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

Abstract 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 m ν tree ≈( θ 2 ) 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) m ν tree falls in the range suggested by the atmospheric neutrino problem; (iii) radiative contributions to neutrino masses are strongly suppressed resulting in Δm 2 solar ≈ few 10 −8 eV 2 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.