Towards hadronic $D$ decays at the SU(3) flavour symmetric point

Parallel talk at the 40th International Symposium on Lattice Field Theory at Fermilab, USA

We present progress towards extracting multi-hadron $D$ decay amplitudes, such as $D \to \pi \pi$, in a pilot study using three ensembles of stabilised Wilson fermions at the SU(3) flavour symmetric point, with $M_\pi=410$ MeV. As the three ensembles differ only in the lattice spacing, with well matched physical volumes, it is possible to perform a continuum limit for finite-volume energies (and eventually weak-decay matrix elements) at fixed physical volume. The talk will summarise the work-flow and challenges of the ongoing calculation with a focus on results for the $a^2$-dependence and continuum limit of the two-to-two pseudoscalar $S$-wave scattering amplitude, determined via the GEVP+Lüscher approach in an exact distillation setup implemented in the Grid and Hadrons software libraries.