Abstract
We apply the method of QCD sum rules to study the $s q \bar s \bar q$ tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$, and extract mass of the lowest-lying state to be $2.33^{+0.19}_{-0.16}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematical analysis on their relevant interpolating currents indicates that: a) this state well decays into the $P$-wave $\rho\phi/\omega\phi$ channel but not into the $\rho f_2(1525)/\omega f_2(1525)/\phi f_2(1270)$ channels, and b) it well decays into the $K^*(892) \bar K_2^*(1430)$ channel but not into the $P$-wave $K^*(892) \bar K^*(892)$ channel.
Highlights
We apply the method of QCD sum rules to study the sqsqtetraquark states with the exotic quantum number JPC 1⁄4 3−þ, and extract mass of the lowest-lying state to be 2.33−þ00
There have been many candidates of exotic hadrons observed in particle experiments, which cannot be well explained in the traditional quark model [1,2,3,4,5,6,7,8,9,10]
There exist some “exotic” quantum numbers that traditional hadrons cannot have, such as the spin-parity quantum numbers JPC 1⁄4 0−−, 0þ−, 1−þ, 2þ−, 3−þ, etc. These exotic quantum numbers are of particular interest, because the hadrons with such quantum numbers cannot be explained as traditional hadrons any more
Summary
There have been many candidates of exotic hadrons observed in particle experiments, which cannot be well explained in the traditional quark model [1,2,3,4,5,6,7,8,9,10]. The same QCD sum rule method was applied to extensively study light tetraquark states of JPC 1⁄4 0−− in Refs. We shall investigate the light qsqs ̄ (q 1⁄4 up=down and s 1⁄4 strange) tetraquark states with such a quantum number. They may exist in the energy region around 2.0 GeV. In this paper we shall investigate the qsqs ̄ tetraquark state with the exotic quantum number JPC 1⁄4 3−þ using the method of QCD sum rules. In the present study we shall improve it by explicitly adding the covariant derivative operator in order to construct the qsqs ̄ tetraquark currents of JPC 1⁄4 3−þ.
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