72
5 Appendix
couplings but without the constraints of the QCD axion. The parameters of the
portal are two: the mass m a of the axion, or the ALP and the scale f a . Often the
ALP is the only member of the dark sector of these models.
The original axion emerged from addressing [5] the strong CP problem induced
by instantons in QCD. Light pseudo-scalar bosons are found in many models of
physics beyond the Standard Model;
• scalar (spin 0): Interaction between a scalar S and the SM Higgs boson H :
(μS + λS
2
)H
† H ,
in this case the operators are of dimension three and four. The experimental limits
are often expressed in terms of the two parameters ν and the mass m S of the scalar
singlet, and neglecting the quartic coupling λ. In most models, the dark sector
states have Yukawa-like interactions with the scalar S.
The idea of a scalar singlet interacting with the Higgs boson originated within
the framework of the next-to-minimal supersymmetric Standard Model [6–8] and
developed independently in [9–11];
• sterile neutrino (spin 1/2): Interaction between a heavy fermion N , which is a SM
singlet, the SM Higgs boson and the SM fermions L:
y N L H N ,
with, again, an operator of dimension four. The existence of heavy lepton-like
fermions is suggested by neutrino see-saw models and the possible origin of
baryon-number asymmetry in the leptonic sector. The experimental searches are
framed in terms of the parameter y N and the mass of the heavy fermion N . The
sterile neutrino can be the only member of the dark sector or be one among many
other dark fermions.
The structure of the neutrino portal closely follows that of the see-saw mechanism [12–15]—which was introduced to generate small masses for the neutrinos—
and, more in general, left-right symmetric models [16–19].
More details on the various portals can be found in the same references cited in
the introduction: [20–27].
5.2 Boltzmann Equation and Relic Density
This appendix includes a short summary of some results necessary to follow the
discussion in the main text about the relic density of dark matter and limits based on
cosmology. We follow the excellent review [28].
The rate for a the interaction between two particles is given as
= n σ v ,
(5.1)
5 Appendix
couplings but without the constraints of the QCD axion. The parameters of the
portal are two: the mass m a of the axion, or the ALP and the scale f a . Often the
ALP is the only member of the dark sector of these models.
The original axion emerged from addressing [5] the strong CP problem induced
by instantons in QCD. Light pseudo-scalar bosons are found in many models of
physics beyond the Standard Model;
• scalar (spin 0): Interaction between a scalar S and the SM Higgs boson H :
(μS + λS
2
)H
† H ,
in this case the operators are of dimension three and four. The experimental limits
are often expressed in terms of the two parameters ν and the mass m S of the scalar
singlet, and neglecting the quartic coupling λ. In most models, the dark sector
states have Yukawa-like interactions with the scalar S.
The idea of a scalar singlet interacting with the Higgs boson originated within
the framework of the next-to-minimal supersymmetric Standard Model [6–8] and
developed independently in [9–11];
• sterile neutrino (spin 1/2): Interaction between a heavy fermion N , which is a SM
singlet, the SM Higgs boson and the SM fermions L:
y N L H N ,
with, again, an operator of dimension four. The existence of heavy lepton-like
fermions is suggested by neutrino see-saw models and the possible origin of
baryon-number asymmetry in the leptonic sector. The experimental searches are
framed in terms of the parameter y N and the mass of the heavy fermion N . The
sterile neutrino can be the only member of the dark sector or be one among many
other dark fermions.
The structure of the neutrino portal closely follows that of the see-saw mechanism [12–15]—which was introduced to generate small masses for the neutrinos—
and, more in general, left-right symmetric models [16–19].
More details on the various portals can be found in the same references cited in
the introduction: [20–27].
5.2 Boltzmann Equation and Relic Density
This appendix includes a short summary of some results necessary to follow the
discussion in the main text about the relic density of dark matter and limits based on
cosmology. We follow the excellent review [28].
The rate for a the interaction between two particles is given as
= n σ v ,
(5.1)