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

TL;DR

This study uses lattice QCD to analyze coupled-channel scattering of D and D* mesons in isospin-1, revealing weak interactions and no bound states, providing essential data for future three-body scattering studies.

Contribution

First lattice QCD determination of coupled D and D* meson scattering amplitudes in isospin-1, including multiple channels and quantum numbers.

Findings

Weakly repulsive S-wave interactions in all channels.

Weak D* D* attraction in J^P=0^+ channel.

No physical state poles found in the amplitudes.

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.