Abstract
Having so far only indirect evidence for the existence of Dark Matter a plethora of experiments aims at direct detection of Dark Matter through the scattering of Dark Matter particles off atomic nuclei. For the correct interpretation and identification of the underlying nature of the Dark Matter constituents higher-order corrections to the cross section of Dark Matter-nucleon scattering are important, in particular in models where the tree-level cross section is negligibly small. In this work we revisit the electroweak corrections to the dark matter-nucleon scattering cross section in a model with a pseudo Nambu-Goldstone boson as the Dark Matter candidate. Two calculations that already exist in the literature, apply different approaches resulting in different final results for the cross section in some regions of the parameter space leading us to redo the calculation and analyse the two approaches to clarify the situation. We furthermore update the experimental constraints and examine the regions of the parameter space where the cross section is above the neutrino floor but which can only be probed in the far future.
Highlights
A particular version of this extension known as the Pseudo Nambu-Goldstone DM model (PNGDM) has a scalar potential invariant under a global U(1) symmetry which would give rise to a Nambu-Goldstone boson
Two calculations that already exist in the literature, apply different approaches resulting in different final results for the cross section in some regions of the parameter space leading us to redo the calculation and analyse the two approaches to clarify the situation
We update the experimental constraints and examine the regions of the parameter space where the cross section is above the neutrino floor but which can only be probed in the far future
Summary
A simple extension of the SM by a scalar gauge singlet is enough to provide a valid DM candidate. The doublet H and singlet S fields are expanded as follows. In order to simplify the potential, an invariance under the Z2 symmetry S → −S has been imposed. The. real part of S develops a vacuum expectation value (VEV), while the doublet develops the usual (SM) VEV that gives mass to the SM fermions and gauge bosons,. The parameters of the potential can be written as functions of the masses, mixing angle and the VEVs as λHS. The potential is invariant under a U(1) symmetry (S → eiαS) that is softly broken by the dimension-two term proportional to m2χ. The Goldstone boson related to the U(1) symmetry acquires a mass proportional to m2χ. Due to the Z2 symmetry there are no more terms contributing to the mass of the pseudo Nambu-Goldstone boson.
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