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 $S_{\rm EE}.$ For this sake, we regularize the divergences occurring in the formal derivation of $S_{\rm EE}$ 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 $S_{\rm EE}$ 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.
Highlights
Entanglement is a significant phenomenon in quantum theories and has been attracting many interests of scientists in various research areas
In Ref. [1] the entanglement in momentum Hilbert space in the scattering process has been studied, and the entanglement entropy of the final state of two particles has been calculated in weak coupling perturbation by applying the method developed by Ref. [2] for momentum space entanglement
Our goal is to find the physical origin of these divergences, identify the divergent factor and propose the way to obtain a finite formula for the entanglement entropy of the two outgoing particles
Summary
Entanglement is a significant phenomenon in quantum theories and has been attracting many interests of scientists in various research areas. [1] the entanglement in momentum Hilbert space in the scattering process has been studied, and the entanglement entropy of the final state of two particles has been calculated in weak coupling perturbation by applying the method developed by Ref. Reference [3] has considered the entanglement in momentum Hilbert space for the elastically scattering particles, but has formulated. Reference [3], as a result, has derived an adequate formalism for the entanglement entropy and has suggested an entropy formula of the two-particle final state after the elastic scattering. In our study, having performed the regularization and using the obtained formula, it is interesting to evaluate the entanglement entropy for concrete particle scattering.
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