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

TL;DR

This paper demonstrates the gauge invariance of muonium-antimuonium oscillation calculations within a modified Standard Model including right-handed neutrinos, and uses experimental limits to set a lower bound on heavy neutrino masses.

Contribution

It explicitly proves gauge invariance of the oscillation time scale in a model with right-handed neutrinos and calculates the leading order matrix element in a gauge-independent manner.

Findings

Gauge invariance is confirmed at leading order in $R_\xi$ gauge.

Experimental non-observation sets a lower limit of about 600 GeV on heavy neutrino masses.

The see-saw mechanism yields three light and three heavy Majorana neutrinos.

Abstract

The gauge invariance of the muonium-antimuonium ($M\bar{M}$) 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 $M_R\gg M_W$. The leading order matrix element contribution to the $M\bar{M}$ 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.