Evaluation of Entanglement Entropy in High Energy Elastic Scattering

Abstract

Entanglement of the two scattered particles is expected to occur in elastic collisions, even at high energy where they are in competition with inelastic ones. We study how to evaluate quantitatively the corresponding entanglement entropy $S_{\mathrm{EE}}.$ For this sake, we regularize the divergences occurring in the formal derivation of $S_{\mathrm{EE}}$ using a regularization procedure acting on the two-particle Hilbert space of final states. A quantitative application is performed in proton-proton collisions at collider energies, comparing the results of $S_{\mathrm{EE}}$ with two different cut-offs and with a volume-regularization obtained by a prescription fixing the finite two-body Hilbert space volume. A significant entanglement is found which persists even at the highest available energies.

Comments: 18 pages, 1 figure; v2: footnote 1 added in Sec.2.1, comments on spin added in Sec. 4, refs added, typos corrected, version for publication