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The addition of gauge singlet fermions to the Standard Model Lagrangian renders the neutrinos massive and allows one to explain all that is experimentally known about neutrino masses and lepton mixing by varying the values of the Majorana mass parameters M for the gauge singlets and the neutrino Yukawa couplings. Here we explore the region of parameter space where M values are much smaller than the neutrino Dirac masses. In this region, neutrinos are pseudo-Dirac fermions. We find that current solar data constrain M values to be less than at least 1E-9 eV, and discuss the sensitivity of future experiments to tiny gauge singlet fermion masses. We also discuss a useful basis for analyzing pseudo-Dirac neutrino mixing effects. In particular, we identify a simple relationship between elements of M and the induced enlarged mixing matrix and new mass-squared differences. These allow one to directly relate bounds on the new mass-squared differences to bounds on the singlet fermion Majorana masses.
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We provide a generic framework to obtain stable dark matter along with naturally small Dirac neutrino masses generated at the loop level. This is achieved through the spontaneous breaking of the global $U(1)_{B-L}$ symmetry already present in Standard Model. The $U(1)_{B-L}$ symmetry is broken down to a residual even $mathcal{Z}_n$; $n geq 4$ subgroup. The residual $mathcal{Z}_n$ symmetry simultaneously guarantees dark matter stability and protects the Dirac nature of neutrinos. The $U(1)_{B-L}$ symmetry in our setup is anomaly free and can also be gauged in a straightforward way. Finally, we present an explicit example using our framework to show the idea in action.
If the sterile neutrino mass matrix in an otherwise conventional seesaw model has a rank less than the number of flavors, it is possible to produce pseudo-Dirac neutrinos. In a two-flavor, sterile rank 1 case, we demonstrate analytic conditions for large active mixing induced by the existence of (and coupling to) the sterile neutrino components. For the three-flavor, rank 1 case, ``3+2 scenarios with large mixing also devolve naturally as we show by numerical examples. We observe that, in this approach, small mass differences can develop naturally without any requirement that masses themselves are small. Additionally, we show that significant three channel mixing and limited experimental resolution can combine to produce extracted two channel mixing parameters at variance with the actual values.
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A solution for the neutrino mass and mixing pattern is proposed which is compatible with all available experimental data on neutrino oscillations. This solution involves Majorana neutrinos of the pseudo-Dirac type, i.e. m_Majorana << m_Dirac. The solar and atmospheric neutrino observations are mainly explained as nu_e - nu_e^S and nu_mu - nu_mu^S oscillations, where S indicates the sterile (``righthanded) partner of each neutrino generation, while the LSND result is interpreted in terms of standard nu_mu - nu_e oscillations. The resulting constraints on nu_mu - nu_tau and nu_tau - nu_tau^S oscillations are also discussed. This solution leaves room for a hierarchical mass and mixing scheme with a nu_tau mass in the few eV range, as favoured by some dark matter scenarios. The apparent conflict with standard Big Bang nucleosynthesis is addressed and the implications for current and future experiments are discussed. It is argued that both short and long baseline accelerator neutrino experiments are needed in order to decide between this solution and other oscillation scenarios.
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