The $J^P=1^{+}$ $ud\bar{s}\bar{s}$ Tetraquark

Abstract

Using the color-magnetic interaction Hamiltonian with SU(3) flavor symmetry breaking, we perform a schematic study of the masses of the $J^P=1^{+}$ tetraquarks in the anti-decuplet representation. After diagonalizing the mass matrix, we find the $ud\bar{s}\bar{s}$ tetraquark lies around 1347 MeV. It decays into $K^{+}{K}^0{\pi }^0,K^{+}{K}^{+}{\pi }^{-},K^0{K}^0{\pi }^{+}$ via P-wave. The dual suppression from the not-so-big three-body phase space and P-wave decay barrier may render this exotic state rather narrow. Future experimental exclusion of this state will cast doubt on the validity of applying the simple color-magnetic Hamiltonian to the multiquark system.