Could the 21-cm absorption be explained by the dark matter suggested by $^8$Be transitions?

The stronger than expected 21-cm absorption was observed by EDGES recently, and another anomaly of $^8$Be transitions would be signatures of new interactions. These two issues may be related to each other, e.g., pseudoscalar $A$ mediated fermionic millicharged dark matter (DM), and the 21-cm absorption could be induced by photon mediated scattering between MeV millicharged DM and hydrogen. This will be explored in this paper. For fermionic millicharged DM $\bar{\chi} \chi$ with masses in a range of $2 m_A<2 m_{\chi}<3 m_A$, the p-wave annihilation $\bar{\chi} \chi \to A A$ would be dominant during DM freeze-out. The s-wave annihilation $\bar{\chi} \chi$ $\to A, \gamma $ $\to e^+ e^-$ is tolerant by constraints from CMB and the 21-cm absorption. The millicharged DM can evade constraints from direct detection experiments. The process of $K^+ \to \pi^+ \pi^0$ with the invisible decay $\pi^0 \to \bar{\chi} \chi$ could be employed to search for the millicharged DM, and future high intensity $K^+$ sources, such as NA62, will do the job.

Here the millicharged DM explanation is of our concern. To obtain the small fraction of millicharged DM, large DM annihilation cross sections caused by new interactions are required during DM freeze-out. In addition, the observations of the cosmic microwave background (CMB) at the recombination [22,23] and the 21-cm absorption at the cosmic dawn [24][25][26] set con- * jialb@mail.nankai.edu.cn straints on DM annihilations with masses of tens of MeV. To evade these constraints, scenarios of DM annihilating into neutrinos [6], or DM annihilations in p-wave [6,27] during DM freeze-out are available. e + e − pairs produced in 8 Be transitions [28], which cannot be explained within nuclear physics [28,29]. A new vector boson X being produced and quickly decaying via X → e + e − was suggested to explain the anomaly, with the mass m X 17 MeV. Possible vector/axial vector couplings of X with SM fermions were analyzed in Refs. [30][31][32][33] (for more discussions, see e.g., Refs. [ [34][35][36][37][38]), and the vector/axial vector X portal DM particles were studied in Refs. [39][40][41][42][43]. In addition, a pseudoscalar A with the mass about 17 MeV may also produce 8 Be anomalous transitions [44].
In the case that the MeV DM suggested by the 8 Be transitions is millicharged, the new interaction portal DM may give an explanation on the EDGES observation. This is of our concern in this paper. For the vector X portal millicharged DM [39], a large X-DM coupling is needed to obtain the small fraction of mil-arXiv:1809.00177v2 [hep-ph] 23 Nov 2018 licharged DM.
In this paper, we focus on the pseudoscalar A mediated fermionic DM, which is millicharged. When DM is heavier than the pseudoscalar mediator, DM can annihilate both in s-wave and p-wave. It may be allowed by the constraints from the CMB and 21-cm absorption observations, and gives an alternative explanation about the 21-cm anomaly. These will be investigated in the following.

II. INTERACTIONS AND TRANSITIONS
The effective couplings of the pseudoscalar A to SM quarks are taken in the form where the vacuum expectation value v is ∼ 246 GeV.
With the assumption of m d ∼ 2m u ∼ 2 × 2.5 MeV [45] and ξ u = ξ c = ξ t , ξ d = ξ s = ξ b , to explain the 8 Be anomaly, the values of ξ u + ξ d ≈ 0.6 and ξ e 4 can be adopted [44]. In addition, the coupling parameter between a new pseudoscalar particle (with a mass ∼ 17 MeV) and electron is ξ e 115 in Ref. [46] (referencing the E141 result [47]). Furthermore, if A couples to muon, it will be constrained by the muon g − 2. The where κ = m 2 µ /m 2 A . The recent result for the discrepancy between experiment and theory is about [49][50][51][52] Suppose A's contribution to the muon g − 2 difference is 1 × 10 −9 . For the case of Higgs-like couplings of A to leptons, i.e., ξ µ = ξ e , this will significantly enlarge the discrepancy. For the case of universal couplings of A to electron and muon, i.e., m µ ξ µ ∼ m e ξ e , we have The effective coupling of A to the fermionic mil-licharged DM χ is taken as For DM being heavier than A, DM can annihilate both in s-wave and p-wave. In addition, to avoid the swave annihilationχχ → AAA after DM freeze-out (see Now we formulate the annihilations of millicharged DMχχ. The annihilation cross section of the p-wave processχχ → AA is where v r is the relative velocity of the annihilating DM pair. The factor 1 2 is for the requiredχχ pair in DM annihilations. In the nonrelativistic limit, the total invariant mass squared s is The s-wave processes of DM annihilations are mainly mediated by A and γ. For the processχχ → A → e + e − , the annihilation cross section is For the DM mass of concern, the electron's mass is negligible compared with DM mass. For photon mediated transitions, the annihilation modeχχ → γ → e + e − is an s-wave process, which is suppressed by η 2 . The corresponding annihilation cross section is Another s-wave processχχ → γγ is deeply suppressed by η 4 , with an annihilation cross section about πα 2 η 4 /2m 2 χ in the nonrelativistic limit. Thus, γ lines in this annihilation is far below constraints from the CMB observation [23] and the 21-cm absorption [26].
In this paper, the p-wave annihilationχχ → AA is dominant during millicharged DM freeze-out.
In addition, the millicharged DM of concern can be produced in neutral π 0 's decay. The transition of π 0 → χχ mediated by A is taken in the form (8) and the decay width Γχ χ is In SM, the process π 0 → vv is forbidden for massless neutrinos [53][54][55]. Thus, the decay π 0 →χχ could be employed to search for the millicharged DM.

