Problems for superstring models with vacuum expectation values for conjugate sneutrinos

Abstract

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 [⪅ 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 ⪅ 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 c ν 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〉 ⪅ 40 KeV .