  The present anomaly in muon anaomalous magnetic moment can be explained by
the presence of a muon-philic $X$ boson which could be a scalar particle or a
vector particle with mass less than twice the mass of muon. The muon-philic $X$
boson could interestingly not be a parity eigenstate as well. If there exists
such a boson, irrespective of its parity, it can be directly observed in the
decay $J/\psi \to \mu^- \mu^+ X$ where $X$ remains invisible. We show that by
using the angular distribution or the distribution of events in the square
Dalitz plot, along with two well defined dimensionless ratios, one can clearly
distinguish among the various spin-parity possibilities. This would constitute
an important probe of both the existence and the nature of this new physics
possibility.
