Exotic tetraquark states with $J^{PC}=0^{+-}$

Abstract

We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $ud\bar{u}\bar{d}$ and hidden-strange $us\bar{u}\bar{s}$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systematically construct all eight possible tetraquark currents in this channel without covariant derivative operator. Our analyses show that the $ud\bar{u}\bar{d}$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $us\bar{u}\bar{s}$ states do not associate with convergent OPE series in the stability regions and only the FESR can provide valid results. We give the mass predictions $1.43\pm 0.09$ GeV and $1.54\pm 0.12$ GeV for the $ud\bar{u}\bar{d}$ and $us\bar{u}\bar{s}$ tetraquark states, respectively. Our results indicate that the $0^{+-}$ isovector $us\bar{u}\bar{s}$ tetraquark may only decay via weak interaction mechanism, e.g. $X_{us\bar{u}\bar{s}}\to K\pi \pi$, since its strong decays are forbidden by kinematics and the symmetry constraints on the exotic quantum numbers. It is predicted to be very narrow, if it does exist. The $0^{+-}$ isoscalar $us\bar{u}\bar{s}$ tetraquark is also predicted to be not very wide because its dominate decay mode $X_{us\bar{u}\bar{s}}\to \varphi \pi \pi$ is in $P$-wave.

arXiv comment11 pages, 4 figures. Typos corrected

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