Chapter 2
Phenomenology of the Massless Dark
Photon
The phenomenology of the massless dark photon depends on the effect of the higherorder operator in Eq. (1.15) which mediates its interaction with the SM particles. This
operator enters the measured observables with an effective scale Λ and the absolute
value
d
i j
M ≡ |D
i j
M |
(2.1)
of the magnetic dipole coefficient (neglecting the CP-odd D E ) which can eventually
be related to the parameters of the underlying UV model like masses and coupling
constants. The experimental searches can thus be framed in terms of the scale Λ,
the dipole coefficient d
i j
M and the dark charge coupling e D , which we rewrite as
α D = e
2
D
/4π. We do not assume this scale and coefficient to be universal. Depending
on the particular experimental set-up, the constraints are further sensitive to which
particular lepton or quark is actually taking part in the interaction. The index, or
indices, i and j keep track on the flavor dependence.
We discuss in Sect. 2.2 the other side of the massless dark photon, namely the
search for dark particles coupled to the ordinary photon by a milli-charge.
2.1 Limits on the Dark Dipole Scale d M /Λ 2
We collect in this section the known constraints on the size of the operator in Eq. (1.15)
(Fig. 2.3).
We show in Figs. 2.1 and 2.2 the more stringent limits. Though these limits are
on the combinations d M /Λ
2 , with a factor depending on α D , we find it convenient
to plot them as d M as a function of Λ so as to easily see what values of the dipole
coefficient are allowed given a value for the scale Λ (and two representative value
of α D ).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
M. Fabbrichesi et al., The Physics of the Dark Photon,
SpringerBriefs in Physics, https://doi.org/10.1007/978-3-030-62519-1_2
21
Phenomenology of the Massless Dark
Photon
The phenomenology of the massless dark photon depends on the effect of the higherorder operator in Eq. (1.15) which mediates its interaction with the SM particles. This
operator enters the measured observables with an effective scale Λ and the absolute
value
d
i j
M ≡ |D
i j
M |
(2.1)
of the magnetic dipole coefficient (neglecting the CP-odd D E ) which can eventually
be related to the parameters of the underlying UV model like masses and coupling
constants. The experimental searches can thus be framed in terms of the scale Λ,
the dipole coefficient d
i j
M and the dark charge coupling e D , which we rewrite as
α D = e
2
D
/4π. We do not assume this scale and coefficient to be universal. Depending
on the particular experimental set-up, the constraints are further sensitive to which
particular lepton or quark is actually taking part in the interaction. The index, or
indices, i and j keep track on the flavor dependence.
We discuss in Sect. 2.2 the other side of the massless dark photon, namely the
search for dark particles coupled to the ordinary photon by a milli-charge.
2.1 Limits on the Dark Dipole Scale d M /Λ 2
We collect in this section the known constraints on the size of the operator in Eq. (1.15)
(Fig. 2.3).
We show in Figs. 2.1 and 2.2 the more stringent limits. Though these limits are
on the combinations d M /Λ
2 , with a factor depending on α D , we find it convenient
to plot them as d M as a function of Λ so as to easily see what values of the dipole
coefficient are allowed given a value for the scale Λ (and two representative value
of α D ).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
M. Fabbrichesi et al., The Physics of the Dark Photon,
SpringerBriefs in Physics, https://doi.org/10.1007/978-3-030-62519-1_2
21