Fully charmed tetraquarks on the Lattice with controlled errors

Abstract

We introduce the lattice quark potential model (LQPM), which discretizes the nonrelativistic quark potential model on a periodic cubic lattice and diagonalizes the resulting many-body Hamiltonian exactly. Unlike variational approaches, which provide only upper bounds on the energy, LQPM removes this variational bias, and its remaining finite-volume uncertainty is removed by extrapolation. Formulated directly in coordinate space, the method is indifferent to the specific form of the potential and accommodates arbitrary interactions, such as including three-body forces and spin-orbit and tensor couplings, that are difficult to treat in conventional few-body approaches. As a benchmark, the charmonium and $\Omega_{ccc}$ spectra are reproduced within a few MeV of experiment. For the fully charmed tetraquark $cc\bar{c}\bar{c}$, we obtain a $J^P=0^+$ ground state at $5934.8(13)~\mathrm{MeV}$, $33.2(13)~\mathrm{MeV}$ below the $\eta_c\eta_c$ threshold, unambiguously identified as a deeply bound tetraquark whose existence is robust against the choice of potential. Such a state can decay into two dileption pairs $2(e^+e^-)$ via $J/\psi e^+e^-$, with significance similar to $X(6400)$, or about one order of magnitude smaller. Lying below the lowest strong-decay channel, it can decay only through electromagnetic and weak interactions. Our results establish exact lattice diagonalization as a controlled, systematically improvable, and broadly applicable route to multiquark spectroscopy, providing a quantitative benchmark for the strong interaction and valuable guidance for future experimental searches for exotic hadrons.