Develop a finite-volume formalism for higher-multiplicity channels

Develop a finite-volume scattering formalism that fully incorporates open channels containing more than three hadrons, including the higher-multiplicity channels relevant to hadronic systems near the D-meson mass.

Background

The paper outlines the general workflow for lattice calculations of decays into multihadron final states and notes that, at physical pion masses and energies corresponding to the D-meson mass, many channels with four or more hadrons can become kinematically accessible. A complete treatment would require a finite-volume formalism capable of handling these coupled higher-multiplicity channels and their effects on the spectrum and decay amplitudes.

The authors state that existing formalisms are established for two-particle systems and have been extended to three-particle and coupled two- and three-particle systems, but that the required generalisation to channels with more than three hadrons is not yet complete. They identify perturbative N-body scattering frameworks as an initial step toward addressing this gap.

References

This also requires a highly sophisticated finite-volume formalism in items 5 and 8, one which, in fact, has not yet been fully developed given the requirement to include channels with more than three hadrons.

— $D \to (K π)_{\mathbf{27}}$ at the SU(3)-flavour-symmetric point I: Methodology and strong phase determination  (2608.30737 - Black et al., 31 Aug 2026) in Section 1, Introduction

Whether this simplification is applicable will ultimately need to be determined by comparison with results from LQCD calculations.

— Accessing the Wess-Zumino-Witten term using Lattice QCD  (2609.05006 - Romero-López et al., 4 Sep 2026) in Section 6, Conclusions and Outlook