Bose, A and Haldar, P and Sinha, A and Sinha, P and Tiwari, SS (2020) Relative entropy in scattering and the S-matrix bootstrap. In: SciPost Physics, 9 (5).
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Abstract
We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include φ4 theory, chiral perturbation theory (χPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In χPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the ρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop χPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin. © 2020 University of Barcelona. All rights reserved.
| Item Type: | Journal Article |
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| Publication: | SciPost Physics |
| Publisher: | SciPost Foundation |
| Additional Information: | The copyright for this article belongs to the AUthor(s). |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 10 Jan 2023 06:20 |
| Last Modified: | 10 Jan 2023 06:20 |
| URI: | https://eprints.iisc.ac.in/id/eprint/78999 |
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