3.3 Limits on the Parameters ε and m A
51
3.3.1 Constraints for m A > 1 MeV with A Decays to Visible
Final States
Two kinds of experiments provide the existing limits on the visible massive dark
photon in the region of m A > 1 MeV: experiments at colliders and at fixed-target
or beam dumps. In both cases the experiments search for resonances over a smooth
background, with a vertex prompt or slightly displaced with respect to the beam
interaction point in case of collider, or highly displaced in case of beam dump based
experiments. The two categories are highly complementary, being the first category
mostly sensitive to relatively large values of the mixing parameter ε, (ε > 10
−3 ) and
the dark photon mass (up to several tens of GeV for pp collider experiments), while
the second is sensitive to relatively small values (10
−7 ∼ < ε ∼ < 10
−3 ) in the low mass
range, m A less than few GeV.
• Experiments at colliders. These experiments search for resonances in the invariant mass distribution of e
+ e
−
, μ
+
μ
− pairs. Different dark-photon production
mechanisms are used in the different experiments: meson decays (π
0
→ γ A
,
NA48/2 [9]), Bremsstrahlung (e
− Z → e
− ZA
, A1 [1]), annihilation (e
+ e
−
→ γ A
,
BaBar [4]), and all these processes in different searches at KLOE [5–8]. In a protonproton (pp) collider the dark photon is produced via the γ − A
mixing in all the
processes where an off-shell photon γ
∗ with mass m(γ
∗
) is produced: meson
decays, Bremsstrahlung, and Drell-Yan production. LHCb [2, 37] has performed
a search for dark photon decaying in μ
+
μ
− final states using 1.6 fb
−1 of data
collected at the LHC pp collisions at 13 TeV centre-of-mass energy. CMS [3] has
performed the same search using 137 fb
−1 of fully reconstructed data and 96.6 fb
−1
of data collected with a reduced trigger information.
Figure 3.3 shows the existing limits for NA48/2, A1, LHCb, and BaBar; only one
set of limits from KLOE is shown since the others have been superseded by the
limits from BaBar.
• Beam-dump experiments. These experiments use the collisions of an electron
or proton beam with a fixed-target or a dump to generate the dark photon via
Bremsstrahlung (electron and proton beams), meson production and QCD processes (proton beams only). The products of the collisions are mostly absorbed
in the dump and the dark photon is searched for as a displaced vertex with two
opposite charged tracks in the decay volume of the experiment.
Figure 3.3 shows the limits from experiments at extracted electron beams
(E141 [11] and E137 [12–14] at SLAC, E774 [10] at Fermilab) and at extracted
proton beams from CHARM at CERN ([17] based on CHARM data [38]).
In addition, bounds on energy losses in supernovae provide further limits in the
region of small masses. These limits where discussed in [39, 40] and updated in [18,
41] by including the effect of finite temperature and plasma density.
Also the electron magnetic moment, with its very precise experimental determination, can be used to set an indirect limit [19]. These limits are included in Fig. 3.3.
51
3.3.1 Constraints for m A > 1 MeV with A Decays to Visible
Final States
Two kinds of experiments provide the existing limits on the visible massive dark
photon in the region of m A > 1 MeV: experiments at colliders and at fixed-target
or beam dumps. In both cases the experiments search for resonances over a smooth
background, with a vertex prompt or slightly displaced with respect to the beam
interaction point in case of collider, or highly displaced in case of beam dump based
experiments. The two categories are highly complementary, being the first category
mostly sensitive to relatively large values of the mixing parameter ε, (ε > 10
−3 ) and
the dark photon mass (up to several tens of GeV for pp collider experiments), while
the second is sensitive to relatively small values (10
−7 ∼ < ε ∼ < 10
−3 ) in the low mass
range, m A less than few GeV.
• Experiments at colliders. These experiments search for resonances in the invariant mass distribution of e
+ e
−
, μ
+
μ
− pairs. Different dark-photon production
mechanisms are used in the different experiments: meson decays (π
0
→ γ A
,
NA48/2 [9]), Bremsstrahlung (e
− Z → e
− ZA
, A1 [1]), annihilation (e
+ e
−
→ γ A
,
BaBar [4]), and all these processes in different searches at KLOE [5–8]. In a protonproton (pp) collider the dark photon is produced via the γ − A
mixing in all the
processes where an off-shell photon γ
∗ with mass m(γ
∗
) is produced: meson
decays, Bremsstrahlung, and Drell-Yan production. LHCb [2, 37] has performed
a search for dark photon decaying in μ
+
μ
− final states using 1.6 fb
−1 of data
collected at the LHC pp collisions at 13 TeV centre-of-mass energy. CMS [3] has
performed the same search using 137 fb
−1 of fully reconstructed data and 96.6 fb
−1
of data collected with a reduced trigger information.
Figure 3.3 shows the existing limits for NA48/2, A1, LHCb, and BaBar; only one
set of limits from KLOE is shown since the others have been superseded by the
limits from BaBar.
• Beam-dump experiments. These experiments use the collisions of an electron
or proton beam with a fixed-target or a dump to generate the dark photon via
Bremsstrahlung (electron and proton beams), meson production and QCD processes (proton beams only). The products of the collisions are mostly absorbed
in the dump and the dark photon is searched for as a displaced vertex with two
opposite charged tracks in the decay volume of the experiment.
Figure 3.3 shows the limits from experiments at extracted electron beams
(E141 [11] and E137 [12–14] at SLAC, E774 [10] at Fermilab) and at extracted
proton beams from CHARM at CERN ([17] based on CHARM data [38]).
In addition, bounds on energy losses in supernovae provide further limits in the
region of small masses. These limits where discussed in [39, 40] and updated in [18,
41] by including the effect of finite temperature and plasma density.
Also the electron magnetic moment, with its very precise experimental determination, can be used to set an indirect limit [19]. These limits are included in Fig. 3.3.