Gauge Invariance of the Muonium-Antimuonium Oscillation Time Scale and Limits on Right-Handed Neutrino Masses

The gauge invariance of the muonium-antimuonium ($Mbar{M}$) oscillation time scale is explicitly demonstrated in the Standard Model modified only by the inclusion of singlet right-handed neutrinos and allowing for general renormalizable interactions. The see-saw mechanism is exploited resulting in three light Majorana neutrinos and three heavy Majorana neutrinos with mass scale $M_Rgg M_W$. The leading order matrix element contribution to the $Mbar{M}$ oscillation process is computed in $R_xi$ gauge and shown to be $xi$ independent thereby establishing the gauge invariance to this order. Present experimental limits resulting from the non-observation of the oscillation process sets a lower limit on $M_R$ roughly of order 600 GeV.