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 term s induce a neutrino mass at tree level m(v)(tree) approximate to (theta (2) )(delta) eV where theta similar or equal to 0.22 is the U(1)(H) breaking pa rameter and delta is an integer number that depends on the horizontal charg es of the leptons. For delta = 1 a unique self-consistent model arises in w hich (i) all the superpotential trilinear R-parity violating couplings are forbidden by holomorphy; (ii) m(v)(tree) falls in the range suggested by th e atmospheric neutrino problem; (iii) radiative contributions to neutrino m asses are strongly suppressed resulting in Deltam(solar)(2) approximate to few 10(-8) eV(2) which only allows for the LOW (or quasi-vacuum) solution t o the solar neutrino problem; (iv) the neutrino mixing angles are not suppr essed by powers of theta and can naturally be large. (C) 2000 Elsevier Scie nce B.V. All rights reserved.