1.1 Massless and Massive Dark Photons
7
Although their implementation is not discussed in this review, other interesting
generalizations—as, for instance, the dark photon to be considered a Kaluza-Klein
state in a model with large extra-dimensions [28] or the interplay between the neutrino
see-saw mechanism and the dark photon [29]—should be borne in mind.
1.1.2 Embedding in a NonAbelian Group
In the massless case, the ordinary photon still couples to the dark sector with a millicharge εe. As reviewed in the next section, there are very stringent limits on the size
of such a milli-charge, at least for reasonably light dark states. To avoid the necessity
of assuming a very small milli-charge, one can assume that the dark U (1) group is
a symmetry left over after the spontaneous breaking of a larger nonAbelian group.
The simplest realization of this symmetry breaking is provided by the group
SU (2) spontaneously broken to U (1) by the vacuum expectation value of the neutral
component of a scalar field in the adjoint representation.
In this scenario, the mixing term in Eq. (1.1) cannot be written because the larger
group has traceless generators. The absence of mixing is in this case protected against
radiative corrections and the dark and the ordinary photons see only their respective
sectors (at least through renormalizable operators).
This scenario is also suggested by the extra Landau pole that otherwise would
be present—assuming that the Landau pole of the ordinary U (1) is removed by the
embedding of the SM in a scenario of grand unified theory.
If we assume that the dark photon arises from a nonAbelian group, there is no
milli-charged coupling of the dark sector to ordinary photons. On the other hand, all
states in the dark sector must come as multiplets of the nonAbelian group and the
possible experimental signatures of this additional structure can be searched for.
1.2 UV Models
Because the massive dark photon couples directly to the SM electromagnetic current, its phenomenology is rather independent of the details of the underlaying UV
completion. The two parameters ε and m A suffice to fully describe the experimental
searches.
The case of the massless dark photon is more complicated because the coupling
to the SM particles only takes place through higher order operators whose structure
heavily depends on the underlaying UV model. Even though it is possible to frame
the experimental search in terms of the effective scale of these operators (as we do in
Sect. 2), the limits thus found begs to be framed in terms of the UV model parameters,
namely the masses and the coupling of the dark sector states, in addition to the dark
photon itself. For this reason, it is useful in this case to introduce a minimal UV
model (as we do in Sect. 2.3) to provide the relationships among the parameters of
7
Although their implementation is not discussed in this review, other interesting
generalizations—as, for instance, the dark photon to be considered a Kaluza-Klein
state in a model with large extra-dimensions [28] or the interplay between the neutrino
see-saw mechanism and the dark photon [29]—should be borne in mind.
1.1.2 Embedding in a NonAbelian Group
In the massless case, the ordinary photon still couples to the dark sector with a millicharge εe. As reviewed in the next section, there are very stringent limits on the size
of such a milli-charge, at least for reasonably light dark states. To avoid the necessity
of assuming a very small milli-charge, one can assume that the dark U (1) group is
a symmetry left over after the spontaneous breaking of a larger nonAbelian group.
The simplest realization of this symmetry breaking is provided by the group
SU (2) spontaneously broken to U (1) by the vacuum expectation value of the neutral
component of a scalar field in the adjoint representation.
In this scenario, the mixing term in Eq. (1.1) cannot be written because the larger
group has traceless generators. The absence of mixing is in this case protected against
radiative corrections and the dark and the ordinary photons see only their respective
sectors (at least through renormalizable operators).
This scenario is also suggested by the extra Landau pole that otherwise would
be present—assuming that the Landau pole of the ordinary U (1) is removed by the
embedding of the SM in a scenario of grand unified theory.
If we assume that the dark photon arises from a nonAbelian group, there is no
milli-charged coupling of the dark sector to ordinary photons. On the other hand, all
states in the dark sector must come as multiplets of the nonAbelian group and the
possible experimental signatures of this additional structure can be searched for.
1.2 UV Models
Because the massive dark photon couples directly to the SM electromagnetic current, its phenomenology is rather independent of the details of the underlaying UV
completion. The two parameters ε and m A suffice to fully describe the experimental
searches.
The case of the massless dark photon is more complicated because the coupling
to the SM particles only takes place through higher order operators whose structure
heavily depends on the underlaying UV model. Even though it is possible to frame
the experimental search in terms of the effective scale of these operators (as we do in
Sect. 2), the limits thus found begs to be framed in terms of the UV model parameters,
namely the masses and the coupling of the dark sector states, in addition to the dark
photon itself. For this reason, it is useful in this case to introduce a minimal UV
model (as we do in Sect. 2.3) to provide the relationships among the parameters of