Regularized Entanglement Entropy of Electron-Positron Scattering with a Witness Photon

TL;DR

This paper calculates regularized quantum information metrics for electron-positron scattering involving a witness photon, revealing how entanglement and scattering parameters relate and are regularized by unitarity.

Contribution

It introduces a method to regularize entanglement entropy in electron-positron scattering with a witness photon, linking quantum information measures to scattering observables.

Findings

Entanglement entropy quantifies uncertainty in the scattering process.

Helicity entropies correlate with muon helicity expectations.

Scattering cross section contributes to entropy, reflecting forward-backward asymmetry.

Abstract

Regularized quantum information metrics are calculated for the scattering process $e^-e^+ \rightarrow \gamma,Z\rightarrow \mu^-\mu^+$ that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon's and witness photon's helicities are found to convey equivalent information. The magnitude of the muon's expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon's helicity entropy and momentum entropy. The muon's differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center of mass energies.