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

TL;DR

This paper proposes a method to determine the spin and parity of a hypothetical muon-philic X boson in J/psi decays, aiding the search for new physics related to the muon magnetic moment anomaly.

Contribution

It introduces a novel approach using angular and Dalitz plot distributions to identify the spin-parity of the X boson regardless of its parity state.

Findings

Method can distinguish scalar and vector X bosons

Utilizes angular distributions and Dalitz plot analysis

Provides a way to probe new physics in J/psi decays

Abstract

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.