Abstract
The inert Higgs doublet model contains a stable neutral boson as a candidate of dark matter. We calculate cross section for spin-independent scattering of the dark matter on nucleon. We take into account electroweak and scalar quartic interactions, and evaluate effects of scattering with quarks at one-loop level and with gluon at two-loop level. These contributions give an important effect for the dark matter mass to be around m h /2, because a coupling with the standard model Higgs boson which gives the leading order contribution should be suppressed to reproduce the correct amount of the thermal relic abundance in this mass region. In particular, we show that the dark matter self coupling changes the value of the spin-independent cross section significantly.
Highlights
The inert two-Higgs doublet model [4, 5] is a simple extension of the SM with a dark matter candidate
These contributions give an important effect for the dark matter mass to be around mh/2, because a coupling with the standard model Higgs boson which gives the leading order contribution should be suppressed to reproduce the correct amount of the thermal relic abundance in this mass region
If the dark matter mass mA is around a half of the SM Higgs boson mass, λA should be suppressed because the SM Higgs boson s-channel exchange diagrams significantly contribute to the annihilation cross section which determines the relic amount of the dark matter
Summary
We formulate how to include radiative corrections to the spin-independent cross section. To calculate the cross section of elastic scattering of dark matter and nucleon, first, we construct the effective interaction of the dark matter and quark/gluon. To calculate the scattering amplitude of nucleon, we need matrix elements of quark/gluon operators, which are given as,. This relation is derived by using the relation obtained from the trace anomaly [58], mN = From this discussion, we can see N |mqqq|N and (αs/4π) N |GaμνGaμν|N are same order. We have checked that the spin-independent cross section of a dark matter and a proton is the almost same as of the a dark matter and a neutron. By using the above matrix elements and the coefficients Γ’s in the effective interaction given in eq (3.1), the scattering amplitude of the nucleon and the dark matter is given as, iM = imN q. What we have to calculate is the effective coupling Γ’s
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