Volume 235, number 1,2 PHYSICS LETTERS B 25 January 1990 LARGE MAGNETIC MOMENTS FOR NEAR MASSLESS NEUTRINOS Debajyoti CHOUDHURY and Utpal SARKAR Theory Group, PhysicalResearch Laboratory, Navrangpura,Ahmedabad 380 009, India Received 18 October 1989 We propose an extension of the standard model including a horizontal O (3) symmetry between generations and new Higgs scalars, where massless neutrinos can have large magnetic moments. Unlike earlier models, all the fermions are treated equally under O (3)n and the breaking of this group results in transition moments of the neutrinos radiatively yet keeping them massless. The question of the compatibility of a large magnetic moment and a very small mass for the neutrinos, apart from being very interesting in itself, is of much importance as a way out of the solar neutrino puzzle [ 1 ]. For the neutrino spin rotation (flavour-changing or otherwise) in conjunction with the matter oscillation effects could lead to a substantial reduction in the re-flux - irrespective of the validity of the adiabatic approximation - thus explaining the discrepancy between the standard solar model prediction [2] and the Davis and the Kamiokande results [ 3 ]. Moreover a substantial neutrino magnetic moment could play a crucial role in super- nova dynamics [4 ]. It was first noticed by Voloshin [ 5] that if v e and v~ transform as a doublet under some SU (2)v symmetry, then while the magnetic moment term is invariant, the mass term behaves as a triplet. This was incorporated in an SU (3) e × U ( 1 ) r electroweak model [ 6 ]. A variant in which SU (2) v was some kind of a horizontal symmetry with (ve v,) as a doublet was also considered [ 7]. In the limit of exact SU (2)v symmetry then, there exists no mass term but only a nonzero magnetic (or transition) moment. The breaking of this symmetry however gen- erates masses, the proportionality of which to the magnetic moments can be kept down only by imposing certain naturalness conditions. In this letter we aim to generalize Voloshin's argument and see if we can have scenarios wherein the neutrino magnetic moment can exist independent of its mass even after the symmetry breaking, thus rendering the natu- ralness conditions redundant. We extend the standard model to include a horizontal symmetry that treats all fermions on an equal footing. The only lepton number violating Higgs (c~) is also responsible for breaking the horizontal symmetry. Thus in the exact symmetry limit, both the Majorana masses and the transition moments -c pv vanish. This is so because 9Cvj and v~au,vjF both violate lepton number. Since we do not have tree level Majorana or Dirac mass terms for the neutrinos, the origin of both the transition moments and the v-mass lie in the radiative corrections. To one-loop order they can be parametrized in terms of dimension-five operators with the mass suppression scale being decided by the internal Higgs particles in the relevant diagrams. Thus if the couplings and the vacuum expectation values (VEV) in the theory could be so chosen that only the antisym- metric terms get any contribution from the diagrams containing (G), then the v's would acquire a transition moment while keeping the mass correction zero. In the case where one of the internal Higgs flowing in the diagram happens to be a horizontal group singlet, this can be ensured simply by seeing to it that the effective VEV structure couples only to antisymmetric combinations of the fermions. The gauge group we consider is SU (3)c × SU (2) L× U ( 1 ) r× O (3) Hwith the particle representations as under (for the scalars the super and subscripts denote the electric charge and the T3H quantum numbers respectively): 0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland ) 1 13