arXiv subjects
Publications and source records attributed to Ernest Ma.
Dark matter (DM) is usually assumed to be stabilized by a symmetry, which is mostly considered to be $Z_2$. For example, in supersymmetry it is $R$ parity, i.e. $(-1)^{3B+L+2j}$. However, it may be $Z_n$ or $U(1)_D$, and derivable from generalized lepton number. In this context, neutrinos may be Majorana or Dirac, and owe their masses to dark matter, i.e. they are scotogenic.
The notion of U(1) lepton number (which may only be softly broken) is applied to models of dark matter which interacts with leptons. Previous scotogenic models of Majorana or Dirac neutrino mass are shown to be derivable in this framework without additional symmetries. Only complete renormalizable theories are considered. An explicit class of models with $Z_n$ ($n \geq 5$) lepton and dark symmetry for Dirac neutrinos is derived, as well as an example of $Z_3$ dark symmetry.
Choosing how gauge $U(1)_χ$ breaks in the context of $SO(10) \to SU(5) \times U(1)_χ$, $Z_4$ lepton number may be obtained which maintains neutrinos as Dirac fermions. Choosing $Δ(27)$ as the family symmetry of leptons, tree-level Dirac neutrino masses may be forbidden. Choosing a specific set of self-interacting dark-matter particles, Dirac neutrino masses and mixing may then be generated in two loops. This framework allows the realization of cobimaximal neutrino mixing, i.e. $θ_{13} \neq 0$, $θ_{23} = π/4$, $δ_{CP} = \pm π/2$, as well as the desirable feature that the light scalar mediator of dark-matter interactions decays only to neutrinos, thereby not disrupting the cosmic microwave background (CMB).
In the context of $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_χ$, where $U(1)_χ$ comes from $SO(10) \to SU(5) \times U(1)_χ$, supplemented by the non-Abelian discrete $Δ(27)$ symmetry for three lepton families, Dirac neutrino masses and their mixing are radiatively generated through dark matter. The gauge $U(1)_χ$ symmetry is broken spontaneously. The discrete $Δ(27)$ symmetry is broken softly and spontaneously. Together, they result in two residual symmetries, a global $U(1)_L$ lepton number and a dark symmetry, which may be $Z_2$, $Z_3$, or $U(1)_D$ depending on what scalar breaks $U(1)_χ$. Cobimaximal neutrino mixing, i.e. $θ_{13} \neq 0$, $θ_{23} = π/4$, and $δ_{CP} = \pm π/2$, may also be obtained.
The standard model of quarks and leptons is extended to include the gauge symmetry $U(1)_χ$ which comes from $SO(10) \to SU(5) \times U(1)_χ$. The radiative generation of Dirac neutrino masses through dark matter is discussed in two examples. One allows for light Dirac fermion dark matter. The other allows for self-interacting scalar dark matter with a light scalar mediator which decays only to two neutrinos.
It has recently been pointed out that the underlying symmetry of dark matter may well be $U(1)_χ$ (coming from $SO(10) \to SU(5) \times U(1)_χ$) with the dark parity of any given particle determined by $(-1)^{Q_χ+2j}$, where $Q_χ$ is its $U(1)_χ$ charge and $j$ its spin angular momentum. Armed with this new insight, previous simple models of dark matter are reinterpreted, and a novel idea is proposed that light seesaw dark matter exists in analogy to light neutrinos and is produced by the rare decay of the standard-model Higgs boson.
In the context of $SO(10) \to SU(5) \times U(1)_χ$, it is shown how seesaw Dirac neutrinos may be obtained. In this framework, $U(1)$ lepton number is conserved, with which self-interaction dark matter with a light scalar dilepton mediator may be implemented. In addition, $U(1)$ baryon number may be broken to $(-1)^{3B}$, thereby generating a baryon asymmetry of the Universe. The axionic solution to the strong $CP$ problem may also be incorporated.
In an $SU(2)_R$ extension of the standard model, it is shown how the neutral fermion $N$ in the doublet $(N,e)_R$ may be assigned baryon number $B=1$, in contrast to its $SU(2)_L$ counterpart $ν$ in the doublet $(ν,e)_L$ which has lepton number $L=1$. This baryon-lepton duplicity allows a scalar $σ$ which couples to $N_L N_L$ to be long-lived dark matter.
In the decomposition of $SO(10)$ grand unification to $SU(5) \times U(1)_χ$, two desirable features are obtained with the addition of one colored fermion octet $Ω$, one electroweak fermion triplet $Σ$ and one complex scalar triplet $S$ to the particle content of the standard model with two Higgs doublets. They are (1) gauge coupling unification of $SU(3)_C \times SU(2)_L \times U(1)_Y$ to $SU(5)$, and (2) the automatic (predestined) emergence of dark matter, i.e. $Ω$, $Σ$ and $S$, with dark parity given by $(-1)^{Q_χ+ 2j}$. It suggests that $U(1)_χ$ may well be the underlying symmetry of the dark sector.
