New U(3) Family Gauge Symmetry and Muonium into Antimuonium Conversion

According to Sumino's idea, a family U(3) gauge symmetry is assumed. SU(2)$_L$ doublet fields $q_L$ and $\ell_L$ are assigned to {\bf 3} of U(3), while singlets $u_R$, $d_R$, $e_R$ and $\nu_R$ are assigned to {\bf 3$^*$} of U(3). Then, current-current interactions with flavor number violations of $|\Delta N_{f}|=2$ ($N_{f}$ is an individual family number) appear via the family gauge boson exchanges. Since the gauge symmetry model has inevitably been brought by Sumino with a specific purpose, the gauge coupling constants g_f and the gauge boson mass spectrum m_{fij}\equiv m(A_i^j) are not free parameters. We estimate m_{f11} \sim 10^{0-1} TeV and m_{f12} \sim 10^{1-2} TeV. As a possible signature of such the flavor number violating interactions, muonium into antimuonium conversion is discussed together with a rare kaon decay K^+ \rightarrow \pi^+ + \mu^- +e^+.