2.1 Limits on the Dark Dipole Scale d M /Λ 2
29
moment is given by
a
A
= −
3
2
α D
π
m v h d
M
Λ 2
2
5
4
+ log
μ
2
m 2
(2.32)
in the M S scheme; contrary to the SM case, the result depends on the subtraction of
a divergence.
We discuss below in Sect. 2.3 how in the UV model, where there are states
coupled to both the dark and the visible photon, the anomalous magnetic moment
can be brought to bear directly on the limits.
The quantity Δa e , the difference between the experimental value of the electron
anomalous magnetic moment [20] and its SM prediction is very small. The uncertainty on this difference (at 1σ) is given by [21]
δ Δa e < 8.1 × 10
−13
.
(2.33)
By requiring that the contribution of the dark photon does not exceed this value, and
therefore does not contribute to the electron magnetic moment, we obtain
Λ
2
√ α D d
e
M
∼ > 0.075 TeV
2
,
(2.34)
by taking the renormalization scale μ = m e .
The analogous quantity Δa μ , the difference between the experimental value of
the muon anomalous magnetic moment [22] and its SM prediction [23], is less than
Δa μ < 2.74 × 10
−9
,
(2.35)
at 2σ level, from which we derive
Λ
2
√
α D d
μ
M
∼ > 0.5 TeV
2
,
(2.36)
for μ = m μ . Notice that the current 3.2σ discrepancy in Δa μ could be explained by
requiring
Λ
2
√ α D d
μ
M
0.27 TeV
2
.
(2.37)
Flavor changing processes can provide constraints on possible dipole operator
contributions to off-diagonal interactions.