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

Abstract

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 $D{D}^{\ast }$ 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 $D{D}^{\ast }$ scattering amplitude using both the standard Lüscher 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 $D{D}^{\ast }$ threshold, in line with LHCb results. We identify that the Wick contraction resembling $t$-channel isovector-vector meson exchanges between $D$ and $D^{\ast }$ 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.

15 pages and 12 figures

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Cited by in corpus (9)

• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• A short review on the compositeness of the $X(3872)$
• Lattice study of scattering phase shifts for $D{D}^{\ast }$ and $B{B}^{\ast }$ systems using twisted boundary conditions: Search for bound state formation
• Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Low-energy $DD$ scattering in lattice QCD
• Exotic hadrons associated with $b$-quark