Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD

Abstract

We present the first lattice QCD study of coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ 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 meson-meson 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 $S$, $P$ and $D$-wave as a function of energy. By analytically continuing the scattering amplitudes to complex energies, we investigate the $S$-matrix singularities. Working at $m_{\pi }\approx 391$ MeV, we find a pole corresponding to a $J^P=0^{+}$ near-threshold bound state with a large coupling to $D\pi$. We also find a deeply bound $J^P=1^{-}$ state, and evidence for a $J^P=2^{+}$ narrow resonance coupled predominantly to $D\pi$. Elastic $D\pi$ scattering in the isospin-$3/2$ channel is studied and we find a weakly repulsive interaction in $S$-wave.