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Energy-Dependent π+π+π+ Scattering Amplitude from QCD

Maxwell T. Hansen, Raul A. Briceño, Robert G. Edwards, Christopher E. Thomas, and David J. Wilson (for the Hadron Spectrum Collaboration)
Phys. Rev. Lett. 126, 012001 – Published 5 January 2021
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Abstract

Focusing on three-pion states with maximal isospin (π+π+π+), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

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  • Received 8 October 2020
  • Accepted 6 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.012001

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

Maxwell T. Hansen1,2,*, Raul A. Briceño3,4,†, Robert G. Edwards3,‡, Christopher E. Thomas5,§, and David J. Wilson5,∥ (for the Hadron Spectrum Collaboration)

  • 1Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
  • 2Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
  • 3Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
  • 4Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA
  • 5DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *maxwell.hansen@cern.ch
  • rbriceno@jlab.org
  • edwards@jlab.org
  • §c.e.thomas@damtp.cam.ac.uk
  • d.j.wilson@damtp.cam.ac.uk

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Vol. 126, Iss. 1 — 8 January 2021

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