Entanglement in Elastic and Inelastic Two-particle Scatterings at High Energy

TL;DR

This paper investigates how two-particle scattering at high energy generates quantum entanglement in transverse momentum, deriving formulas for entanglement entropy in elastic and inelastic cases, and comparing their magnitudes using experimental data.

Contribution

It formulates the entanglement entropy in terms of cross sections for elastic and inelastic scattering, providing a new quantitative analysis of entanglement in high-energy particle interactions.

Findings

Inelastic scattering produces more entanglement than elastic scattering in the proton-neutron sector.

Derived formulas relate entanglement entropy to measurable cross sections.

Applied the framework to experimental data for neutron-proton reactions.

Abstract

We study the entanglement produced in transverse momentum by two-particle scattering at high energy. Employing the S-matrix framework for the derivation of reduced density matrices, we formulate the entanglement entropy for an inelastic scattering as well as an elastic one. We display the formulas of the entanglement entropy in terms of two-body cross sections. We also derive the entanglement density as a function of the transverse momentum. As an application, we then focus on both forward elastic ($pn \to pn$) and inelastic ($pn \to np$) channels scattering allowing for a fruitful comparison of the two reactions with the same proton-neutron content. We evaluate the elastic and inelastic entanglement entropy by using known parameterizations of experimental data for neutron-proton reactions. Comparing those entanglement entropies, we observe that the inelastic scattering produces more overall entanglement than the elastic one in the $pn$ sector.