Light neutralino dark matter in the next-to-minimal supersymmetric standard model

Neutralino dark matter is generally assumed to be relatively heavy, with a mass near the electroweak scale. This does not necessarily need to be the case, however. In the next-to-minimal supersymmetric standard model (NMSSM) and other supersymmetric models with an extended Higgs sector, a very light $CP$-odd Higgs boson can naturally arise making it possible for a very light neutralino to annihilate efficiently enough to avoid being overproduced in the early Universe. In this article, we explore the characteristics of a supersymmetric model needed to include a very light neutralino, $100\mathrm{MeV}<m_{{\tilde{\chi }}_1^0}<20\mathrm{GeV}$, using the NMSSM as a prototype. We discuss the most important constraints from Upsilon decays, $b\to s\gamma$, $B_s\to {\mu }^{+}{\mu }^{-}$ and the magnetic moment of the muon, and find that a light bino or singlino neutralino is allowed, and can be generated with the appropriate relic density. It has previously been shown that the positive detection of dark matter claimed by the DAMA collaboration can be reconciled with other direct dark matter experiments such as CDMS II if the dark matter particle is rather light, between about 6 and 9 GeV. A singlino or binolike neutralino could easily fall within this range of masses within the NMSSM. Additionally, models with sub-GeV neutralinos may be capable of generating the 511 keV gamma-ray emission observed from the galactic bulge by the INTEGRAL/SPI experiment. We also point out measurements which can be performed immediately at CLEO, BABAR, and Belle using existing data to discover or significantly constrain this scenario.

Figure 1

On the left, we show regions of $\lambda -\kappa$ parameter space for which the ${\tilde{\chi }}_1^0$ is singlinolike (defined by ${ϵ}_s^2>0.5$) and binolike (defined by ${ϵ}_s^2\le 0.5$). On the right, we plot $m_A$ vs $m_{{\tilde{\chi }}_1^0}$ for singlinolike neutralinos with ${ϵ}_s^2>0.9$. Each point shown is consistent with all LEP constraints.

Figure 2

The branching ratio for ${\rm Y}(1S)\to \gamma {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$ via 3-body decay (i.e. either $m_{A_1}<2m_{{\tilde{\chi }}_1^0}$ or $m_{A_1}>m_{{\rm Y}}$) is plotted vs the LSP mass (left) and relic density $\Omega h^2$ (right). All points shown are consistent with all LEP constraints. Points marked by an x are excluded by one of: ${\rm Y}\to \gamma {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$ (3-body decay) (that which is plotted); ${\rm Y}\to \gamma A_1$ (2-body decay) with $A_1\to {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$ (2-body decay); or ${\rm Y}\to \gamma A_1$ (2-body decay) where the $A_1$ decays visibly.

Figure 3

The $CP$-odd Higgs mass required to obtain the measured relic density for a light neutralino in the MSSM. Models above the curves produce more dark matter than is observed. These results are for the case of a binolike neutralino with a small Higgsino admixture (${ϵ}_B^2=0.94$, ${ϵ}_u^2=0.06$). Results for two values of $\tan \beta$ (10 and 50) are shown. The horizontal dashed line represents the lower limit on the $CP$-odd Higgs mass in the MSSM from collider constraints. To avoid overproducing dark matter, the neutralino must be heavier than about 8 (22) GeV for $\tan \beta =50$ (10).

Figure 4

We display contours in $m_{A_1}-m_{{\tilde{\chi }}_1^0}$ parameter space for which Eq. (40) yields $\Omega h^2=0.1$. Points above or below each pair of curves produce more dark matter than is observed; inside each set of curves less dark matter is produced than is observed. These results are for a binolike neutralino with a small Higgsino admixture (${ϵ}_B^2=0.94$, ${ϵ}_u^2=0.06$). Three values of $\tan \beta$ (50, 15, and 3) have been used, shown as solid, dashed, and dot-dashed lines, respectively. The dotted line is the contour corresponding to $2m_{{\tilde{\chi }}_1^0}=m_A$. For each set of lines, we have set ${cos}^2{\theta }_A=0.6$. The $\tan \beta =50$ case is highly constrained for very light neutralinos, and is primarily shown for comparison with the MSSM case.