Solar Active-Sterile Neutrino Conversion with Atomic Effects at Dark Matter Direct Detection Experiments

Abstract

The recent XENON1T excess can be explained by the solar active-sterile neutrino conversion with bound electrons via light mediator. Nevertheless, the atomic effects are usually omitted in the solar neutrino explanations. We systematically establish a second quantization formalism for both bound and ionized electrons to account for the atomic effects. This formalism is of great generality to incorporate various interactions for both neutrino and dark matter scatterings. Our calculation shows that the change in the cross section due to atomic effects can have important impact on the differential cross section. It is necessary to include atomic effects in the low-energy electron recoil signal at dark matter direct detection experiments even for energetic solar neutrinos. With the best-fit values to the XENON1T data, we also project the event rate at PandaX-4T, XENONnT, and LZ experiments.

Revisiting the Fermionic Dark Matter Absorption on Electron Target

“…The atomic binding effect could be large enough to affect the direct detection event rate. We follow the general formalism developed with second quantization for both the initial bound and final ionized electron states [111]. The differential cross section is then a convolution of the particle scattering amplitude |M| 2 and the atomic K-factor K nl (T r , |q|),…”

“…On the other hand, the solid angle integration dΩ q ≡ d cos θ q dφ q contains the information of momentum transfer direction. However, neither the K-factor K nl (T r , |q|) [111] nor the scattering matrix element |M(q)| 2 has dependence on the angular coordinates of q. For the latter, the angular independence happens due to the fact that the DM velocity is negligible in the absorption process.…”

“…The pseudo-scalar (P) case is quite special since the matrix element intrinsically has momentum transfer dependence as elaborated in [111]. For comparison, the others have exactly the same structure.…”