c_2\{4\}$) in an accurate agreement with pp collision experimental measurements. In particular, the sign of the four-point correlation function is the same as the observation, which failed to be described correctly in previous studies. I also predict a signal for the sign change in the hydrodynamic response that can be inspected in future experimental measurements of two-point and four-point correlation functions at lower multiplicities.