Light double-gluon hybrid states with the exotic quantum numbers $J^{PC} = 1^{-+}$ and $3^{-+}$

Abstract

We apply the QCD sum rule method to study the double-gluon hybrid states with the quarkgluon contents qqgg (q = u/d) and ssgg. We construct twenty-eight double-gluon hybrid currents, eleven of which are found to be zero due to some internal symmetries between the two gluons fields. We concentrate on the non-vanishing currents with the exotic quantum numbers J P C = 1 −+ and 3 −+ . Their masses are calculated to be M |qqgg;1 −+ = 4.35 +0.26 −0.30 GeV, M |ssgg;1 −+ = 4.49 +0.25 −0.30 GeV, M |qqgg;3 −+ = 3.02 +0.24 −0.31 GeV, and M |ssgg;3 −+ = 3.16 +0.22 −0.28 GeV. The decay behaviors of the J P C = 3 −+ states are studied, and we propose to search for them in the πa1(1260)/ρω/φφ channels in future particle experiments.