Possible s-wave annihilation for MeV dark matter with the 21-cm absorption

The CMB observation sets stringent constraints on MeV dark matter (DM) annihilating into charged states/photons in s-wave, and the recent observation of the 21-cm absorption at the cosmic dawn reported by EDGES is also very strict for s-wave annihilations of MeV DM. The millicharged DM with p-wave dominant annihilations during the freeze-out period are considered in literatures to give an explanation about the 21-cm absorption, with photon mediated scattering cooling the hydrogen. In this paper, we focus on the annihilation of millicharged DM being s-wave dominant. To explain the 21-cm absorption and meanwhile be compatible with the CMB and 21-cm absorption bounds on DM annihilations, we consider the annihilation close to the resonance, with the new mediator (here is dark photon) mass being slightly above twice of the millicharged DM mass. In this case, the annihilation cross section at the temperature $T \to 0$ could be much smaller than that at $T_f$, which would be tolerated by the bounds on DM annihilations, avoiding the excess heating from DM s-wave annihilations to the hydrogen gas. The beam dump and lepton collider experiments can be employed to hunt for millicharged DM via the production of the invisible dark photon.


I. INTRODUCTION
For dark matter (DM) particles with masses in a range of ten MeV to hundreds TeV, the relic abundance of DM can be obtained via the thermal freeze-out of DM. One DM candidate extensively concerned is weakly interacting massive particles (WIMPs) with masses in GeV-TeV scale, and results from recent DM direct detections [1][2][3][4][5][6][7][8] set stringent constraints on WIMP-nucleon scatterings. In case of DM being lighter and in MeV scale, the MeV DM could evade the DM-target nucleus scattering hunters. Thus, the MeV DM is of our concern.
The bulk of the cosmological matter density (about 84%) is contributed by DM [9], and the typical annihilation cross section of DM during the freeze-out period is about 3 × 10 −26 cm 3 /s. Furthermore, the cosmic microwave background (CMB) observations at the recombination epoch set upper limits on s-wave annihilations of MeV DM with the annihilation products being of charged states/photons [9,10], which are much below the annihilation cross section required by the relic abundance of DM. In addition, the constraint from the recent observation of the 21-cm absorption [11] at the cosmic dawn is also very strict for the s-wave annihilation of MeV DM * jialb@mail.nankai.edu.cn [12][13][14], as the energy injection from DM s-wave annihilations would heat the hydrogen gas. Therefore, the MeV DM with p-wave dominant annihilations during the freeze-out period are generally considered in literatures [15][16][17].
Is it possible to explain the 21-cm anomaly with the millicharged DM which being s-wave dominant annihilations during the freeze-out period? Maybe some extraordinary annihilation mechanism could do the job.
For DM s-wave annihilations at the temperature T → 0, if twice of the DM mass is around the mediator mass, the resonant DM annihilation at T → 0 would be different from that at the freeze-out period [43][44][45]. Generally, for the mediator mass being slightly below twice of the DM mass, the annihilation cross section of DM at T → 0 could be larger than that at the freeze-out temperature T f ; for the mediator mass being slightly above twice of the DM mass, the annihilation cross section of DM at T → 0 could be smaller than that at T = T f . In the case of the new mediator mass being slightly above twice of the millicharged DM mass, the millicharged DM with s-wave dominant annihilations may cause the 21cm anomaly and meanwhile evade constraints from CMB and the 21-cm absorption. This will be investigated in this paper. Here we consider the fermionic millicharged DM with dark photon as the new mediator, and now the two mediators are photon and dark photon. The scenario is that: the small fraction of millicharged DM is due to dark photon mediated s-wave annihilations during the freeze-out period, and the 21-cm absorption at the cosmic dawn is caused by photon mediated scattering between millicharged DM and hydrogen. Furthermore, we should keep in mind that there may be more particles in the dark sector, and we focus on the particles that play key roles in transitions/interactions between millicharged DM and ordinary matter.
Besides the fermionic millicharged DM carries a millicharge ηe, here the DM is also dark charged, and dark photon fieldÂ mediates dark electromagnetism in the dark sector. The dark photon-photon kinetic mixing where J µ em is the electromagnetic current. In addition, A couples to the fermionic millicharged DM χ in forms For fermionic millicharged DM, the annihilationχχ → A → SM mediated by dark photon A is an s-wave process, which could be dominant during DM freeze-out. To be able to significantly lower the s-wave annihilation of millicharged DM at low temperature after DM freeze-out, here we consider the case that the mass of dark photon is slightly above twice of the millicharged DM mass. For teens of MeV millicharged DM indicated by the 21-cm absorption, the main annihilation products in SM are e + e − , and the annihilation cross section is about where v r is the relative velocity of the two DM particles, the factor 1 2 is for the requiredχχ pair in DM annihilations, and s is the total invariant mass squared. The The relic density of millicharged DM f DM Ω D h 2 (Ω D h 2 is the total relic density of DM, and f DM is the fraction of millicharged DM) is set by the thermally averaged annihilation cross section σ 1 v r via the relation [54,55] with The parameter x is x = m χ /T , and x f = m χ /T f at the freeze-out temperature T f (see e.g., Ref. [54] for the calculation of T f ). For a pair of DM particles annihilating at T (here T m χ ), the thermally averaged annihilation cross section can be obtained with methods derived in Ref. [55]. The value of x f J ann is a typical annihilation cross section related to the relic abundance of millicharged DM.
For the temperature of DM T → 0 (T compared with DM mass), the corresponding annihilation cross section of DM mediated by A is different from that at DM freezeout period. Forχχ → e + e − at T → 0, contributions from A and photon are considered, and the annihilation cross section is In addition, the s-wave annihilation modeχχ → γγ is deeply suppressed by η 4 .

III. NUMERICAL ANALYSIS
The millicharged DM is colder than hydrogen at the cosmic dawn. To cool the hydrogen and produce the     Fig. 2. It can be seen that, the s-wave annihilationχχ → A → e + e − at T → 0 could be much smaller than that at T = T f , e.g., for 0.02 ξ − 1 0.13, the ratio is 10 −2 . Thus, for millicharged DM in MeV scale, the s-wave dominant DM annihilation during the freeze-out period may be allowed by constraints from CMB and the 21-cm absorption, and this will be further analyzed in the following.
The annihilation cross section of millicharged DM at the freeze-out period is set by the relic density of millicharged DM f DM Ω D h 2 , with Ω D h 2 = 0.120 ± 0.001 [9]. to the Earth's surface. In addition, for underground experiments, the terrestrial effect of a particle penetrating the earth and strongly interacting with overburden matter (e.g., photon/dark photon mediated large interactions related to the electric charge of nucleus) could deplete the particle's energy and significantly reduce the detection sensitivity [67,68]. For the millicharged DM, the reference cross sectionσ e (see, e.g. Ref. [69] for more) of χ−electron scattering with photon as the mediator is in a range of ∼ 3.5 ×10 −26 − 3.5 ×10 −24 cm 2 , and the rock/concrete shielding with depths of ∼ 3 − 10 meters could result in little detection signal of millicharged DM [68]. In this case, the millicharged DM of concern will evade constraints from underground experiments, such as XENON10 [70,71], XENON100 [71], and DarkSide-50 [72]. Moreover, the above case may be not the whole thing for the millicharged DM, as analyzed in Ref. [73].
The millicharged DM could be accelerated by supernova shocks, and the evacuation of millicharged DM from the disk may not be effective due to the diffusion of millicharged DM from the halo [73]. 18LZX415.