Maximum value of the spin-independent cross section in the 2HDM+a

Abstract

Abstract We investigate the maximum value of the spin-independent cross section (σSI) in a dark matter (DM) model called the two-Higgs doublet model + a (2HDM+a). This model can explain the measured value of the DM energy density by the freeze-out mechanism. Also, σSI is suppressed by the momentum transfer at the tree level, and loop diagrams give the leading contribution to it. The model prediction of σSI highly depends on values of c1 and c2 that are the quartic couplings between the gauge singlet CP-odd state (a0) and Higgs doublet fields (H1 and H2), c 1 a 0 2 H 1 † H 1 and c 2 a 0 2 H 2 † H 2 $$ {c}_1{a}_0^2{H}_1^{\dagger }{H}_1\kern0.33em and\kern0.33em {c}_2{a}_0^2{H}_2^{\dagger }{H}_2 $$ . We discuss the upper and lower bounds on c1 and c2 by studying the stability of the electroweak vacuum, the condition for the potential bounded from the below, and the perturbative unitarity. We find that the condition for the stability of the electroweak vacuum gives upper bounds on c1 and c2. The condition for the potential to be bounded from below gives lower bounds on c1 and c2. It also constrains the mixing angle between the two CP-odd states. The perturbative unitarity bound gives the upper bound on the Yukawa coupling between the dark matter and a0 and the quartic coupling of a0. Under these theoretical constraints, we find that the maximum value of the σSI is ∼ 5 × 10−47 cm2 for mA = 600 GeV, and the LZ and XENONnT experiments can see the DM signal predicted in this model near future.

Keywords

• Beyond Standard Model
• Higgs Physics