Searching for a hidden charm $h_1$ state in the $X(4660)\to \eta h_1$ and $X(4660)\to \eta D^{\ast }{\bar{D}}^{\ast }$ decays

Abstract

We explore the possibility of experimentally detecting a predicted $h_1[I^G(J^{PC})=0^{-}(1^{+-})]$ state of hidden charm made out from the $D^{\ast }{\bar{D}}^{\ast }$ interaction. The method consists in measuring the decay of X(4660) into $\eta D^{\ast }{\bar{D}}^{\ast }$, determining the binding energy with respect to the $D^{\ast }{\bar{D}}^{\ast }$ threshold from the shape of the $D^{\ast }{\bar{D}}^{\ast }$ invariant mass distribution. A complementary method consists in looking at the inclusive $X(4660)\to \eta X$ decay, searching for a peak in the $X$ invariant mass distribution given by the missing X(4660), $\eta$ mass. We make calculations to determine the partial decay width of $X(4660)\to \eta h_1$ from the measured $X(4660)\to \eta D^{\ast }{\bar{D}}^{\ast }$ distribution. This estimation should serve in an experiment to foresee the possibility of detecting the $h_1$ state on top of the background of inclusive events.