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

TL;DR

Addresses momentum-space entanglement generated by high-energy two-body scattering and develops a parallel S-matrix framework for elastic and inelastic final states. It derives reduced density matrices and entanglement entropies for the final two-body states, expressing them in terms of two-body cross sections and introducing a volume-regularization scheme to tame the infinite momentum-space volume. The authors apply the formalism to forward pn scattering, using experimental parameterizations for elastic and inelastic cross sections, and find that inelastic scattering yields larger entanglement than elastic for the same pn content. They also define and compute the transverse-momentum entanglement-density, revealing how entanglement flows with momentum transfer and how non-vacuum exchange enhances entanglement in the inelastic channel.

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.

Figures (6)

• Figure 1: (i) the elastic channel: $pn\to pn$. (ii) the inelastic channel: $pn\to np$.
• Figure 2: The elastic entanglement entropy ${\tilde{S}}_{\rm el}$ (solid line) and the inelastic one ${\tilde{S}}_{\rm inel}$ (dashed line).
• Figure 3: (i) The difference $\Delta {\tilde{S}}$ and (ii) the asymmetry ${\rm asym}\,{\tilde{S}}$ of entanglement entropies between the elastic and inelastic channels.
• Figure 4: The elastic density $D_{\rm el}$ (solid line) and the inelastic one $D_{\rm inel}$ (dashed line) as functions of $|t|$ at $\sqrt{s}=20$ GeV
• Figure 5: The elastic density $D_{\rm el}$ as a function of $|t|$ at $\sqrt{s}=20$ GeV (solid line), 50 GeV (dashed line) and 100 GeV (dotted line).