The constructions of the new high-intensity muon beamlines are progressing in facilities around the world, and new physics searches related to the muons are expected. The facilities can observe the transverse positron polarization of the polarized $μ^+$ decay to test the standard model. The transition of muonium into antimuonium (Mu-to-$\bar{\text{Mu}}$ transition), which is one of the interesting possibilities in the models beyond the standard model, can be also tested. The near-future observation of the transition gives us a great impact since it indicates that there is an approximate discrete symmetry in the lepton sector. If the Mu-to-$\bar{\text{Mu}}$ transition operator is generated, a new muon decay operator can exist and it may interfere with the standard model muon decay operator to induce the corrections to the transverse positron polarization in the $μ^+$ decay. In this paper, we examine the possibility that the Mu-to-$\bar{\text{Mu}}$ transition and the correction to the transverse positron polarization are related, and we show that those two are related in the model of a neutral flavor gauge boson. We also investigate the models to generate the Mu-to-$\bar{\text{Mu}}$ transition, such as an inert $SU(2)_L$ doublet, a $SU(2)_L$ triplet for the type-II seesaw model, a dilepton gauge boson, and a left-right model. The non-zero value of the transverse polarization for one of the two directions, $P_{\rm T_2}$, violates the time-reversal invariance, and the experimental constraint of the electron electric dipole moment can provide a severe constraint on $P_{\rm T_2}$ depending on the model.
Conceptual Design of the Muonium-to-Antimuonium Conversion Experiment (MACE)
Sun Yat-sen University（中山大学）；Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Hunan University（湖南大学）；Liaoning University（辽宁大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Southern Center for Nuclear Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）
Registration of hydrogen-like leptonic bound states (e^- mu^+) and (e^+ mu^-) in reactions of high-energy scattering of polarized electrons and positrons by nuclei with Z ~ 100 and analysis of CPT invariance
计算了高能电子（正电子）与核e^-（e^+）+ Z -> Z + M^0（反M^0）+ mu^-（mu^+）散射产生μ偶素（反μ偶素）反应的截面，该截面依赖于初始电子（正电子）的能量和极化以及最终μ ^-（mu^+）-介子的极化.由于相干现象，截面与Z ^2成正比。对于Z ~ 100，由于因子Z ^2，截面足够大，可以在DESY中的HERA对撞机上测量。结果进行了讨论，在与CPT不变性的测试。
