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

The muonium-to-antimuonium transition experiment is about to be updated. Notably, the experiment at Japan Proton Accelerator Research Complex (J-PARC) 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 China Spallation Neutron Source (CSNS). 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.

Figure 1

Magnetic field dependence of the ratios of time-dependent probabilities to those at $B=0$, corresponding to various transition operators.

Figure 2

$s$-channel exchange of a pseudoscalar (left) and $t$-channel exchange of a scalar (right) for the Mu-to-$\overline{\mathrm{Mu}}$ transition.

Figure 3

$t$-channel exchange of a doubly charged scalar (left) and vector boson (right).

Figure 4

Trajectories in the $R_1-R_2$ plain while varying the value of $G_3/G_0$ under $\mathrm{Im}{G}_3/G_0=0$ with different values of muon polarization $P_{\mu }$ in the produced Mu (top) and trajectories for different phases of $G_3/G_0$ with a fixed muon polarization $P_{\mu }=0.5$ (bottom).

Figure 5

Contour plots illustrating $\mathrm{\Delta }{a}_e$ for two ALP masses, $m_a=300\mathrm{MeV}$ and $m_a=10\mathrm{GeV}$. The green dashed lines delineate contours of $\overline{P}=8.3\times {10}^{-11}$, which correspond to the bound of the Mu-to-$\overline{\mathrm{Mu}}$ transition given by the PSI experiment.

Figure 6

Plot depicting the relation between the contribution to the electron $g-2$ ($\mathrm{\Delta }{a}_e$) and the transition probability ratio ($R_1$) in the ALP model for $m_a=300\mathrm{MeV}$ (indicated by the green dashed line) and $m_a=10\mathrm{GeV}$ (indicated by the blue solid line) when the time-integrated transition probability is just same as the PSI bound, $\overline{P}=8.3\times {10}^{-11}$. The horizontal dotted line corresponds to $R_1=1/2$.

Figure 7

Contour plots illustrating the ratio of the transition probabilities (upper two plots) and the contribution to the electron $g-2$ (lower two plots) for a fixed mass of $m_H=150\mathrm{GeV}$ and varying values of ${\rho }_{12}$. The green dashed lines represent contours corresponding to $\overline{P}=8.3\times {10}^{-11}$, which is the bound of the Mu-to-$\overline{\mathrm{Mu}}$ transition set by the PSI experiment.