One-loop contribution to dark-matter-nucleon scattering in the pseudo-scalar dark matter model

Abstract

Recent dark matter (DM) direct searches place very stringent constraints on the possible DM candidates proposed in extensions of the Standard Model. There are however models where these constraints are avoided. One of the simplest and most striking examples comes from a straightforward Higgs portal pseudoscalar DM model featured with a softly broken U (1) symmetry. In this model the tree-level DM-nucleon scattering cross section vanishes in the limit of zero momentum-transfer. It has also been argued that the leading-order DM-nucleon cross section appears at the one-loop level. In this work we have calculated the exact cross section in the zero momentum-transfer at the leading-order i.e., at the one-loop level of perturbative expansion. We have concluded that, in agreement with expectations, the amplitude for the scattering process is UV finite and approaches zero in the limit of vanishing DM masses. Moreover, we made clear that the finite DM velocity correction at tree-level is subdominant with respect to the one-loop contribution. Based on the analytic formulae, our numerical studies show that, for a typical choice of model parameters, the DM nuclear recoiling cross section is well below O(10 −50 cm 2 ), which indicates that the DM direct detection signal in this model naturally avoids the present strong experimental limits on the cross section.

Global fit of pseudo-Nambu-Goldstone Dark Matter

“…We computed the pNG DM-nucleon cross section at one-loop level for all of our samples after utilising the results of ref. [27]. We found that none of the points in our scan are challenged by current direct detection limits from XENON1T (2018).…”

“…1 Thus, a pNG DM model offers a natural way of evading the strong direct detection limits. A leading-order contribution to the pNG DM-nucleon cross section in the zero-momentum limit appears at the one-loop level [27,28]. For typical DM velocities in our galaxy, v χ ∼ 10 −3 , it can easily dominate over the tree-level contribution.…”

“…Note that F is proportional to m 2 χ , and the fact that both the C 2 and D 3 functions behave as constants in the limit of m χ → 0 [23,27], the direct detection amplitude indeed vanishes in this limit.…”

“…The elastic spin-independent (SI) pNG DM-nucleon cross section is momentum-suppressed at tree-level (see Appendix A) and given by [27] σ tree-level…”

“…In ref. [27], the authors point out that the approximate one-loop cross section in eq. (3.19) can under/overestimate the actual cross section by several orders of magnitude depending on the model parameters.…”