Dark photon portal dark matter with the 21-cm anomaly

A strong absorption profile was reported by the EDGES Collaboration, which indicates the hydrogen gas being colder than expected. It could be signatures of non-gravitational interactions between normal matter and dark matter (DM), and a potential explanation is that a small fraction of millicharged DM scatters with normal matter, with the DM mass in tens of MeV. To obtain the small fraction of millicharged DM and meanwhile being tolerant with by the constraints, the dark photon portal scalar and vector millicharged DM are explored in this paper. We consider that the mass of dark photon is slightly above twice of the millicharged DM mass, and thus the millicharged DM predominantly annihilates in p-wave during the freeze-out period, with the annihilation being enhanced near the resonance. The dark photon mainly decays into millicharged DM, and couplings of dark photon with SM particles could be allowed by the lepton collision experiments. The corresponding parameter spaces are derived. Future lepton collision experiments can be employed to search for millicharged DM via the production of the invisible dark photon.


I. INTRODUCTION
In the Universe, about 84% of the cosmological matter density is contributed by dark matter (DM) [1], while little has been known about particle properties of DM by now. Recently, an absorption profile around 78 MHz in the sky-averaged spectrum was reported by the EDGES Collaboration [2], and the magnitude of the absorption was enhanced with 3.8σ discrepancy.
This enhancement would indicate the hydrogen gas being colder than expected, and it may be signatures of non-gravitational interactions between normal matter and DM from the cosmic dawn [2][3][4][5][6].
To cool the hydrogen gas via the scatterings between DM and hydrogen, residual electrons and protons, the mass of DM should be not much heavier than the hydrogen mass. 1 Meanwhile, to explain the absorption profile, velocity-independent scatterings seem to be in tension with the cosmic microwave background (CMB) observation, and velocity-dependent scatterings are available [3,4] [16][17][18][19][20][21][22] for more), where A is the dark photon field.
In addition, the CMB observation [1,23] and the 21cm absorption profile from the cosmic dawn [2,24] set stringent on s-wave annihilations of DM with masses in the MeV scale. A possible way is that the millicharged DM predominantly annihilates in p-wave during the freeze-out period, and thus the scalar and vector DM with masses being lighter than the dark photon are of our concern.
Due to a small fraction of DM being millicharged, the couplings of dark photon with SM particles may be not very small, and this will be restricted by the arXiv:1804.07934v2 [hep-ph] 2 May 2018 lepton collision experiments [25][26][27][28]. Here we consider the case that the mass of dark photon is slightly above twice of the millicharged DM mass. In this case, dark photon can mainly decay into millicharged DM. The annihilations of millicharged DM are significantly enhanced near the resonance, and the couplings of dark photon with SM particles could be allowed by the lepton collision experiments. The corresponding parameter space will be derived in this paper.

II. INTERACTIONS AND TRANSITIONS
Here we consider the photon and dark photon A mediate the transitions between millicharged DM and SM sector. The interaction of A boson with SM charged fermion is taken as For scalar (vector) millicharged DM φ (V ), the electric charge is taken as εe (ε ∼ 10 −6 − 10 −4 [12][13][14]), and the dark charge is e D . Here we focus on the case that the main decay products of A are invisible, i.e., A mainly decaying into DM pairs φφ * (V V * ) with the mass 2m φ (2m V ) < m A . During millicharged DM freeze-out, the required large annihilation cross section is mainly contributed by A . For the DM mass range of concern, the p-wave annihilation process φφ * (V V * ) To enhance DM annihilations, here we consider that where v r is the relative velocity of the annihilating DM pair, and the factor 1 2 is included here for the required φφ * pair in DM annihilations. s is the total invariant mass squared, with s = 4m 2 φ + m 2 φ v 2 r + O(v 4 r ) in the nonrelativistic limit. Here the electron mass is negligible for the DM mass of concern. Γ A is the decay For vector millicharged DM V , the annihilation cross In the nonrelativistic limit, one has s = 4m 2 . (5) Here we give a brief discussion about the photon me- The total relic density of DM is Ω D h 2 = 0.1197 ± 0.0042 [1]. For scalar (vector) millicharged DM, to obtain the large annihilation cross section at the freezeout epoch indicated by the small f DM , we consider the annihilation being close to the resonance. Here we give a brief discussion about the detection of millicharged DM by the underground experiments. For tens MeV DM, the results of XENON10 [31,32] and COHERENT [33] seem to be sensitive for the scattering mediated by massless mediators (or the mediator's mass being very tiny). However, for the millicharged DM of concern, the exclusion region is feasible for the millicharge parameter ε 10 −7 [13,34], accounting for the terrestrial effect when a charged particle penetrating the earth. Moreover, due to the magnetic fields in the Milky Way, the millicharged DM is expected to be evacuated from the Galactic disk [3,35,36], and hence will be absent from DM direct detections. Thus, DM with the millicharge parameter ε of concern is allowed by the direct detection experiments (see e.g., Ref. [13]  The value e D = 1 is adopted here. For the band of a given ξ, the upper, lower limits are for fDM = 0.003, 0.02 respectively. The upper limit of with constraints from NA64 [27] and BaBar [28], and the region preferred by the muon g−2 [30] are denoted in the figure. for more).

IV. CONCLUSION AND DISCUSSION
The dark photon portal scalar, vector millicharged DM was studied in this paper, which could cool the 17LZX323.