$\mu \to e$ Conversion in the Electroweak-scale Right-handed Neutrino Model

Within the framework of the Electroweak-scale right-handed neutrino (EW-$\nu_R$) model, we calculate the rate for $\mu \to e$ conversion with a particular aim at the sensitivities of the upcoming experiments, Mu2e ($6 \times 10^{-17}$) and COMET ($3 \times 10^{-17}$). Our calculations show a direct relationship between the rate for $\mu \to e$ conversion and that for $\mu \rightarrow e \gamma$. Upon comparing the projected sensitivities with the present limit from SINDRUM II ($6.1 \times 10^{-13}$) and including the upper bound on $\mu \rightarrow e \gamma$ ($5.7 \times 10^{-13}$), we found that approximately only half of the allowed parameter space between the SINDRUM II limit and the sensitivities of Mu2e and COMET is available ($\sim 10^{-17} - 10^{-15}$).