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.
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.
In an unconventional realization of left-right symmetry, the particle corresponding to the left-handed neutrino nu_L (with SU(2)_L interactions) in the right-handed sector, call it n_R (with SU(2)_R interactions), is not its Dirac mass partner, but a
different particle which may be a dark-matter candidate. In parallel to leptogenesis in the SU(2)_L sector, asymmetric production of n_R may occur in the SU(2)_R sector. This mechanism is especially suited for n_R mass of order 1 to 10 keV, i.e. warm dark matter, which is a possible new paradigm for explaining the structure of the Universe at all scales.
In the context of A_4 symmetry, neutrino tribimaximal mixing is achieved through the breaking of A_4 to Z_3 (Z_2) in the charged-lepton (neutrino) sector respectively. The implied vacuum misalignment of the (1,1,1) and (1,0,0) directions in A_4 space
is a difficult technical problem, and cannot be treated without many auxiliary fields and symmetries (and perhaps extra dimensions). It is pointed out here that an alternative scenario exists with A_4 alone and no redundant fields, if neutrino masses are scotogenic, i.e. radiatively induced by dark scalar doublets as recently proposed.
The Supersymmetric Standard Model is a benchmark theoretical framework for particle physics, yet it suffers from a number of deficiencies, chief among which is the strong CP problem. Solving this with an axion in the context of selected new particles
, it is shown in three examples that other problems go away automatically as well, resulting in (-)^L and (-)^{3B} conservation, viable combination of two dark-matter candidates, successful baryogenesis, seesaw neutrino masses, and verifiable experimental consequences at the TeV energy scale.
The multiplicative conservation of both lepton and baryon numbers, i.e. (-)^L and (-)^{3B}, is connected to an axionic solution of the strong CP problem in a supersymmetric, unifiable model of quark and lepton interactions. New particles are predicte
d at the TeV scale, with verifiable consequences at the Large Hadron Collider.
