Abstract
If dark matter (DM) is a fermion and its interactions with the standard model particles are mediated by pseudoscalar particles, the tree-level amplitude for the DM-nucleon elastic scattering is suppressed by the momentum transfer in the non-relativistic limit. At the loop level, on the other hand, the spin-independent contribution to the cross section appears without such suppression. Thus, the loop corrections are essential to discuss the sensitivities of the direct detection experiments for the model prediction. The one-loop corrections were investigated in the previous works. However, the two-loop diagrams give the leading order contribution to the DM-gluon effective operator left(overline{chi}chi {G}_{mu nu}^{alpha }{G}^{alpha mu nu}right) and have not been correctly evaluated yet. Moreover, some interaction terms which affect the scattering cross section were overlooked. In this paper, we show the cross section obtained by the improved analysis and discuss the region where the cross section becomes large.
Highlights
The Higgs sector is extended into the two-Higgs doublet models (THDMs) to make the gauge singlet pseudoscalar interact with the standard model (SM) sector at the renormalizable level
We read out the scalar trilinear couplings from Vport and from VTHDM
We have discussed the physics of the dark matter (DM) direct detection in the pseudoscalar mediator DM model
Summary
If DM is a Majorana fermion, the relevant effective operators for the evaluation of the DM-nucleon SI scattering cross section are given by. We use the following relations to evaluate the SI cross section from these operators [35],. The gluon matrix element (fTNG) is given as follows: [23]. The DM-nucleon SI scattering cross section is given by σSI. In the rest of this section, we calculate these Wilson coefficients at the leading order. Diagrams at the one-loop level give the leading order contributions to Cq, Cq(1), and Cq(2). For CG, the leading order contribution arises at the two-loop level. Note that the gluon matrix element is defined with the one-loop factor in eq (3.4), and the contribution from CG to σSI is the same order of magnitude as the contributions from the other Wilson coefficients.
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