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Register a new userMajorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
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We provide theoretical evidence that the neutrino is a Majorana fermion. This evidence comes from assuming that the standard model and beyond-standard-model physics can be described through division algebras, coupled to a quantum dynamics. We use the division algebras scheme to derive mass ratios for the standard model charged fermions of three generations. The predicted ratios agree well with the observed values if the neutrino is assumed to be Majorana. However, the theoretically calculated ratios completely disagree with known values if the neutrino is taken to be a Dirac particle. Towards the end of the article we discuss prospects for unification of the standard model with gravitation if the assumed symmetry group of the theory is $E_6$, and if it is assumed that space-time is an 8D octonionic space-time, with 4D Minkowski space-time being an emergent approximation. Remarkably, we find evidence that the precursor of classical gravitation, described by the symmetry $SU(3)_{grav} times SU(2)_R times U(1)_{grav}$ is the right-handed counterpart of the standard model $SU(3)_{color} times SU(2)_L times U(1)_Y$.
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We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CP-breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.
In this paper, we obtain the light neutrino masses and mixings consistent with the experiments, in the democratic texture approach. The essential ansatz is that $ u_{Ri}$ are assumed to transform as right-handed fields $bf 2_{R} + 1_{R}$ under the $S_{3L} times S_{3R}$ symmetry. The symmetry breaking terms are assumed to be diagonal and hierarchical. This setup only allows the normal hierarchy of the neutrino mass, and excludes both of inverted hierarchical and degenerated neutrinos. Although the neutrino sector has nine free parameters, several predictions are obtained at the leading order. When we neglect the smallest parameters $zeta_{ u}$ and $zeta_{R}$, all components of the mixing matrix $U_{rm PMNS}$ are expressed by the masses of light neutrinos and charged leptons. From the consistency between predicted and observed $U_{rm PMNS}$, we obtain the lightest neutrino masses $m_{1}$ = (1.1 $to$ 1.4) meV, and the effective mass for the double beta decay $vev{m_{ee}} simeq$ 4.5 meV.
Dedicated to Ludwig Faddeev on his 80th birthday. Ludwig exemplifies perfectly a mathematical physicist: significant contribution to mathematics (algebraic properties of integrable systems) and physics (quantum field theory). In this note I present an exercise which bridges mathematics (restricted Clifford algebra) to physics (Majorana fermions).
The parity transformation law of the fermion field $psi(x)$ is usually defined by the $gamma^{0}$-parity $psi^{p}(t,-vec{x}) = gamma^{0}psi(t,-vec{x})$ with eigenvalues $pm 1$, while the $igamma^{0}$-parity $psi^{p}(t,-vec{x})=igamma^{0}psi(t,-vec{x})$ is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majorana neutrinos constructed from chiral neutrinos in an extension of the Standard Model, the Majorana neutrinos can be characterized by CP symmetry although C and P are separately broken. It is then shown that either choice of the parity operation, $gamma^{0}$ or $igamma^{0}$, in the level of the starting fermions gives rise to the consistent and physically equivalent descriptions of emergent Majorana neutrinos both for Weinbergs model of neutrinos and for a general class of seesaw models. The mechanism of this equivalence is that the Majorana neutrino constructed from a chiral neutrino, which satisfies the classical Majorana condition $psi(x)=Coverline{psi(x)}^{T}$, allows the phase freedom $psi(x)=e^{ialpha} u_{L}(x) + e^{-ialpha}Coverline{ u_{L}(x)}^{T}$ with $alpha=0 {rm or} pi/4$ that accounts for the phase coming from the different definitions of parity for $ u_{L}(x)$ and ensures the consistent definitions of CP symmetry $({cal CP})psi(x)({cal CP})^{dagger}= pm igamma^{0}psi(t,-vec{x})$.
The texture zero mass matrices for the leptons and the seesaw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses.
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