Tetraquark operators in lattice QCD and exotic flavour states in the charm sector

TL;DR

This study uses lattice QCD to analyze tetraquark operators and their impact on the spectrum of exotic states in the charm sector, finding no strong evidence for bound states or narrow resonances.

Contribution

It introduces a class of tetraquark operators with various symmetries and demonstrates their use in lattice QCD calculations to study exotic charm states.

Findings

Spectra are insensitive to tetraquark operator inclusion.

Multiple energy levels match expected non-interacting meson-meson levels.

No evidence of bound states or narrow resonances found.

Abstract

We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_\pi =$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Therefore, there is no strong indication for any bound state or narrow resonance in the channels we study.