2
1 Introduction
As explained in detail in Sect. 1.1, there are actually two kinds of dark photons: The
massless and the massive—whose theoretical frameworks as well as experimental
signatures are quite distinct. They give rise to dark sectors with different features;
their characteristic physics and experimental searches are best reviewed separately.
The massive dark photon has been receiving so far most of the attention because it
couples directly to the SM currents and is more readily accessible in the experimental
searches. The massless dark photon arises from a sound theoretical framework and,
as we shall argue, provides, with respect to the massive case, a comparably rich, if
perhaps more challenging, experimental target.
We look into the ultraviolet (UV) completion of models of the dark photon in
Sect. 1.2 to better understand the origin of their interactions with the SM particles.
Section 1.3 describes the interplay between the dark photon and dark matter and
introduces many of the definitions used in the experimental searches.
We survey the current and future experimental limits on the parameters of the
massless and massive dark photons together with the related bounds on milli-charged
fermions. We discuss all these constrains for the massless case in Sect. 2 and for the
massive case in Sect. 3. At the best of our knowledge, these two sections provide the
reader with a comprehensive review of the physics of the dark photon.
We collect in three appendices a number of definitions and equations, which the
reader may find useful to better follow the discussion in the main text.
In the past few years a number of reports on the dark sector (and the massive
dark photon within it) have been published [7–14]. The interested reader can therein
find different points of view to complement the present review as well as additional
details on the other portals. A previous discussion of the astrophysical, cosmological
and other constraints for the massless dark photon can be found in [15].
1.1 Massless and Massive Dark Photons
The most general kinetic part of the Lagrangian of two Abelian gauge bosons,
described by two gauge groups U (1) a and U (1) b , is given by
L 0 = −
1
4
F aμν F
μν
a −
1
4
F bμν F
μν
b −
ε
2
F aμν F
μν
b .
(1.1)
The gauge boson A
μ
b is taken to couple to the current J μ of ordinary SM matter,
the other, A
μ
a , to the current J
μ , which is made of dark-sector matter, to give the
Lagrangian
L = e J μ A
μ
b + e
J
μ A
μ
a ,
(1.2)
with e and e
the respective coupling constants.
To discuss the physics arising from the Lagrangians in Eqs. (1.1) and (1.2), it is
useful to identify from the very beginning two kinds of dark photons:
1 Introduction
As explained in detail in Sect. 1.1, there are actually two kinds of dark photons: The
massless and the massive—whose theoretical frameworks as well as experimental
signatures are quite distinct. They give rise to dark sectors with different features;
their characteristic physics and experimental searches are best reviewed separately.
The massive dark photon has been receiving so far most of the attention because it
couples directly to the SM currents and is more readily accessible in the experimental
searches. The massless dark photon arises from a sound theoretical framework and,
as we shall argue, provides, with respect to the massive case, a comparably rich, if
perhaps more challenging, experimental target.
We look into the ultraviolet (UV) completion of models of the dark photon in
Sect. 1.2 to better understand the origin of their interactions with the SM particles.
Section 1.3 describes the interplay between the dark photon and dark matter and
introduces many of the definitions used in the experimental searches.
We survey the current and future experimental limits on the parameters of the
massless and massive dark photons together with the related bounds on milli-charged
fermions. We discuss all these constrains for the massless case in Sect. 2 and for the
massive case in Sect. 3. At the best of our knowledge, these two sections provide the
reader with a comprehensive review of the physics of the dark photon.
We collect in three appendices a number of definitions and equations, which the
reader may find useful to better follow the discussion in the main text.
In the past few years a number of reports on the dark sector (and the massive
dark photon within it) have been published [7–14]. The interested reader can therein
find different points of view to complement the present review as well as additional
details on the other portals. A previous discussion of the astrophysical, cosmological
and other constraints for the massless dark photon can be found in [15].
1.1 Massless and Massive Dark Photons
The most general kinetic part of the Lagrangian of two Abelian gauge bosons,
described by two gauge groups U (1) a and U (1) b , is given by
L 0 = −
1
4
F aμν F
μν
a −
1
4
F bμν F
μν
b −
ε
2
F aμν F
μν
b .
(1.1)
The gauge boson A
μ
b is taken to couple to the current J μ of ordinary SM matter,
the other, A
μ
a , to the current J
μ , which is made of dark-sector matter, to give the
Lagrangian
L = e J μ A
μ
b + e
J
μ A
μ
a ,
(1.2)
with e and e
the respective coupling constants.
To discuss the physics arising from the Lagrangians in Eqs. (1.1) and (1.2), it is
useful to identify from the very beginning two kinds of dark photons: