Ⅱ-6. Particle Physics

RIKEN Accel. Prog. Rep. 51 (2018)

Unified scenario for composite right-handed neutrinos
and dark matter†
H. Davoudiasl,∗1 P. P. Giardino,∗1 E. T. Neil,∗2,∗3 and E. Rinaldi∗3
The Standard Model of particle physics is our mostprecise theoretical description of Nature and it has
been tested to great precision in high energy particle colliders, like LHC. However, we know it represents
only a partial description and the most notable missing
ingredients are neutrino masses and dark matter, forwhich there exists a wealth of experimental evidence.
From the theoretical point of view, it is interesting to entertain the possibility that these two physical phenomena are related and emerge from a uniﬁed
underlying dynamics. In this paper we introduce a
new “dark sector” with a conﬁning force, similar tothe one of Quantum Chromodynamics (QCD), basedon the dark gauge group SU (3)D and with three darkquarks. This dark sector has small interactions with
the Standard Model particles, but more interestingly
it contains a large number of composite states (darkmesons, dark baryons etc...) which can be used tosuccessfully construct a low-energy theory with darkmatter and right-handed neutrinos.
The construction starts from the dark sector Lagrangian LDQCD for the SU (3)D theory, which is wellknown and identical to the QCD one with three ﬂavors,
and proceeds with the addition of three types of higherdimensional operators, deriving from diﬀerent highenergy eﬀective scales ΛX , such that L = LDQCD +Leﬀ :Leﬀ =H̃ ∗ L̄f [ψi3 ] [ψi6 ] ψ̄i ψi H † H+ H.C.,+ 5 +
Λ3f
ΛN
ΛH(1)

where H̃ ∗ = ϵab H a∗ , with H the Standard Model Higgs
doublet, and Lf is a lepton doublet of the Standard
Model family f = 1, 2, 3. In Eq. (1) i = 1, 2, 3 and [ψin ]represents any SU (3)D singlet and Lorentz invariant
combinations of n ψi quarks that are Z2 even. The Z2
symmetry imposed upon the operators in the theory isnecessary to have a stable dark matter candidate.
It is important to note that the nature of the operators in Eq. (1) is determined by conﬁnement of the darkgauge group, giving rise to composite states: e.g. theoperator [ψi3 ] will transmute into a dark baryonic-like
operator below the conﬁnement scale µD such that theﬁrst term in Eq. (1) describes the interaction between
the Higgs, the leptons and a “dark neutron” state, thesecond term describes oscillations between “dark neutrons,” and the third terms describes masses for the†
∗1
∗2
∗3

Condensed from the article in Phys. Rev. D 96, 115003(2017)
Department of Physics, Brookhaven National Laboratory
Department of Physics, University of Colorato
RIKEN Nishina Center- 125 -Π✲ EvHµDΛH , ΛS , ΛFFig. 1. The figure shows the separation of energy scales.

dark quarks. The dark neutron oscillations are necessary to create neutrino masses: in our framework,
dark neutrons are identiﬁed with right-handed neutrinos. Hence, the low-energy description in Eq. (1) will
give rise to neutrino massesmν ∼

2
µ10
D vH,
65Λf ΛN(2)

where vH ≈ 246 GeV is the electroweak energy scale.
The other scales in Eq. (2) are chosen to reproduce thecurrent known limits for neutrino masses of the orderof mν ≲ 0.1 eV: µD ∼ 1 TeV and Λf,N ∼ 10 TeV.
The conﬁning nature of the dark sector is also responsible for the presence of a dark matter candidatein the spectrum. Similarly to QCD, the lightest composite particles are dark mesons, states that are madeof a pair of dark quark and dark anti-quark. Without loss of generality, we assume that the dark quark
masses generated by interactions with the Higgs boson
are small and hierarchically distributed m1 < m2 <m3 ≪ µD . Hence, the octet of lightest mesons comprises the three statesP ∼ ψ̄1 ψ2 , κ ∼ ψ̄1 ψ3 , κ′ ∼ ψ̄2 ψ3 ,(3)their antiparticles, and two linear combinations P ′ andP ′′ of the ﬂavor-diagonal bilinear ψ̄i ψi , analogues ofthe π 0 and η in QCD.
We will denote these states collectively with the symbol Π, and their masses are compared to the otherscales in the theory in Fig. 1. The “dark kaons” κ andκ′ , containing only one ψ3 , are the only states thatare odd under the Z2 symmetry, because we assume
that Z2 (ψ3 ) = −1 = −Z2 (ψ1,2 ). The dark kaons are
the lightest Z2 -odd hadrons and κ will provide a dark
matter candidate in this model, since Mκ < Mκ′ . The
mass of κ is related to the conﬁnement scale through alow-energy eﬀective chiral description of the spectrum(similar to QCD) yielding Mκ ∼ 10 GeV. Such a lightmass for composite dark matter is very interesting fromthe experimental point of view, and our scenario canbe probed in future experimental setups.