Can Precision Measurements of Slepton Masses Probe Right Handed Neutrinos?

In a supersymmetric model, the presence of a right handed neutrino with a large Yukawa coupling $f_{\nu}$ would affect slepton masses via its contribution to the renormalization group evolution between the grand unification and weak scales. Assuming a hierarchichal pattern of neutrino masses, these effects are large for only the third generation of sleptons. We construct mass combinations to isolate the effect of $f_{\nu}$ from mass corrections already expected from tau Yukawa couplings. We then analyze the size of these effects, assuming that the Super-Kamiokande data constrain 0.033 eV $\alt m_{\nu_{\tau}} \alt 0.1$ eV and that neutrino masses arise via a see-saw mechanism. We also explore whether these effects might be detectable in experiments at future $e^+e^-$ linear colliders. We find that $m_{\tnu_{\tau}}$ needs to be measured with a precision of about 2-3% to measure the effect of $f_{\nu}$ if the neutrino and top Yukawa couplings unify at the grand unification scale. In a simple case study, we find a precision of only 6-10% might be attainable after several years of operation. If the neutrino Yukawa coupling is larger, or in more complicated models of neutrino masses, a determination of $\ttau_1$ and $\tnu_{\tau}$ masses might provide a signal of a Yukawa interaction of neutrinos.