Coupled-channel scattering of $DD, DD^*$ and $D^* D^*$ in isospin-$1$ from lattice QCD

Abstract

The first coupled-channel determination of two-body $D$ and $D^*$ scattering amplitudes in isospin-$1$ from lattice quantum chromodynamics is presented. Using three lattice volumes at $m_\pi \approx 391~\mathrm{MeV}$, finite-volume energies relevant for the channels of interest are determined. Through the L\"uscher formalism, these energies are used to constrain amplitudes of coupled $J^P=0^+$ $DD - DD^*$, $J^P=1^+$ $DD^*- D^*D^*$ and $J^P=2^+$ $DD - DD^* - D^* D^*$ scattering. All channels feature weakly repulsive interactions in $S$ wave, except for a weak $D^* D^*$ attraction in $J^P=0^+$. No amplitude singularities corresponding to physical states are found. Some of these amplitudes will be a necessary component of future lattice QCD analyses of $DD\pi$ and $DD^*$ scattering taking into account three-body and left-hand cut effects.