Lattice QCD Evidence for Exotic Tetraquark Resonance

TL;DR

This lattice QCD study provides evidence for an exotic tetraquark resonance around 1 GeV, using advanced boundary conditions to distinguish resonances from scattering states, and suggests a possible identification with known scalar mesons.

Contribution

The paper introduces the Hybrid Boundary Condition method in lattice QCD to identify compact tetraquark resonances, demonstrating its effectiveness in distinguishing them from scattering states.

Findings

Identified a 4Q resonance about 100 MeV below the two-meson threshold.

Found the scalar tetraquark f0(udbar ubar d) to have a mass around 1.1 GeV, consistent with f0(980).

Suggested the existence of an exotic D_s0^{++} tetraquark around 1 GeV in the SU(4)_f limit.

Abstract

We study the manifestly exotic tetraquark D$_{\rm s0}^{++}(cu\bar s \bar d)$ and the scalar tetraquark $f_0(ud \bar u \bar d)$ in SU(3)$_c$ anisotropic quenched lattice QCD with the $O(a)$-improved Wilson (clover) fermion with various quark masses including the idealized SU(4)$_f$ case. For $f_0(ud\bar u \bar d)$ etc., we only consider connected diagrams at the quenched level, i.e., the tetraquark $f_0(ud\bar u\bar d)$ is identical with D$_{\rm s0}^{++} (cu\bar s \bar d)$ in the idealized SU(4)$_f$ case. First, for comparison, we study the lowest $q\bar q$ scalar meson, and find that it has a large mass of about 1.37GeV after chiral extrapolation, which corresponds to $f_0(1370)$. Second, we investigate the lowest 4Q state in the spatial periodic boundary condition, and find that it is just a scattering state of two pseudoscalar mesons, as is expected. Third, to extract spatially-localized 4Q resonances, we use the Hybrid Boundary Condition (HBC) method, where anti-periodic and periodic boundary conditions are imposed on quarks ($c$,$u$) and antiquarks ($\bar s$,$\bar d$), respectively. By applying the HBC on a finite-volume lattice, the threshold of the two-meson scattering state is raised up, while the mass of a compact 4Q resonance is almost unchanged. In HBC, we find a nontrivial 4Q resonance state about 100 MeV below the two-meson threshold in some quark-mass region. Its chiral behavior largely differs from a two-meson scattering state. The scalar tetraquark $f_0(ud\bar u\bar d)$ is found to have the mass of about 1.1GeV after chiral extrapolation, and seems to correspond to $f_0(980)$. Then, the manifestly exotic tetraquark D$_{\rm s0}^{++}(cu\bar s \bar d)$ would exist around 1GeV in the idealized SU(4)$_f$ chiral limit. Finally, MEM analysis is applied to obtain the spectral function of the 4Q system.