A simple and elegant mechanism is proposed to resolve the problem of having a light scalar mediator for self-interacting dark matter and the resulting disruption to the cosmic microwave background (CMB) at late times by the former's enhanced Sommerfeld production and decay. The crucial idea is to have Dirac neutrinos with the conservation of U(1) lepton number extended to the dark sector. The simplest scenario consists of scalar or fermion dark matter with unit lepton number accompanied by a light scalar dilepton mediator, which decays to two neutrinos.
In the $SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{(B-L)/2}$ extension of the standard model, a minimal (but asymmetric) scalar sector consists of one $SU(2)_R \times U(1)_{(B-L)/2}$ doublet and one $SU(2)_L \times SU(2)_R$ bidoublet. Previous and recent studies have shown that this choice is useful for understanding neutrino mass as well as dark matter. The constraints from flavor changing neutral currents mediated by the scalar sector are discussed in the context of the latest experimental data.
The well-known baryon and lepton numbers of the standard model of quarks and leptons are extended to include new fermions and bosons in a simple structure with several essential features. The usual heavy right-handed neutrino singlets (for neutrino mass and leptogenesis) are related to the axion which solves the strong CP problem. At the same time, baryon number is broken softly, allowing the proton to decay. Associated with this breaking, a long-lived dark-matter candidate (called the pseudo-sakharon) emerges. This new insight connects proton decay to a new component of dark matter.
The original spontaneously broken U(1) gauge model with one complex Higgs scalar field has been known in recent years as a possible prototype dark-matter model. Its antecedents in the context of SU(2) are discussed. Three specific examples are described, with one dubbed "quantum scotodynamics".
In any gauge extension of the standard model (SM) of quarks and leptons, there is a minimal set of fermion and scalar multiplets which encompasses all the particles and interactions of the SM. Included within this set, there may be a suitable dark-matter candidate. If not, one may still exist from the judicious addition of a simple fermion or scalar multiplet without any imposed symmetry. Some new examples of such predestined dark matter are discussed.
An extra $SU(2)_D$ gauge factor is added to the well-known left-right extension of the standard model (SM) of quarks and leptons. Under $SU(2)_L \times SU(2)_R \times SU(2)_D$, two fermion bidoublets $(2,1,2)$ and $(1,2,2)$ are assumed. The resulting model has an automatic dark $U(1)$ symmetry, in the same way that the SM has automatic baryon and lepton $U(1)$ symmetries. Phenomenological implications are discussed, as well as the possible origin of this proposal.
The alternative $[SU(3)]^4$ model of leptonic color and dark matter is discussed. It unifies at $M_U \sim 10^{14}$ GeV and has the low-energy subgroup $SU(3)_q \times SU(2)_l \times SU(2)_L \times SU(2)_R \times U(1)_X$ with $(u,h)_R$ instead of $(u,d)_R$ as doublets under $SU(2)_R$. It has the built-in global $U(1)$ dark symmetry which is generalized $B-L$. In analogy to $SU(3)_q$ quark triplets, it has $SU(2)_l$ hemion doublets which have half-integral charges and are confined by $SU(2)_l$ gauge bosons (stickons). In analogy to quarkonia, their vector bound states (hemionia) are uniquely suited for exploration at a future $e^-e^+$ collider.
The smallness of neutrino mass, the strong CP problem, and the existence of dark matter are explained in an economical way. The neutrino mass is generated by the colored version of a radiative seesaw mechanism by using color adjoint mediators. The Majorana mass term of the adjoint fermion, which carries lepton number U(1)_L, is induced by its spontaneous breaking, resulting in a Majoron which doubles as the QCD (quantum chromodynamics) axion, thereby solving the strong CP problem. The breaking of U(1)_L sets simultaneously the seesaw scale for neutrino mass and the Peccei-Quinn breaking scale. This axion is a good candidate for dark matter as usually assumed.
Two theoretically well-motivated gauge extensions of the standard model are $SU(3)_C \times SU(3)_L \times SU(3)_R$ and $SU(3)_q \times SU(3)_L \times SU(3)_l \times SU(3)_R$, where $SU(3)_q$ is the same as $SU(3)_C$ and $SU(3)_l$ is its color leptonic counterpart. Each as three variations, according to how $SU(3)_R$ is broken. It is shown here for the first time that a built-in dark $U(1)_D$ gauge symmetry exists in all six versions, and may be broken to discrete $Z_2$ dark parity. The available dark matter candidates in each case include fermions, scalars, as well as {\it vector gauge bosons}. This work points to the unity of matter with dark matter, the origin of which is not {\it ad hoc}.