Abstract
We extend the formalism of dark matter directional detection to arbitrary one-body dark matter-nucleon interactions. The new theoretical framework generalizes the one currently used, which is based on 2 types of dark matter-nucleon interaction only. It includes 14 dark matter-nucleon interaction operators, 8 isotope-dependent nuclear response functions, and the Radon transform of the first 2 moments of the dark matter velocity distribution. We calculate the recoil energy spectra at dark matter directional detectors made of CF4, CS2 and 3He for the 14 dark matter-nucleon interactions, using nuclear response functions recently obtained through numerical nuclear structure calculations. We highlight the new features of the proposed theoretical framework, and present our results for a spherical dark matter halo and for a stream of dark matter particles. This study lays the foundations for model independent analyses of dark matter directional detection experiments.
Highlights
We extend the formalism of dark matter directional detection to arbitrary onebody dark matter-nucleon interactions
We calculate the recoil energy spectra at dark matter directional detectors made of CF4, CS2 and 3He for the 14 dark matter-nucleon interactions, using nuclear response functions recently obtained through numerical nuclear structure calculations
In this work we extend the formalism of dark matter directional detection to arbitrary one-body dark matter-nucleon interactions
Summary
We start with a brief review of the effective theory of one-body dark matter-nucleon interactions [39]. Under the assumption of one-body dark matter-nucleon interactions, the Hamiltonian density. The four operatorsl0τ , ˆlτ, ˆlτM , andlτE depend on the dark matter particle spin operator. We refer to the 8 functions Rkττ in eq (2.4) as dark matter response functions They are quadratic in matrix elements of the operators in eq (2.3), and depend on q2/m2N and on vT⊥2 = v2 − q2/(4μ2T ), where v is the dark matter-nucleus relative velocity, mN is the nucleon mass, and μT the reduced dark matter-nucleus mass. Which for arbitrary interactions is a function of the momentum transfer, and of the dark matter-nucleus relative velocity
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