40
2 Phenomenology of the Massless Dark Photon
As displayed in the equations above, all these limit can be made weaker by taking
m χ (or m Q ) sufficiently light or by varying the corresponding mixing parameters
η s , η φ . In the UV model is thus possible to play with the parameters to make room
for larger values of the dipole coefficient by absorbing part of the suppression in
the connection between the scale Λ and the mass ratios m χ /m
2
φ and m Q /m S . For
instance a scale Λ = 1 TeV for the new physics of the dark sector is still allowed by
the stringent bound in Eq. (2.35) if we take m χ sufficiently small. This way, there is
some additional freedom in comparing limits from different processes as compared
to the model-independent case where the scale Λ is taken to be the same for all
bounds.
2.4 Future Experiments
The massless dark photon has been neglected so far from the experimental point of
view as compared to the massive one. It is one of the aims of the present review to
boost the community scrutiny in this direction. In the past few year several proposals
have been put forward and new experiments are in the planning:
• Flavor physics: This is one of the most promising areas for searching for the dark
photon and the dark sector in general because none of the stringent astrophysical
constrains discussed in Sect. 2.1 applies given the flavor off-diagonal nature of the
dipole operator in these cases.
Proposals exist for processes in Kaon physics at NA62 [63]. The Kaon decay
K → π A
is forbidden by the conservation of angular momentum but the decay
K
+
→ π
0
π
+ A
is allowed and the estimated branching ratio [61] is within reach
of the current sensitivity. The rare decays K
+
→ π
+
ν ¯
ν [64] and K L → π
0
ν ¯
ν [65]
are other two processes where the physics of the dark photon can play a crucial
role [66]. Also Hyperion decays can be used for detecting the production of A
[67]
and in the decay of charmed hadrons [68] and BESIII.
In addition, decays into invisible states of B-mesons at BaBar [69] and Belle [70]
and K L ,S and other neutral mesons at NA64 [71, 72] can be used to study the
dark sector (assuming the invisible states belong to it). These decays are greatly
enhanced by the Fermi-Sommerfeld [73, 74] effect due to their interaction with the
dark photon—the same way as ordinary decays, like the β-decay, are enhanced
by the same effect—making this another exciting area for searching the dark
sector [56].
• Higgs and Z physics: The striking signature of a mono-photon plus missing energy
can be used to search Higgs [75–77] and Z -boson [78, 79] decay into a visible and
a dark photon. Again, the stringent astrophysical constrains discussed in Sect. 2.1
do not apply because the size of the dipole operator is dominated (in the loop
diagram) by the heavy-quark contribution’s giving raise to the coupling to the
dark photon, as discussed in Sect. 2.3.
2 Phenomenology of the Massless Dark Photon
As displayed in the equations above, all these limit can be made weaker by taking
m χ (or m Q ) sufficiently light or by varying the corresponding mixing parameters
η s , η φ . In the UV model is thus possible to play with the parameters to make room
for larger values of the dipole coefficient by absorbing part of the suppression in
the connection between the scale Λ and the mass ratios m χ /m
2
φ and m Q /m S . For
instance a scale Λ = 1 TeV for the new physics of the dark sector is still allowed by
the stringent bound in Eq. (2.35) if we take m χ sufficiently small. This way, there is
some additional freedom in comparing limits from different processes as compared
to the model-independent case where the scale Λ is taken to be the same for all
bounds.
2.4 Future Experiments
The massless dark photon has been neglected so far from the experimental point of
view as compared to the massive one. It is one of the aims of the present review to
boost the community scrutiny in this direction. In the past few year several proposals
have been put forward and new experiments are in the planning:
• Flavor physics: This is one of the most promising areas for searching for the dark
photon and the dark sector in general because none of the stringent astrophysical
constrains discussed in Sect. 2.1 applies given the flavor off-diagonal nature of the
dipole operator in these cases.
Proposals exist for processes in Kaon physics at NA62 [63]. The Kaon decay
K → π A
is forbidden by the conservation of angular momentum but the decay
K
+
→ π
0
π
+ A
is allowed and the estimated branching ratio [61] is within reach
of the current sensitivity. The rare decays K
+
→ π
+
ν ¯
ν [64] and K L → π
0
ν ¯
ν [65]
are other two processes where the physics of the dark photon can play a crucial
role [66]. Also Hyperion decays can be used for detecting the production of A
[67]
and in the decay of charmed hadrons [68] and BESIII.
In addition, decays into invisible states of B-mesons at BaBar [69] and Belle [70]
and K L ,S and other neutral mesons at NA64 [71, 72] can be used to study the
dark sector (assuming the invisible states belong to it). These decays are greatly
enhanced by the Fermi-Sommerfeld [73, 74] effect due to their interaction with the
dark photon—the same way as ordinary decays, like the β-decay, are enhanced
by the same effect—making this another exciting area for searching the dark
sector [56].
• Higgs and Z physics: The striking signature of a mono-photon plus missing energy
can be used to search Higgs [75–77] and Z -boson [78, 79] decay into a visible and
a dark photon. Again, the stringent astrophysical constrains discussed in Sect. 2.1
do not apply because the size of the dipole operator is dominated (in the loop
diagram) by the heavy-quark contribution’s giving raise to the coupling to the
dark photon, as discussed in Sect. 2.3.