Ruling out large sneutrino vacuum expectation values

Minimal supersymmetric models can generate a large $\tau$ sneutrino vacuum expectation value (VEV). However, neutrino mass limits constrain the sneutrino VEV to be small ($〈{\tilde{\nu }}_{\tau }〉\lesssim 10$ GeV) unless the gaugino mass is unnaturally large ($M \gtrsim 1$ TeV) or the Higgs-boson-Higgs-boson coupling is small ($\left|\mu \right|\lesssim 10$ GeV). We show that the latter case is now ruled out by CERN LEP data and gluino mass limits.