Dissipative corrections to the particle momentum spectrum of a decoupling fluid

TL;DR

This paper develops a quantum statistical field theory approach to calculate dissipative corrections to particle momentum spectra in relativistic fluids, revealing memory effects from initial conditions that influence observed spectra.

Contribution

It introduces a gradient expansion of the Wigner function based on initial thermodynamic fields, including a novel zeroth order term reflecting initial state memory.

Findings

Memory effects influence particle spectra in relativistic collisions.

Gradient expansion reveals long-distance correlations.

Initial state differences affect decoupling particle distributions.

Abstract

We present an \emph{ab initio} calculation within quantum statistical field theory and linear response theory, of the dissipative correction to the momentum spectrum of scalar particles emitted at decoupling (freeze-out) from a relativistic fluid assuming the initial state to be in local thermodynamic equilibrium. We obtain an expansion of the Wigner function of the interacting quantum field in terms of the gradients of the classical thermo-hydrodynamic fields - four-temperature vector and reduced chemical potential - evaluated on the initial local-equilibrium hypersurface, rather than on the decoupling (freeze-out) hypersurface as usual in kinetic theory. The gradient expansion includes an unexpected zeroth order term depending on the differences between thermo-hydrodynamic fields at the decoupling and the initial hypersurface. This term encodes a memory of the initial state which is related to the long-distance persistence of the correlation function between Wigner operator and stress-energy tensor and charged current that is discussed in detail. We address the phenomenological implications of these corrections for the momentum spectra measured in relativistic nuclear collisions.