Doubly charm tetraquark channel with isospin $1$ from lattice QCD

Experimentally, the doubly charm tetraquark channel $cc\bar q\bar q$ with $q\!=\!u,d$ features an exotic hadron, $T_{cc}$, with isospin $I\!=\!0$ near the $DD^*$ threshold, while no peak was observed for $I\!=\!1$. We present a lattice QCD study of this channel with $I\!=\!1$, $J^P\!=\!1^+$ and $m_\pi\simeq 280~$MeV. Finite-volume energies calculated across five charm quark masses consistently feature a positive energy shift with respect to non-interacting energies, indicating repulsive interaction at energies near threshold. These energies are used to compute the $DD^*$ scattering amplitude using both the standard L\"uscher method and the recently proposed effective-field-theory-based approach in the plane-wave basis, which incorporates the long-range interactions and the left-hand cut. Both analyses render a small negative scattering length and the scattering amplitude that does not feature any poles in the energy region near the $DD^*$ threshold, in line with LHCb results. We identify that the Wick contraction resembling $t$-channel isovector-vector meson exchanges between $D$ and $D^*$ plays a key role in distinguishing between the $I=0$ and $I=1$ channels, leading to repulsion in the $I=1$ and attraction in the $I=0$ channel.