32
2 Phenomenology of the Massless Dark Photon
accordingly parameterized in terms of the mass m χ and the electromagnetic coupling
(modulated by ε) of the supposedly milli-charged dark-sector particle.
The physics of stellar evolution for horizontal branches, red giants, and white
dwarves (RGWD [32]), together with supernovae (SN1987 [33]) provide bounds
in the region of small masses (m χ ∼ < 1 MeV). In this region constraints on N e f f
during nucleosynthesis and in the cosmic microwave background (N e f f BBN and
CMB [32]) limits the possibility of having milli-charged particles. These limits are
derived along the same lines discussed in the case of the massless dark photon.
Further limits can be derived from precision measurements in QED, notably from
the Lamb shift in the transition 2S 1/2 -2P 3/2 in the Hydrogen atom [45] and the nonobservation of the invisible decay of ortho-positronium (oPS [34]). Limits in the
intermediate mass range 1 − 100 MeV come from a SLAC dedicated experiment
(SLAC milliQ [35]) and from the reinterpretation of data from the neutrino experiments LSND and miniBooNE [36].
Searches at LEP [37] and LHC [38] cover larger values of the mass (100 MeV
∼ < m χ ∼ < 1 TeV).
Finally, for very large masses (m χ ∼ > 10 TeV) the impact on the cosmological
parameters severely restricts the possible values of milli-charges (WMAP and dark
matter relic density constraint, [38] and references therein).
All these limits are shown as filled area in the plot of Fig. 2.4.
Milli-charged particles as dark matter have been proposed (see for example [46]
and [47]) to explain the anomalous 21 cm hydrogen absorption signal reported by
the EDGES experiment [48]. Given the preliminary nature of the results, we have
not included them in Fig. 2.4.
The projected limits of future experiments are depicted in Fig. 2.5 together with the
current limits in gray background to show the expected advances. Of these, the most
significative for masses around 1 GeV comes from the proposed milliQAN experiment [42] proposed to be installed on the surface above one of the LHC interaction
points. MilliQAN could improve the collider limits by two orders of magnitude.
The range in mass between 10-100 MeV can be optimally covered by the FerMINI
experiment [41] proposed in the DUNE near detector hall at Fermilab. Finally the
search for milli-charged particles below 10 MeV mass may be improved by almost
two orders of magnitude by the LDMX experiment [43] proposed both at CERN [49]
and at SLAC [50].
2.3 A Minimal Model of the Dark Sector
As discussed in Chap. 1, it is useful to underpin the phenomenology of the massless
dark photon to a UV model. We consider a minimal model consisting of dark fermions
that are, by definition, singlets under the SM gauge interactions. These dark fermions
interact with the visible sector through a portal provided by scalar messengers which
carry both SM and dark-sector charges. These scalars are phenomenologically akin
to the sfermions of supersymmetric models.
2 Phenomenology of the Massless Dark Photon
accordingly parameterized in terms of the mass m χ and the electromagnetic coupling
(modulated by ε) of the supposedly milli-charged dark-sector particle.
The physics of stellar evolution for horizontal branches, red giants, and white
dwarves (RGWD [32]), together with supernovae (SN1987 [33]) provide bounds
in the region of small masses (m χ ∼ < 1 MeV). In this region constraints on N e f f
during nucleosynthesis and in the cosmic microwave background (N e f f BBN and
CMB [32]) limits the possibility of having milli-charged particles. These limits are
derived along the same lines discussed in the case of the massless dark photon.
Further limits can be derived from precision measurements in QED, notably from
the Lamb shift in the transition 2S 1/2 -2P 3/2 in the Hydrogen atom [45] and the nonobservation of the invisible decay of ortho-positronium (oPS [34]). Limits in the
intermediate mass range 1 − 100 MeV come from a SLAC dedicated experiment
(SLAC milliQ [35]) and from the reinterpretation of data from the neutrino experiments LSND and miniBooNE [36].
Searches at LEP [37] and LHC [38] cover larger values of the mass (100 MeV
∼ < m χ ∼ < 1 TeV).
Finally, for very large masses (m χ ∼ > 10 TeV) the impact on the cosmological
parameters severely restricts the possible values of milli-charges (WMAP and dark
matter relic density constraint, [38] and references therein).
All these limits are shown as filled area in the plot of Fig. 2.4.
Milli-charged particles as dark matter have been proposed (see for example [46]
and [47]) to explain the anomalous 21 cm hydrogen absorption signal reported by
the EDGES experiment [48]. Given the preliminary nature of the results, we have
not included them in Fig. 2.4.
The projected limits of future experiments are depicted in Fig. 2.5 together with the
current limits in gray background to show the expected advances. Of these, the most
significative for masses around 1 GeV comes from the proposed milliQAN experiment [42] proposed to be installed on the surface above one of the LHC interaction
points. MilliQAN could improve the collider limits by two orders of magnitude.
The range in mass between 10-100 MeV can be optimally covered by the FerMINI
experiment [41] proposed in the DUNE near detector hall at Fermilab. Finally the
search for milli-charged particles below 10 MeV mass may be improved by almost
two orders of magnitude by the LDMX experiment [43] proposed both at CERN [49]
and at SLAC [50].
2.3 A Minimal Model of the Dark Sector
As discussed in Chap. 1, it is useful to underpin the phenomenology of the massless
dark photon to a UV model. We consider a minimal model consisting of dark fermions
that are, by definition, singlets under the SM gauge interactions. These dark fermions
interact with the visible sector through a portal provided by scalar messengers which
carry both SM and dark-sector charges. These scalars are phenomenologically akin
to the sfermions of supersymmetric models.