We show that L I =L, -L,, L > = L p -L p , and L3=L, -L , (where L,,,,, are the family lepton numbers) are anomaly free and can thus be gauged. Three simple theories featuring a flavorconserving second Z boson ( Z 1 . 2 , ) ) result. Bounds on the Z,' coupling constant (g,') and mass are derived. The mass of Zi has a lower bound of 60-150 GeV at 90% confidence level for reasonable values of gi. The mass of Zi has a best-fit value of about 60 GeV. The physics of these bosons in the KEK TRISTAN and CERN LEP window of 63-87 GeV is discussed. Constraints on Z ; interactions are derived from (g -2),.Because of the absence of right-handed neutrinos, the three-generation minimal standard model ( M S M ) Lagrangian is invariant under the three global symmetries of family lepton number: U ( l ) r , , U ( l )L,, and U (~) L~. These symmetries are present for all choices of the Yukawa coupling constants. Although some effort has been put into the search for family lepton-number-violating processes, none have been observed. For example, the current upper limits on the branching ratios for --
We propose a spontaneous A 4 flavour symmetry breaking scheme to understand the observed pattern of quark and neutrino mixing. The fermion mass eigenvalues are arbitrary, but the mixing angles are constrained in such a way that the overall patterns are explained while also leaving sufficient freedom to fit the detailed features of the observed values, including CP-violating phases. The scheme realises the proposal of Low and Volkas to generate zero quark mixing and tribimaximal neutrino mixing at tree level, with deviations from both arising from small corrections after spontaneous A 4 breaking. In the neutrino sector, the breaking is A 4 → Z 2 , while in the quark and charged-lepton sectors it is A 4 → Z 3 ∼ = C 3 . The full theory has A 4 completely broken, but the two different unbroken subgroups in the two sectors force the dominant mixing patterns to be as stated above. Radiative effects within each sector are shown to deviate neutrino mixing from tribimaximal, while maintaining zero quark mixing. Interactions between the two sectors -"cross-talk" -induce nonzero quark mixing, and additional deviation from tribimaximal neutrino mixing. We discuss the vacuum alignment challenge the scenario faces, and suggest three generic ways to approach the problem. We follow up one of those ways by sketching how an explicit model realising the symmetry breaking structure may be constructed.
We show that there is an analogous Aharonov-Casher topological effect on a neutral particle with electric dipole moment interacting with a magnetic field produced by magnetic monopoles.
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