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

TL;DR

This study uses lattice QCD to analyze coupled-channel scattering involving D mesons and pions, revealing bound states and resonances, and providing detailed scattering amplitudes in multiple partial waves.

Contribution

First lattice QCD investigation of coupled-channel Dπ, Dη, and D_sK scattering in isospin-1/2 across multiple partial waves, identifying bound states and resonances.

Findings

Identified a near-threshold J^P=0^+ bound state with strong Dπ coupling.

Discovered a deeply bound J^P=1^- state.

Found a narrow J^P=2^+ resonance mainly coupled to Dπ.

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 L\"uscher'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.