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

TL;DR

This paper explores how magnetic field dependence in muonium-to-antimuonium transitions can reveal properties of new physics, including parameters related to electron electric dipole moments and the nature of mediators, aiding future experiments.

Contribution

It analyzes the extraction of model-independent parameters from transition probabilities across magnetic fields, linking them to new physics and electron dipole moments, with implications for upcoming experiments.

Findings

Feasibility of determining transition amplitude parameters from experimental data.

Relationship between transition probability ratios and the nature of mediators.

Connection of the physical phase to the electron electric dipole moment.

Abstract

The muonium-to-antimuonium transition experiment is about to be updated. Notably, the experiment at J-PARC in Japan can explore the magnetic field dependence of the transition probability. In this paper, we investigate the information that we can extract from the transition probabilities across different magnetic field strengths, while also taking into account a planned transition experiment at CSNS in China. There are two model-independent parameters in the transition amplitude, and we ascertain the feasibility of determining these parameters, including their relative physical phase, from experimental measurements. This physical phase can be related to the electron electric dipole moment, which is severely constrained by experiments. The underlying mediator responsible for the transition can be either doubly charged particles or neutral particles. In the former case, typical magnetic fields yield specific probability ratios, while the latter presents a range of the probability ratio. We investigate several models with neutral mediators, and elucidate that the probability ratio is linked to the sign of new physics contribution to the electron $g-2$. The pivotal role of the J-PARC transition experiment in shedding light on these insights is emphasized.