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In this paper, we explore a new avenue to a natural explanation of the observed tiny neutrino masses with a dynamical realization of the three-generation structure in the neutrino sector. Under the magnetized background based on $T^2/Z_2$, matter consists of multiply-degenerated zero modes and the whole intergenerational structure is dynamically determined. In this sense, we can conclude that our scenario is favored by minimality, where no degree of freedom remains to deform the intergenerational structure by hand freely. Under the consideration of brane-localized Majorana-type mass terms for an $SU(2)_L$ singlet neutrino, it is sufficient to introduce one Higgs doublet for reproducing the observed neutrino data. In all reasonable flux configurations with three right-handed neutrinos, phenomenologically acceptable parameter configurations are found.
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We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos $m_ u$ and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix $f$, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution $f$, there is a dual solution $hat{f}=m_ u/v_L-f$, where $v_L$ is the VEV of the triplet Higgs. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix $f$. For $n$ lepton generations the number of solutions is $2^n$. We develop an exact analytic method of solving the seesaw non-linear matrix equation for $f$.
We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U_omega times a matrix constrained by a well-defined Z_2 symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature.
Cascade seesaw mechanism generates neutrino mass at higher dimension (5+4n) operators through tree level diagram which bring the seesaw scale down to TeV and provide collider signatures within LHC reach. In particular, both Type-II scalar and Type-III heavy fermion seesaw signatures exist in such a scenario. Doubly charged scalar decays into diboson is dominant. We perform a thorough study on the LHC signals and the Standard Model background. We draw the conclusion that multilepton final state from interplay of doubly charged scalar and heavy fermion can provide distinguishable signatures from conventional seesaw mechanisms.
It is shown that the specific charge conjugation transformation used to define the Majorana fermions in the conventional seesaw mechanism, namely $( u_{R})^{C}=Cbar{ u_{R}}^{T}$ for a chiral fermion $ u_{R}$ (and similarly for $ u_{L}$), is a hidden symmetry associated with CP symmetry, and thus it formally holds independently of the P- and C-violating terms in the CP invariant Lagrangian and it is in principle applicable to charged leptons and quarks as well. This hidden symmetry, however, is not supported by a consistent unitary operator and thus it leads to mathematical (operatorial) ambiguities. When carefully examined, it also fails as a classical transformation law in a Lorentz invariant field theory. To distinguish it from the standard charge conjugation symmetry, we suggest for it the name of pseudo C-symmetry. The pseudo C-symmetry is effective to identify Majorana neutrinos analogously to the classical Majorana condition. The analysis of CP breaking in weak interactions is performed using the conventional CP transformation, which is defined independently of the pseudo C-transformation, in the seesaw model after mass diagonalization. A way to ensure an operatorially consistent formulation of C-conjugation is to formulate the seesaw scheme by invoking a relativistic analogue of the Bogoliubov transformation.
We discuss a mechanism where charged lepton masses are derived from one-loop diagrams mediated by particles in a dark sector including a dark matter candidate. We focus on a scenario where the muon and electron masses are generated at one loop with new ${cal O}(1)$ Yukawa couplings. The measured muon anomalous magnetic dipole moment, $(g-2)_mu$, can be explained in this framework. As an important prediction, the muon and electron Yukawa couplings can largely deviate from their standard model predictions, and such deviations can be tested at High-Luminosity LHC and future $e^+e^-$ colliders.
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