The spontaneous conversion of muonium to antimuonium is one of the interesting charged lepton flavor violation phenomena offering a sensitive probe of potential new physics and serving as a tool to constrain the parameter space beyond the Standard Model. The Muonium-to-Antimuonium Conversion Experiment (MACE) is designed to utilize a high-intensity muon beam, a Michel electron magnetic spectrometer, a positron transport system, and a positron detection system, to either discover or constrain this rare process with a conversion probability of $\mathcal{O}(10^{-13})$. This article presents an overview of the theoretical framework as well as a detailed description of the experimental design for the search for muonium-to-antimuonium conversion.

We address the nature of the $X(2370)$ resonance observed in the $J/\psi$ radiative decays, $J/\psi\rightarrow\gamma K^{+} K^{-}\eta'$, $J/\psi\rightarrow\gamma K_S K_S\eta'$ and $J/\psi\rightarrow\gamma \pi^{+}\pi^{-}\eta'$. By studying the invariant mass spectra we confirm that decays of the $X(2370)$ into three pseudo-scalars are well described by an effective chiral Lagrangian. We extract the branching ratio of $J/\psi\to X(2370)\gamma$ and show that it is an order of magnitude larger compared to the glueball production rate predicted by lattice QCD. This indicates that $X(2370)$ is not likely to be a glueball candidate.

In this paper, we employ chiral effective field theory to study the process of electron-positron annihilation into four pions in the low energy region within $E_{c.m.}\leq 0.6$ GeV. The prediction of the cross-section is obtained through $SU(3)$ chiral perturbation theory up to the next-to-leading order, which is smaller than the experimental data in the energy region [0.6-0.65] GeV, though the data has only a few points and poor statistics. Then, the resonance chiral theory is applied to include the resonance contribution, with the lightest scalars and vectors written in the effective Lagrangians. A series of relevant decay widths and the masses of the vectors are studied to fix the unknown couplings. The resonance contribution should be one order larger than that of the chiral perturbation theory but still one to two orders smaller than the data. The significant discrepancy urged the new experimental measurements to give more guidance. We also compute the hadronic vacuum polarization contribution from the four pion channels to the anomalous magnetic moment of the muon, $(g-2)_\mu$. In the energy range from threshold up to 0.6 GeV within RChT, the contributions are $a_\mu=(0.6678\pm0.0933)\times10^{-16}$ and $a_\mu=(0.4575\pm0.0517)\times10^{-16}$ for the processes of $e^+e^-\to\pi^+\pi^+\pi^-\pi^-$, $\pi^0\pi^0\pi^+\pi^-$, respectively.