Bilinear R-parity violation and small neutrino masses: a self-consistent framework

We study extensions of supersymmetric models without R-parity which include an anomalous U(1)H horizontal symmetry. Bilinear R-parity violating terms induce a neutrino mass at tree level mνtree≈(θ2)δ eV where θ≃0.22 is the U(1)H breaking parameter and δ is an integer number that depends on the horizontal charges of the leptons. For δ=1 a unique self-consistent model arises in which (i) all the superpotential trilinear R-parity violating couplings are forbidden by holomorphy; (ii) mνtree falls in the range suggested by the atmospheric neutrino problem; (iii) radiative contributions to neutrino masses are strongly suppressed resulting in Δm2solar≈ few 10−8 eV2 which only allows for the LOW (or quasi-vacuum) solution to the solar neutrino problem; (iv) the neutrino mixing angles are not suppressed by powers of θ and can naturally be large.