D → (K π)27 at the SU(3)-flavour-symmetric point I: Methodology and strong phase determination
Abstract
We present part one of an SU(3)-flavour-symmetric lattice QCD calculation of the amplitude for a D-meson decaying to a Kπ final state in the 27-dimensional irreducible representation of the flavour symmetry group, denoted (Kπ)27. The Wilson--clover gauge ensembles used in this work, generated by the OpenLat collaboration, are tuned such that Mπ= MK ≈ 410 MeV. Using the distillation framework, we construct a matrix of Euclidean correlation functions from pairs of single-hadron operators projected to definite spatial momentum. Solving a generalised eigenvalue problem yields the finite-volume energy spectrum that is used to determine the scattering phase shift from threshold up to 4 Mπ≈ 1640 MeV, which sits below but plausibly within reach of MDSU(3) ≃ 1900 MeV. The calculation is performed across three lattice spacings, and we apply two strategies in which the continuum limit is taken at different stages of the computation: (i) on the extracted scattering parameters and (ii) on the finite-volume energies at fixed physical volume before extracting the scattering parameters. We find consistent results across these methods for the scattering phase shift as a function of the centre-of-mass energy, δ27(Esf cm). Taking a scattering-length-only parametrisation, we infer a value for the strong phase of the weak decay, δ27(MDSU(3))=−38.4(2.4)∘. We further describe the methodology for using the same operator basis to compute three-point correlation functions to extract ⟨ (Kπ)27| HW| D⟩, for the tree-level effective weak Hamiltonian HW, and for relating such finite-volume matrix elements to the full decay amplitude. The complete analysis leading to the latter will be presented in a forthcoming manuscript.
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BibTeX
@misc{black2026π27,
title = {{$D \to (K π)_\mathbf27$ at the SU(3)-flavour-symmetric point I: Methodology and strong phase determination}},
author = {Matthew Black and Felix Erben and Maxwell T. Hansen and Fabian Joswig and Nelson Pitanga Lachini and Rajnandini Mukherjee and Srijit Paul and Antonin Portelli},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30737},
eprint = {2608.30737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30737},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - D → (K π)_27 at the SU(3)-flavour-symmetric point I: Methodology and strong phase determination
AU - Matthew Black
AU - Felix Erben
AU - Maxwell T. Hansen
AU - Fabian Joswig
AU - Nelson Pitanga Lachini
AU - Rajnandini Mukherjee
AU - Srijit Paul
AU - Antonin Portelli
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30737
UR - https://arxiv.org/abs/2608.30737
AB - We present part one of an SU(3)-flavour-symmetric lattice QCD calculation of the amplitude for a D-meson decaying to a Kπ final state in the 27-dimensional irreducible representation of the flavour symmetry group, denoted (Kπ)_27. The Wilson--clover gauge ensembles used in this work, generated by the OpenLat collaboration, are tuned such that M_π= M_K ≈ 410 MeV. Using the distillation framework, we construct a matrix of Euclidean correlation functions from pairs of single-hadron operators projected to definite spatial momentum. Solving a generalised eigenvalue problem yields the finite-volume energy spectrum that is used to determine the scattering phase shift from threshold up to 4 M_π≈ 1640 MeV, which sits below but plausibly within reach of M_D^SU(3) ≃ 1900 MeV. The calculation is performed across three lattice spacings, and we apply two strategies in which the continuum limit is taken at different stages of the computation: (i) on the extracted scattering parameters and (ii) on the finite-volume energies at fixed physical volume before extracting the scattering parameters. We find consistent results across these methods for the scattering phase shift as a function of the centre-of-mass energy, δ_27(E_sf cm). Taking a scattering-length-only parametrisation, we infer a value for the strong phase of the weak decay, δ_27(M_D^SU(3))=−38.4(2.4)^∘. We further describe the methodology for using the same operator basis to compute three-point correlation functions to extract ⟨ (Kπ)_27| H_W| D⟩, for the tree-level effective weak Hamiltonian H_W, and for relating such finite-volume matrix elements to the full decay amplitude. The complete analysis leading to the latter will be presented in a forthcoming manuscript.
ER -