1.3 Dark Matter and the Dark Photon
11
The limit in Eq. (1.17) is subject to a number of uncertainties and assumptions; it
is less stringent than earlier results, such as the original bound from soft scattering
quoted in [48],
G N m
4
χ N
8α 2
D
∼ > 50 log
G N m
2
χ N
2α D
,
(1.18)
where N is the number of dark-matter particles and G N is Newton’s constant, as
well about a factor of 3.5 weaker than [49] (see, also, [66, 67]). On the other hand,
results on galaxies from N -body simulations in self-interacting dark matter cosmologies [68], which take into account predicted ellipticities and dark matter densities
in the central regions, seem to go in the direction of milder constraints, about at the
same level or slightly weaker than the value quoted in Eq. (1.17)—again subject to
uncertainties, such as the role played by the central baryonic component of NGC720.
1.3.2 Massless Dark Photon and Dark-Matter Relic Density
All the stable fields within the dark sector provide a multicomponent candidate for
dark matter whose relic density depends on the value of their couplings to the dark
photons and SM fermions (into which they may annihilate, depending on the UV
model) and masses.
Not all of the dark fermions contribute to the relic density. If these fermions are
relatively light, their dominant annihilation is into dark photons (see Fig. 1.2)
χχ → A
A
(1.19)
with a rate given by
σ χχ→A A v =
2πα
2
d
m 2
χ
.
(1.20)
For a strength α d 0.01, all fermions with masses up to around 1 TeV have a large
cross section and their relic density(see Eq. (5.15) in the Sect. 5.2)
χ h
2
≈
2.5 × 10
−10 GeV
−2
σ χχ→A A v
(1.21)
is only a percent of the critical one; it is roughly 10
−4 the critical one for dark fermions
in the 1 GeV range, even less for lighter states. These dark fermions are not part of
dark matter; they have (mostly) converted into dark photons by the time the universe
reaches our age and can only be produced in high-energy events. This is fortunate
because, as we have seen, they are ruled out as possible dark matter candidates by
the limit on galaxy dynamics.
11
The limit in Eq. (1.17) is subject to a number of uncertainties and assumptions; it
is less stringent than earlier results, such as the original bound from soft scattering
quoted in [48],
G N m
4
χ N
8α 2
D
∼ > 50 log
G N m
2
χ N
2α D
,
(1.18)
where N is the number of dark-matter particles and G N is Newton’s constant, as
well about a factor of 3.5 weaker than [49] (see, also, [66, 67]). On the other hand,
results on galaxies from N -body simulations in self-interacting dark matter cosmologies [68], which take into account predicted ellipticities and dark matter densities
in the central regions, seem to go in the direction of milder constraints, about at the
same level or slightly weaker than the value quoted in Eq. (1.17)—again subject to
uncertainties, such as the role played by the central baryonic component of NGC720.
1.3.2 Massless Dark Photon and Dark-Matter Relic Density
All the stable fields within the dark sector provide a multicomponent candidate for
dark matter whose relic density depends on the value of their couplings to the dark
photons and SM fermions (into which they may annihilate, depending on the UV
model) and masses.
Not all of the dark fermions contribute to the relic density. If these fermions are
relatively light, their dominant annihilation is into dark photons (see Fig. 1.2)
χχ → A
A
(1.19)
with a rate given by
σ χχ→A A v =
2πα
2
d
m 2
χ
.
(1.20)
For a strength α d 0.01, all fermions with masses up to around 1 TeV have a large
cross section and their relic density(see Eq. (5.15) in the Sect. 5.2)
χ h
2
≈
2.5 × 10
−10 GeV
−2
σ χχ→A A v
(1.21)
is only a percent of the critical one; it is roughly 10
−4 the critical one for dark fermions
in the 1 GeV range, even less for lighter states. These dark fermions are not part of
dark matter; they have (mostly) converted into dark photons by the time the universe
reaches our age and can only be produced in high-energy events. This is fortunate
because, as we have seen, they are ruled out as possible dark matter candidates by
the limit on galaxy dynamics.