Speaker
Description
We report on recent progress in extracting multi-hadron $D$ decay amplitudes in a pilot study using three ensembles of stabilised Wilson fermions at the SU(3) flavour-symmetric point. Our focus is on the analogue of $D \to K\pi$, where the final state is in the flavour 27-plet. The calculation involves two key steps: determining the finite-volume spectrum for five total spatial momenta in a variational analysis and extracting the relevant finite-volume weak matrix elements from lattice three-point functions. We summarise the challenges and progress of the ongoing calculation, including continuum extrapolation strategies for finite-volume energies across the three ensembles and for S-wave scattering parameters. We also discuss the extraction of finite-volume matrix elements of four-quark weak Hamiltonian operators that describe $D$-meson transitions to two-hadron final states. This is achieved using optimal final-state operators constructed from the scattering analysis. Finally, we provide an initial indication of the signal that can be achieved once all parts of the calculation are combined, including the Lellouch-Lüscher and renormalisation factors relating the finite-volume matrix elements to the physical amplitudes. The calculation uses exact distillation, implemented in the Grid and Hadrons software libraries.