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 $\eta\pi$, $\eta'\pi$, $f_{ 1}\pi$ 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 $\eta'\pi$, 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}}
Categories: hep-ph