Coupled-channel $\textit{Dπ}$, $\textit{Dη}$ and $\textit{D$_{s}$$\bar K$}$ scattering from lattice QCD

Abstract

We present the first lattice QCD study of coupled-channel $\textit{Dπ}$, $\textit{Dη}$ and $\textit{D$_{s}$$\bar K$}$ scattering in isospin-1/2 in three partial waves. Using distillation, we compute matrices of correlation functions with bases of operators capable of resolving both meson and mesonmeson contributions to the spectrum. These correlation matrices are analysed using a variational approach to extract the finite-volume energy eigenstates. Utilising Lüscher’s method and its extensions, we constrain scattering amplitudes in $\textit{S}$, $\textit{P}$ and $\textit{D}$-wave as a function of energy. By analytically continuing the scattering amplitudes to complex energies, we investigate the $\textit{S}$-matrix singularities. Working at $\textit{m$_{π}$}$ ≈ 391 MeV, we find a pole corresponding to a $\textit{J$^{P}$}$ = 0$^{+}$ near-threshold bound state with a large coupling to $\textit{Dπ}$. We also find a deeply bound J$^{P}$ = 1$^{-}$ state, and evidence for a $\textit{J$^{P}$}$ = 2$^{+}$ narrow resonance coupled predominantly to $\textit{Dπ}$. Elastic $\textit{Dπ}$ scattering in the isospin-3/2 channel is studied and we find a weakly repulsive interaction in $\textit{S}$-wave.