Lattice QCD Evidence for Exotic Tetraquark Resonance

الأصل · EN

We study the manifestly exotic tetraquark D s0⁺⁺(cu s d) and the scalar tetraquark f₀(ud u 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 f₀(ud u d) etc., we only consider connected diagrams at the quenched level, i.e., the tetraquark f₀(ud u d) is identical with D s0⁺⁺ (cu s d) in the idealized SU(4)f case. First, for comparison, we study the lowest q q scalar meson, and find that it has a large mass of about 1.37GeV after chiral extrapolation, which corresponds to f₀(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 (s, 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 f₀(ud u d) is found to have the mass of about 1.1GeV after chiral extrapolation, and seems to correspond to f₀(980). Then, the manifestly exotic tetraquark D s0⁺⁺(cu s 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.