Document Type

Article

Publication Date

9-2019

DOI

10.1103/PhysRevD.100.054508

Publication Title

Physical Review D

Volume

100

Issue

5

Pages

054508 (19 pg.)

Abstract

Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)] derived a relation between the scattering amplitude of three identical bosons,M3, and a real function referred to as the divergence-free K matrix and denoted Kdf;3. The result arose in the context of a relation between finite-volume energies and Kdf;3, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between Kdf;3 and M3. We show that, for any real choice of Kdf;3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf;3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

Comments

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Original Publication Citation

Briceno, R. A., Hansen, M. T., Sharpe, S. R., & Szczepaniak, A. P. (2019). Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism. Physical Review D, 100(5), 054508. doi:10.1103/PhysRevD.100.054508

ORCID

0000-0003-1109-1473 (Briceño)

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