Doubly charmed tetraquark: isospin channels and diquark-antidiquark interpolators

Abstract

We perform a lattice simulation to investigate the doubly charmed tetraquark $T_{cc}^{+}$ observed by the LHCb collaboration, slightly below the $D^{\ast +}{D}^0$ threshold, with flavor content $cc\bar{u}\bar{d}$ and isospin-$0$. Two-meson interpolators are implemented to explore the isospin quantum numbers $I=0$ and $I=1$. We observe attraction near the $D{D}^{\ast }$ threshold for $I=0$ and repulsion for $I=1$. Moreover, we also include diquark-antidiquark interpolators to study their effect on the energy spectrum. There is no significant shift in the ground state energy when adding diquark-antidiquark interpolators to the interpolator basis when the heavy quark mass is close to the physical charm quark mass. However, we observe a non-negligible shift in the second energy level. This effect has to be taken into account to extract the scattering amplitude of the $T_{cc}^{+}$. Finally, with a higher mass (close to the bottom quark), the ground state is shifted down significantly. The simulation is performed on $N_f=2+1$ CLS ensembles with $m_{\pi }\simeq 280$ MeV.

Comments: IMSc/2023/06