Neutrino masses within the minimal supersymmetric standard model.

We investigate the possibility of accommodating neutrino masses compatible with the MSW study of the Solar neutrino deficit within the minimal supersymmetric Standard Model. The “gravity-induced” seesaw mechanism based on an interplay of nonrenormalizable and renormalizable terms in the superpotential allows neutrino masses mν ∝ mu/MI , with mu the corresponding quark mass and MI ≃ 4 × 1011 GeV, while at the same time ensuring the grand desert with the gauge coupling unification at MU ≃ 2× 1016 GeV. The proposed scenario may be realized in a class of string vacua, i.e., large radius (R2/α′ = O(20)) (0, 2) CalabiYau spaces. In this case M2 U = M 2 C/O(2R/α) and MI = O(e−R 2′)MC . Here MC = g × 5.2× 1017GeV is the scale of the tree level (genus zero) gauge coupling (g) unification. PACS # 12.10,11.15,11.17 Precise data from the LEP experiments indicate that the gauge couplings of the Standard Model meet at MU ≃ (1−4)×1016 GeV in the minimal supersymmetric extension of the Standard Model. 1 Another set of intriguing data arise from the Solar neutrino experiments. The deficit of Solar neutrinos can most efficiently be explained through the MSW 2 mechanism of matter-enhanced neutrino oscillations. In particular, current data favor 3 the mass splitting of the electron and muon neutrinos to be ∆m2 ≡ |mνμ − mνe | ≃ (2 − 5) × 10−7eV 2 if the mixing angle θνμνe ≃ O(θC), where θC is the Cabibbo angle. For arbitrary mixing angles the nonadiabatic MSW solution favors ∆m2 ≃ (1− 16)× 10−7eV. In many grand unified theory (GUT) models the lepton mixing matrix Vl and the Cabibbo-Kobayashi-Maskawa matrix VCKM are predicted to be approximately equal 4 . However, these same models predict me/mμ ≃ md/ms (≃ 1/20), which fails by an order of magnitude. Small perturbations on the models which rescue this mass relation 5 may also modify the mixing angle predictions. In theories with no explicit intra-family unification VCKM and Vl are not expected to be equal, but could well be of the same order of magnitude. We will assume sin 2θνμνe ∼ sin 2θC ∼ 0.18 for the central value in our discussion, but will consider the entire range 4× 10−3 − 1 allowed by the nonadiabatic MSW solution. Assuming mνμ ≫ mνe , the corresponding values of mνμ are (5 − 7) × 10−4eV for θνμνe ∼ θC and (3− 40)× 10−4eV for general θνμνe . In the GUT seesaw scenario 6 masses of light neutrinos are given by mνe,μ ≃ c mu,c/MI , where mu,c are the corresponding quark masses and c ≃ 0.05− 0.09 is a factor due to the renormalization down to the low energy scale 3 . This implies that MI ≃ (4± 3)× 1011 GeV, the central value corresponding to θνμνe ∼ θC . If the same scale applies to the third family, then mντ ≃ cmt /MI could be in the