The decay of the observed $J^{PC}=1^{-+}$ (1400) and $J^{PC}=1^{-+}$(1600) hybrid candidates

Abstract

We study the possible interpretation of the two exotic resonances $J^{PC}=1^{-+}$ at 1400 and 1600 MeV, claimed to be observed by BNL, decaying respectively into $\eta \pi$, ${\eta }^{\prime }\pi$, $f_1\pi$ and $\rho \pi$. These objects are interpreted as hybrid mesons, in the quark-gluon constituent model using a chromoharmonic confining potentiel. The quantum numbers $J^{PC}{I}^G=1^{-+}{1}^{-}$ can be considered in a constituent model as an hybrid meson ($q\bar{q}g$). The lowest $J^{PC}=1^{-+}$states may be built in two ways : $l_g$=1 (gluon-excited) corresponding to an angular momentum between the gluon and ($q\bar{q}$) system, while $l_{q\bar{q}}=1$ (quarks-excited) corresponds to an angular momentum between $q$ and $\bar{q}$. For the gluon-excited mode $1^{-+}$ hybrids, we find the decay dominated by the $b_1\pi$ channel, and by the $\rho \pi$ channel for the quark-excited mode. In our model, neither the quark-excited nor the gluon-excited $1^{-+}$ (1400 MeV) hybrids can decay into $\eta \pi$ and ${\eta }^{\prime }\pi$, in contradiction with experiment. Hence, the 1400 MeV resonance seems unlikely to be an hybrid state. The $1^{-+}$ (1600 MeV) gluon-excited hybrid is predicted with too large a total decay width, to be considered as an hybrid candidate. On the contrary the quark-excited mode has a total decay width around 165 MeV, with a $\rho \pi$ preferred decay channel, in agreement with BNL. Our conclusion is that {\it{this resonance may be considered as a hybrid meson in the quark-excited mode}}

Comments: 13 pages, 1 figure