Light single-gluon hybrid states with various (exotic) quantum numbers

Abstract

We apply the QCD sum rule method to study the light single-gluon hybrid states with various (exotic) quantum numbers. We construct twenty-four single-gluon hybrid currents, and use eighteen of them to calculate the masses of forty-four single-gluon hybrid states with the quark-gluon contents $\bar{q}qg$ ($q=u/d$) and $\bar{s}sg$. We concentrate on the hybrid states with the exotic quantum number $J^{PC}=1^{-+}$, whose masses and widths are calculated to be $M_{|\bar{q}qg;1^{-}{1}^{-+}⟩}=1.67_{-0.17}^{+0.15}$ GeV, ${\Gamma }_{|\bar{q}qg;1^{-}{1}^{-+}⟩}=530_{-330}^{+540}$ MeV, $M_{|\bar{q}qg;0^{+}{1}^{-+}⟩}=1.67_{-0.17}^{+0.15}$ GeV, ${\Gamma }_{|\bar{q}qg;0^{+}{1}^{-+}⟩}=120_{-110}^{+160}$ MeV, $M_{|\bar{s}sg;0^{+}{1}^{-+}⟩}=1.84_{-0.15}^{+0.14}$ GeV, and ${\Gamma }_{|\bar{s}sg;0^{+}{1}^{-+}⟩}=100_{-80}^{+110}$ MeV. Our results support the interpretations of the ${\pi }_1(1600)$ and ${\eta }_1(1855)$ as the hybrid states $|\bar{q}qg;1^{-}{1}^{-+}⟩$ and $|\bar{s}sg;0^{+}{1}^{-+}⟩$, respectively. Considering the uncertainties, our results suggest that the ${\pi }_1(1600)$ and ${\eta }_1(1855)$ may also be interpreted as the hybrid states $|\bar{q}qg;1^{-}{1}^{-+}⟩$ and $|\bar{q}qg;0^{+}{1}^{-+}⟩$, respectively. To differentiate these two assignments and to verify whether they are hybrid states or not, we propose to examine the $a_1(1260)\pi$ decay channel in future experiments.

Comments: 18 pages 5 figures, 3 tables, revised version to be published in PRD