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The present anomaly in muon anaomalous magnetic moment can be explained bythe presence of a muon-philic $X$ boson which could be a scalar particle or avector 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 existssuch a boson, irrespective of its parity, it can be directly observed in thedecay $J/\psi \to \mu^- \mu^+ X$ where $X$ remains invisible. We show that byusing the angular distribution or the distribution of events in the squareDalitz plot, along with two well defined dimensionless ratios, one can clearlydistinguish among the various spin-parity possibilities. This would constitutean important probe of both the existence and the nature of this new physicspossibility.

Methodology to determine the spin-parity of muon-philic $X$ boson in $J/\psi \rightarrow \mu^- \mu^+ X$ decay