Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD

Abstract

The first coupled-channel determination of two-body $D$ and $D^{\ast }$ 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 Lüscher formalism, these energies are used to constrain amplitudes of coupled $J^P=0^{+}$ $DD-D{D}^{\ast }$, $J^P=1^{+}$ $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ and $J^P=2^{+}$ $DD-D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering. All channels feature weakly repulsive interactions in $S$ wave, except for a weak $D^{\ast }{D}^{\ast }$ 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 $D{D}^{\ast }$ scattering taking into account three-body and left-hand cut effects.