We consider the case of light dark matter ($sim 10$ GeV). We discuss a simple $Z_2$ model of scalar self-interacting dark matter, as well as a related model of unstable long-lived dark matter which can explain the anomalous Kolar events observed decades ago.
In all scalar extensions of the standard model of particle interactions, the one Higgs boson responsible for electroweak symmetry breaking always mixes with other neutral scalars at tree level unless a symmetry prevents it. An unexplored important op
tion is that the mixing may be radiative, and thus guaranteed to be small. Two first such examples are discussed. One is based on the soft breaking of the discrete symmetry $Z_3$. The other starts with the non-Abelian discrete symmetry $A_4$ which is then softly broken to $Z_3$, and results in the emergence of an interesting dark-matter candidate together with a light mediator for the dark matter to have its own long-range interaction.
It is shown that in extensions of the standard model of quarks and leptons where additive lepton number $L$ is broken by two units, so that $Z_2$ lepton parity, i.e. $(-1)^L$ which is either even or odd, remains exactly conserved, there is the possib
ility of stable dark matter without additional symmetry. This applies to many existing simple models of Majorana neutrino mass with dark matter, including some radiative models. Several well-known examples are discussed. This new insight leads to the construction of a radiative Type II seesaw model of neutrino mass with dark matter where the dominant decay of the doubly charged Higgs boson $xi^{++}$ is into $W^+W^+$ instead of the expected $l_i^+ l_j^+$ lepton pairs for the well-known tree-level model.
A model proposed in 2004 using the non-Abelian discrete symmetry S3 for understanding the flavor structure of quarks and leptons is updated, with special focus on the quark and scalar sectors. We show how the approximate residual symmetries of this m
odel explain both the pattern of the quark mixing matrix and why the recently observed particle of 126 GeV at the Large Hadron Collider is so much like the one Higgs boson of the Standard Model. We identify the strongest phenomenological bounds on the scalar masses of this model, and predict a possibly observable decay b -> s tau- mu+, but not b -> s tau+ mu-.
A new idea for neutrino mass was proposed recently, where its smallness is not due to the seesaw mechanism, i.e. not inversely proportional to some large mass scale. It comes from a one-loop mechanism with dark matter in the loop consisting of single
t Majorana fermions $N_i$ with masses of order 10 keV and neutrino masses are scaled down from them by factors of about $10^{-5}$. We discuss how this model may be implemented with the non-Abelian discrete symmetry $A_4$ for neutrino mixing, and consider the phenomenology of $N_i$ as well as the extra scalar doublet $(eta^+,eta^0)$.
The non-Abelian discrete symmetry D(7) of the heptagon is successfully applied to both quark and lepton mass matrices, including CP violation.
A new and novel idea for a predictive neutrino mass matrix is presented, using the non-Abelian discrete symmetry A(4) and the seesaw mechanism with only two heavy neutral fermion singlets. Given the components of the one necessarily massless neutrino
eigenstate, the other two massive states are automatically generated. A realistic example is discussed with predictions of a normal hierarchy of neutrino masses and maximal CP violation.
A new and radical scenario of the simple 2006 model of radiative neutrino mass is proposed, where there is no seesaw mechanism, i.e. neutrino masses are not inversely proportional to some large mass scale, contrary to the prevalent theoretical thinki
ng. The neutral singlet fermions in the loop have masses of order 10 keV, the lightest of which is absolutely stable and the others are very long-lived. All are components of warm dark matter, which is a possible new paradigm for explaining the structure of the Universe at all scales.
Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek scotos meaning darkness, and using the non-Abelian discrete symmetry $A_4$, we propose a model of neutrino ma
sses and mixing with nonzero $theta_{13}$ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.
In a new simple application of the non-Abelian discrete symmetry $A_4$ to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of $sin^2 2 theta_{13} simeq 0.1$, leptonic CP violation is necessarily large, i.e. $|tan delta_{CP}| > 1.3$.
