Triaxial shapes and the angular structure of nuclear three-body correlations

TL;DR

This paper links three-nucleon correlations in nuclei to three-particle correlations in collider experiments, revealing how nuclear shape parameters influence observable flow and momentum fluctuation patterns.

Contribution

It provides an analytical framework connecting nuclear triaxial deformation parameters to measurable three-particle correlations in high-energy collisions.

Findings

Covariance of $v_2^2$ and $[p_T]$ fluctuations are proportional to $eta_2^3 ext{cos}(3 ext{γ})$.

Analytical understanding of empirical correlations between shape parameters and final-state observables.

Derived the form of two- and three-body nucleon distributions using a Gaussian Ansatz.

Abstract

Relativistic nuclear collisions have emerged as a new tool for probing many-body correlations of nucleons in the ground states of atomic nuclei. Here, we investigate the connection between three-nucleon correlations inside nuclei and three-particle correlations measured in collider final states. We work within a classical rigid-rotor picture of the colliding ions, whereby correlations in the lab frame arise solely from the averaging over orientations of an intrinsic-frame nucleon density with a triaxial quadrupole deformation, characterized by Bohr parameters $\beta_2$ and $\gamma$. With a Gaussian Ansatz for the density, we derive the leading-order form of the resulting two- and three-body nucleon distributions and perform a detailed analysis of their harmonic structure. With this, we provide an analytical understanding of empirical results linking shape parameters to final-state observables, notably, the fact that the covariance of the squared elliptic flow ($v_2^2$) with the mean transverse momentum ($[p_T]$), as well as the skewness of $[p_T]$ fluctuations, are to leading order proportional to $\beta_2^3 \cos(3\gamma)$. This elucidates the connection between three-nucleon densities, nuclear triaxiality, and three-particle correlations in high-energy nuclear collisions.