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QCD Predictions for Physical Multimeson Scattering Amplitudes

Sebastian M. Dawid ¹, Zachary T. Draper ¹, Andrew D. Hanlon ², Ben Hörz ³, Colin Morningstar ⁴, Fernando Romero-López ^5,6, Stephen R. Sharpe ¹, and Sarah Skinner ⁴

¹Physics Department, University of Washington, Seattle, Washington 98195-1560, USA
²Department of Physics, Kent State University, Kent, Ohio 44242, USA
³Intel Deutschland GmbH, Dornacher Straße 1, 85622 Feldkirchen, Germany
⁴Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
⁵Albert Einstein Center, Institute for Theoretical Physics, University of Bern, 3012 Bern, Switzerland
⁶Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

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Phys. Rev. Lett. 135, 021903 – Published 7 July, 2025

DOI: https://doi.org/10.1103/6nql-yrhw

Abstract

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $π^{+}$ and $K^{+}$ , at a lattice spacing $a = 0.063 fm$ , and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for $π^{+} K^{+}$ and $2 K^{+}$ being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

Physics Subject Headings (PhySH)

Corrections

11 December, 2025

Correction: A missing funding statement has been added to the Acknowledgments.

Article Text

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Phys. Rev. Lett. 135, 021903– Published 7 July, 2025

Vol. 135, Iss. 2 — 11 July 2025

Received 3 March 2025
Revised 21 May 2025
Accepted 28 May 2025
Corrected 11 December 2025

DOI: https://doi.org/10.1103/6nql-yrhw

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.

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QCD Predictions for Physical Multimeson Scattering Amplitudes

Abstract

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Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

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