Characterizing the initial state of hydrodynamics in pp and pA collisions
Gabriel Rabelo-Soares, Gojko Vujanovic, Giorgio Torrieri
TL;DR
This work tackles the problem of defining the initial state for hydrodynamics in small collision systems (pp and pA) where a quantum initial state must be connected to a classical fluid description. It argues that conventional 3D nucleon structure descriptors (GPDs and TMDs) do not directly set the hydrodynamic start, and that the relevant information comes from entanglement-driven entropy content encoded in Wigner/Husimi phase-space distributions. By invoking light-cone wave functions, Wigner function formalism, and a Gaussian partition function, it introduces a localization scale Lambda that converts quantum phase-space content into an initial energy-momentum density and entropy density. The framework offers a route to predict initial eccentricities and flow observables (e.g., $v_n$) in pp and pA, and outlines how upcoming measurements at EIC and RHIC, including spin-dependent effects, could test or refine the approach.
Abstract
The observation of seeming hydrodynamic-like behavior in proton-proton and proton-nucleus collisions presents us with the conceptual problem of how the initial state of such a hydrodynamic evolution should be characterized. This is an issue because, while nuclei can reasonably be approximated as ``large'' systems w.r.t. the characteristic Fermi momentum of their constituents, this is no longer true for nucleons. Hence, one would need to match a ``quantum'' theory, whose observables are described via highly non-commuting operators, to a ``classical'' hydrodynamics. Operationally assuming a ``fast'' thermalization, we survey what kind of object is best suited to such a matching condition. We show that it cannot be any of the objects usually associated with ``the 3D structure of the nucleon'' but rather a measure associated with entanglement entropy.