Blind spots for neutralino dark matter in the MSSM with an intermediate $m_A$

We study the spin-independent neutralino dark matter scattering off heavy nuclei in the minimal supersymmetric Standard Model. We identify analytically the blind spots in direct detection for intermediate values of $m_A$. In the region where $\mu$ and $M_{1,2}$ have opposite signs, there is not only a reduction of the lightest $CP$-even Higgs coupling to neutralinos, but also a destructive interference between the neutralino scattering through the exchange of the lightest $CP$-even Higgs and that through the exchange of the heaviest $CP$-even Higgs. At critical values of $m_A$, the tree-level contribution from the light Higgs exchange cancels the contribution from the heavy Higgs, so the scattering cross section vanishes. We denote these configurations as blind spots, since they provide a generalization of the ones previously discussed in the literature, which occur at very large values of $m_A$. We show that the generalized blind spots may occur in regions of parameter space that are consistent with the obtention of the proper neutralino relic density and can be tested by nonstandard Higgs boson searches and EWino searches at the LHC and future linear colliders.

Figure 1

Feynman diagram for a neutralino scattering off a heavy nucleus through a $CP$-even Higgs.

Figure 2

SI scattering cross section as a function of $m_A$ for $\tan \beta =50$ (up left), $\tan \beta =30$ (up right), $\tan \beta =10$ (down left), $\mu \sim -2M_1$ and $\tan \beta =30$, $\mu \sim -4M_1$ (down right). The red dots (the upper dotted line) are for the $\mu >0$ case, and the blue dots (the lower dotted line) are for the $\mu <0$ case. The (green) shaded areas are excluded by the CMS $H$, $A\to \tau \tau$ searches. The orange line (the upper solid line) is the LUX limit, and the blue line (the lower solid line) is the projected Xenon 1T limit.

Figure 3

SI scattering cross section at the traditional blind spots, where $m_{\chi }+\mu \sin 2\beta =0$ for $\tan \beta =50$ (up left), $\tan \beta =30$ (up right), $\tan \beta =10$ (down left) and $\tan \beta =5$ (down right). The (green) shaded areas are excluded by CMS $H$, $A\to \tau \tau$ searches.

Figure 4

SI DDMD cross section in the $\mu \text{−}{M}_1$ plane for various values of $\tan \beta$ and $m_A$, in pb. The purple dots (the dotted line) are where the calculated relic density agrees with the WMAP value. The blue lines (the solid straight lines to the right) show the blind spot calculated from Eq. (19), and the red lines (the solid straight lines to the left) show the traditional blind spot where $m_{\chi }+\mu \sin 2\beta =0$.

Figure 5

$\mathrm{\Delta }{a}_{\mu }$ at the blind spot as a function of $m\tilde{l}$ for $\tan \beta =10$ (purple), 30 (blue) and 50 (orange). The solid red line is the central value of $\mathrm{\Delta }{a}_{\mu }$, and the two dashed red lines are the $\pm 3\sigma$ of $\mathrm{\Delta }{a}_{\mu }$.

Figure 6

Ratio of $\mu$ and $m_{\chi }$ at the blind spot for given values of $\tan \beta$ and $m_A$ [see Eq. (21)]. The orange line is the current limit from CMS $H$, $A\to \tau \tau$ searches.

Figure 7

Neutralino pair production cross section at LHC14, as a function of the absolute value of the Higgsino mass parameter $\mu$, for gaugino mass unification and $M_1=100\mathrm{GeV}$.