• Open Access

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Raúl A. Briceño, Maxwell T. Hansen, Stephen R. Sharpe, and Adam P. Szczepaniak
Phys. Rev. D 100, 054508 – Published 18 September 2019

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).

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  • Received 30 June 2019

DOI:https://doi.org/10.1103/PhysRevD.100.054508

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nuclear PhysicsParticles & Fields

Authors & Affiliations

Raúl A. Briceño1,2,*, Maxwell T. Hansen3,†, Stephen R. Sharpe4,‡, and Adam P. Szczepaniak5,6,1,§

  • 1Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
  • 2Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA
  • 3Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
  • 4Physics Department, University of Washington, Seattle, Washington 98195-1560, USA
  • 5Physics Department, Indiana University, Bloomington, Indiana 47405, USA
  • 6Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47403, USA

  • *rbriceno@jlab.org
  • maxwell.hansen@cern.ch
  • srsharpe@uw.edu
  • §aszczepa@indiana.edu

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Issue

Vol. 100, Iss. 5 — 1 September 2019

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