Elastic cross section is entanglement entropy

Low, Ian; Yin, Zhewei

doi:10.1103/PhysRevD.111.065027

Elastic cross section is entanglement entropy

Journal Article · Mon Mar 31 00:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.111.065027· OSTI ID:2544406

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We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the cross section, which is the primary observable for high-energy particle scattering, by employing a careful formulation of wave packets for the incoming particles. For 2-to-2 elastic scattering with no initial entanglement and subdividing the system along particle labels, we show that both the Rényi and Tsallis entropies in the final states are directly proportional to the elastic cross section in units of the transverse size for the initial wave packets, which is then interpreted as the elastic scattering probability. The relations do not depend on the underlying dynamics of the quantum field theory and are valid to all orders in coupling strengths. Furthermore, computing quantum correlations between momentum and nonkinematic data leads to entanglement entropies expressed as various semi-inclusive elastic cross sections. Our result gives rise to a novel “area law” for entanglement entropy in a two-body system.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-06CH11357; SC0023522

OSTI ID:: 2544406

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 6 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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