Open Access

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

Sebastian M. Dawid ¹, Zachary T. Draper ¹, Andrew D. Hanlon ², Ben Hörz³, 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. D 112, 014505 – Published 7 July, 2025

DOI: https://doi.org/10.1103/bx16-lp3r

Abstract

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with $a \approx 0.063 fm$ , including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading $s$ wave, but also $p$ and $d$ waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for $3 π^{+}$ , $3 K^{+}$ , $π^{+} π^{+} K^{+}$ , and $K^{+} K^{+} π^{+}$ systems. These are determined for total angular momentum $J^{P} = 0^{-}$ , $1^{+}$ , and $2^{-}$ . We also obtain accurate results for $2 π^{+}$ , $π^{+} K^{+}$ , and $2 K^{+}$ phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.

Physics Subject Headings (PhySH)

Corrections

23 December, 2025

Correction: The omission of a support statement in the Acknowledgments has been fixed.

Article Text

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Phys. Rev. D 112, 014505– Published 7 July, 2025

Vol. 112, Iss. 1 — 1 July 2025

Received 3 March 2025
Accepted 27 May 2025
Corrected 23 December 2025

DOI: https://doi.org/10.1103/bx16-lp3r

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

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QCD Predictions for Physical Multimeson Scattering Amplitudes

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