Millicharged cosmic rays and low recoil detectors

We consider the production of a “fast flux” of hypothetical millicharged particles (mCPs) in the interstellar medium. We consider two possible sources induced by cosmic rays: (a) $pp\to (\mathrm{meson})\to (\mathrm{mCP})$, which adds to atmospheric production of mCPs, and (b) cosmic-ray upscattering on a millicharged component of dark matter. We notice that the galactic magnetic fields retain mCPs for a long time, leading to an enhancement of the fast flux by many orders of magnitude. In both scenarios, we calculate the expected signal for direct dark matter detection aimed at electron recoil. We observe that in scenario (a) neutrino detectors (ArgoNeuT and Super-Kamiokande) still provide superior sensitivity compared to dark matter detectors (XENON1T). However, in scenarios with a boosted dark matter component, the dark matter detectors perform better, given the enhancement of the upscattered flux at low velocities. Given the uncertainties, both in the flux generation model and in the actual atomic physics leading to electron recoil, it is still possible that the XENON1T-reported excess may come from a fast mCP flux, which will be decisively tested with future experiments.

Figure 1

A cartoon depiction of the leaky-box or disk-diffusion model [46]. A cosmic ray collides with a proton in the ISM, producing an mCP pair via an intermediate meson. This results in a fast-moving mCP that diffuses slowly about the leaky box. The long-retention time due to magnetic diffusion results in a greatly enhanced flux of mCPs sourced from the ISM [4, 47].

Figure 2

A comparison of the flux of mCPs arriving at Earth produced from (i) scenario (a): cosmic-ray interactions in the upper atmosphere $\mathrm{d}\mathrm{\Phi }=2\pi {\mathcal{I}}_{\chi }^{\mathrm{Atm}}$, (ii) scenario (a): cosmic-ray interactions in the ISM including magnetic retention (with ${\ell }_{\mathrm{LB}}=10\mathrm{kpc}$) $\mathrm{d}\mathrm{\Phi }=2\pi {\mathcal{I}}_{\chi }^{\mathrm{ISM}}$, (iii) scenario (b): from RBDM with $f_{\chi }={10}^{-6}$, $\mathrm{d}\mathrm{\Phi }=2\pi {\mathcal{I}}_{\chi }^{\mathrm{RB}}$, and (iv) virial dark matter: from the local dark matter density with a millicharged fraction of $f_{\chi }={10}^{-6}$, $\mathrm{d}\mathrm{\Phi }=f_{\chi }{n}_{\mathrm{DM}}vf(v)$, where $\int \mathrm{d}vf(v)=1$. Benchmark values of $m_{\chi }=200\mathrm{MeV}$ and $\epsilon =3\times {10}^{-3}$ have been chosen, corresponding to viable parameter space to explain the EDGES anomaly as depicted in Fig. 1 of Ref. [30].

Figure 3

Comparison of Eq. (5) and the data from Ref. [50] (triangles) as well as the parameterization of Ref. [51] (squares).

Figure 4

Behavior of $g({\beta }_{\chi }{\gamma }_{\chi },m_{\chi })$ [see Eq. (12)] for $m_{\chi }=25\mathrm{MeV}$, 250 MeV, 1 GeV, and 5 GeV.

Figure 5

Minimum required $\beta \gamma$ for an mCP to penetrate 3650 mwe (XENON1T) of overburden as a function of ${\epsilon }^2/m_{\chi }$ for different values of initial $\beta {\gamma }_{\mathrm{th}}$. Calculated using pstar proton range tables [65] in water and the continuous slowing-down approximation.

Figure 6

Scenario (a). Limits on mCPs arising from meson decays in the ISM from XENON1T data in the $S_2$-only bins [48] are shown in black. Also shown is the parameter space that explains the excess events in the 1–7 keV bins in $S_1\text{−}{S}_2$ data [49] in red. In gray, we show a compilation of current terrestrial limits on mCPs [45] and also include the recent milliQan-demonstrator results [8].

Figure 7

Scenario (a). Left: comparison of limits from the $S_2$-only (0.5–1 keV) bin with and without magnetic retention. Right: projections for the $S_2$-only (0.5–1 keV) bin for $10\times$ and $100\times$ the flux $\times$ experimental sensitivity.

Figure 8

Scenario (b). Left: Limits on mCPs making up a fraction $f_{\chi }=0.004$ and accelerated by CR in the ISM, arising from XENON1T data in the $S_2$-only bins [48], are shown in black. Also shown is the parameter space that explains the excess events in the 1–7 keV bins in $S_1\text{−}{S}_2$ data [49] in red. In gray, we show a compilation of current terrestrial limits on mCPs as well as direct detection limits and its ceiling [67]. Right: comparison of excess events for the parameter choice $m_{\chi }=100\mathrm{MeV}$, $\epsilon ={10}^{-3}$, and $f_{\chi }=0.004$, a sample point from the left panel with the data taken from Ref. [49].

Figure 9

Scenario (b). Here, we illustrate the dramatic consequences of magnetic retention by plotting the parameter space that yields an expected rate of five events in the 0.5–1 keV bin of the $S_2$-only analysis. We show the parameter space accounting for magnetic retention (solid line) relative to the parameter space that would be expected without magnetic retention (dashed line). A RBDM flux that remains unenhanced could occur if scattering is mediated by a light, but not massless, gauge boson such that astrophysical magnetic fields are effectively screened. We choose an unrealistically large concentration of mDM ($f_{\chi }\times \exp =4$ with exp denoting experimental sensitivity) so that the unenhanced parameter space is visible to the reader.

Figure 10

Scenario (b). Projections are shown for different $f_{\chi }\times \exp$ with exp standing for experimental sensitivity. Increased experimental sensitivity could be achieved either via detector improvements (e.g., longer exposure) or because of an enhanced flux of RBDM relative to our conservative estimate. For example, a local overconcentration of mDM in the Galactic disk can enhance the flux by a factor of 20 relative to our estimates (see Table 1). Limits correspond to the XENON1T $S_2$-only 0.5–1 keV bin.

Figure 11

Sensitivity of XENON1T to a monoenergetic flux of mCPs moving with a velocity of ${\beta }_{\chi }=0.1$. We find that XENON1T robustly excludes an mCP-induced plasmon excess (as proposed in Ref. [75]), because ${\beta }_{\chi }=0.1$ is sufficiently fast to penetrate the overburden at Gran Sasso and kick electrons above the XENON1T thresholds. For lower velocities $\beta \le 0.02$, the electron recoil drops below the thresholds for XENON1T’s $S_2$-only analysis. Since a plasmon excitation requires ${\beta }_{\chi }\gtrsim 0.00675$, it is possible for a fast flux of mCPs to explain the plasmon excess claimed in Ref. [75] without being in tension with XENON1T provided $0.00675\le {\beta }_{\chi }\le 0.02$.

Figure 12

Ionization cross section of atomic hydrogen within various approximations. The Sommerfeld or Fermi factor [with $S(k)$] clearly overestimates the cross section at low momentum transfers. We use the piecewise approximation labeled “free electron.”