Highly excited and exotic fully-strange tetraquark states

Abstract

Abstract Some hadrons have the exotic quantum numbers that the traditional $$\bar{q} q$$ q ¯ q mesons and qqq baryons can not reach, such as $$J^{PC} = 0^{--}/0^{+-}/1^{-+}/2^{+-}/3^{-+}/4^{+-}$$ J PC = 0 - - / 0 + - / 1 - + / 2 + - / 3 - + / 4 + - , etc. We investigate for the first time the exotic quantum number $$J^{PC}=4^{+-}$$ J PC = 4 + - , and study the fully-strange tetraquark states with such an exotic quantum number. We systematically construct all the diquark–antidiquark interpolating currents, and apply the method of QCD sum rules to calculate both the diagonal and off-diagonal correlation functions. The obtained results are used to construct three mixing currents that are nearly non-correlated, and we use one of them to extract the mass of the lowest-lying state to be $$2.85^{+0.19}_{-0.22}$$ 2 . 85 - 0.22 + 0.19 GeV. We apply the Fierz rearrangement to transform this mixing current to be the combination of three meson–meson currents, and the obtained Fierz identity suggests that this state dominantly decays into the P-wave $$\phi (1020) f_2^\prime (1525)$$ ϕ ( 1020 ) f 2 ′ ( 1525 ) channel. This fully-strange tetraquark state of $$J^{PC}=4^{+-}$$ J PC = 4 + - is a purely exotic hadron to be potentially observed in future particle experiments.