III. NUMERICAL ANALYSIS
The total relic abundance of DM is Ω D h 2 = 0.1197 ± 0.0042 [22]. The CMB observation [22,23] and the 21-cm absorption profile [25,26] set constraints on the s-wave annihilationsχχ → A, γ → e + e − . Note an annihilation cross section σ 2e v r ≡ (σ 1 + σ 2 )v r for the annihi-  Here we give a brief discussion about the search of millicharged DM at underground experiments. For MeV scale millicharged DM, considering the terrestrial effect of a charged particle penetrating the earth, the exclusion regions of XENON10 [56,57] and CO-HERENT [58] are sensitive for DM with a millicharge parameter η 10 −7 [7,59]. In addition, the millicharged DM residing in the Galactic disk is rare, which is prevented by the magnetic fields in the Milky Way [2,60,61]. Thus, the millicharged DM of concern is tolerant by the DM direct detections. Group [49]. Substituting the corresponding values into Eq. (9), the decay width Γχ χ is about which is in units of GeV. The mean lifetime of π 0 is τ π 0 = (8.52 ± 0.18) × 10 −17 s [49], and thus the branching ratio of the invisible decay π 0 →χχ is Experimentally, signatures of the decay π 0 → "invisible" can be searched via the process K + → π + π 0 with π 0 → "invisible", which could be identified in kinematics (see e.g., Refs. [62,63] for more). The upper limit of π 0 's invisible decay given by E949 experiment indicates the branching ratio of π 0 → "invisible" < 2.7 × 10 −7 [62]. For the case of Higgs-like couplings of A to quarks, i.e., ξ u = ξ d ≈ 0.3, the decay mode π 0 →χχ will exceed the upper limit set by the experiment, and thus this case is excluded. For the case of universal couplings of A to up and down quarks, i.e., m u ξ u ∼ m d ξ d , the branching ratio B π 0 →χχ will be reduced. Specifically, for (m u ξ u − m d ξ d )/m d ξ d < 0.12, the invisible decay π 0 →χχ will be allowed by the upper limit from E949. The millicharged DM of concern can be explored at future high intensity K + sources, such as NA62. With ∼ 10 13 K + decays being collected, NA62 would reach a limit of ∼ 10 −9 [63] for the branching ratio of π 0 → "invisible".

IV. CONCLUSION AND DISCUSSION
The pseudoscalar A mediated fermionic millicharged DM has been studied in this paper, with 8 Be anomalous transitions induced by A, and contributions from The millicharged DM with a millicharge ηe of concern could evade constraints from direct detection experiments. The π 0 's invisible decay can be employed to search for the millicharged DM in the process of K + → π + π 0 with π 0 → "invisible" (for other approaches, see e.g., Ref. [64]). For the case of m u ξ u ∼ m d ξ d and (m u ξ u − m d ξ d )/m d ξ d < 0.12, the invisible decay π 0 →χχ can be allowed by the upper limit of E949 [62]. With O(10 13 ) K + decays, NA62 would set a limit of ∼ 10 −9 [63] for B π 0 →χχ . We look forward to the future accurate 21-cm absorption observations and the run of NA62 experiment, at which the millicharged DM of concern can be tested. where M 1,2,3 is M 1,2,3 = λ 3v (p 2 )γ 5 / k 3 / k 1 u(p 1 ) (m 2 A − 2p 2 · k 3 )(m 2 A − 2p 1 · k 1 ) .
In the limit of p µ 1 /m χ → (1, ε), we have where a ij is .
Here we give an estimate about this type DM annihilation. For f DM ∼ 0.4% and m χ ∼ 30 MeV, the value of f 2 DM σ I 3 v r is about 2 × 10 −31 cm 3 /s, which is below constraints from the CMB observation [23] and the 21-cm absorption profile [26]. Now consider the quartic term of A,