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The muonium-to-antimuonium transition experiment is about to be updated.Notably, the experiment at J-PARC in Japan can explore the magnetic fielddependence of the transition probability. In this paper, we investigate theinformation that we can extract from the transition probabilities acrossdifferent magnetic field strengths, while also taking into account a plannedtransition experiment at CSNS in China. There are two model-independentparameters in the transition amplitude, and we ascertain the feasibility ofdetermining these parameters, including their relative physical phase, fromexperimental measurements. This physical phase can be related to the electronelectric dipole moment, which is severely constrained by experiments. Theunderlying mediator responsible for the transition can be either doubly chargedparticles or neutral particles. In the former case, typical magnetic fieldsyield specific probability ratios, while the latter presents a range of theprobability ratio. We investigate several models with neutral mediators, andelucidate that the probability ratio is linked to the sign of new physicscontribution to the electron $g-2$. The pivotal role of the J-PARC transitionexperiment in shedding light on these insights is emphasized.

Insights from the magnetic field dependence of the muonium-to-antimuonium transition