Problems for superstring models with vacuum expectation values for conjugate sneutrinos

Superstring models compactified on Calabi-Yau manifolds contain two new neutral scalars in each 27 generation of chiral supermultiplets. We consider implications of a vacuum expectation value for one of the neutral scalars, the conjugates neutrino ν_L^c:〈0|;ν_L^c|;0〉 y. Apart from a coupling from a coupling which generates a Dirac neutrino mass and which must be small [{less-than or approximate} O(10^-9)], its only superpotential interaction is with D_Ld_L, so there would be D-d mixing if y ≠ 0. The fact that m_d is not much less than m_e or m_u then tells us that y {less-than or approximate} O (few TeV). When the four-dimensional gauge group has rank 5, a pseudo-Goldstone boson, a_ν, arises if y ≠ 0, and the D-d mixing would then induce the decay K → π + a_ν at an unacceptable rate. Regardless of the gauge group rank, we show that the combined constraints on D-d mixing, and on the flavour-changing neutral currents it would induce, are sufficient to rule out D_Ld_L^cν_L^c superpotential coupling large enough to produce 〈0|;ν_L^c|;0〉 ≠ 0. These problems are avoided in models with a rank-5 gauge group and 〈0|;ν_L^c|;0〉 {less-than or approximate} 40 KeV.