Singlet extension of the MSSM as a solution to the small cosmological scale anomalies

In this work we show that the general singlet extension of the minimal supersymmetric standard model (MSSM) can naturally provide a self-interacting singlino dark matter to solve the small cosmological scale anomalies (a large Sommerfeld enhancement factor can also be obtained). However, we find that the NMSSM (the singlet extension of the MSSM with $Z_3$ symmetry) cannot achieve this due to the restricted parameter space. In our analysis we introduce the concept of symmetric and antisymmetric viscosity cross sections to deal with the nonrelativistic Majorana-fermion dark matter scattering.

Figure 1

Dark matter interactions: annihilation to SM particles in the left diagram, scattering off quarks in the middle diagram, and self-scattering in the right diagram.

Figure 2

The Sommerfeld enhancement factor at different velocities with the coupling strength ${\alpha }_{\chi }=0.01$. Here $v=10\mathrm{km}/\mathrm{s}$, $200\mathrm{km}/\mathrm{s}$, $1000\mathrm{km}/\mathrm{s}$ correspond to the characteristic speeds of dwarf halos, the Milky Way, and clusters, respectively.

Figure 3

The bird’s-eye view of transfer and viscosity cross sections ${\sigma }_T$, ${\sigma }_{VS}$, ${\sigma }_{VA}$ in the parameter space $(a,b)$.

Figure 4

The spin-independent cross section of DM scattering off the proton versus the DM mass in different scenarios in the NMSSM. $\square$ denotes singlino-dominant DM scenarios, most of which are excluded by the DM direct detection limits; $△$ denotes bino-dominant DM scenarios, among which the red ones are excluded while the green ones survive; $\circ$ (around 1 TeV) denotes Higgsino-dominant DM scenarios, among which the pink ones are excluded while the green ones survive. All the samples satisfy the DM relic density constraints.

Figure 5

Feynman diagram of DM annihilation to SM fermions through a pseudoscalar $a$.

Figure 6

The scatter plots of parameter space allowed by DM relic density shown in the plane of $M_{a_1}$ versus the DM mass. The left panel is the singlino-dominant DM scenario, where most of the samples are excluded points by direct detection limits of LUX-2013. The right panel is the bino-dominant DM scenario, where the red ones are excluded points by direct detection limits of LUX-2013 while the green ones survive.

Figure 7

Same as Fig. 4, but showing the spin-independent cross section versus $\lambda$ in the NMSSM.

Figure 8

The same as Fig. 7, but showing the nonrelativistic viscosity cross section between DM in the NMSSM. For each allowed sample in Fig. 7, we use three velocities corresponding to the three small cosmological scales (dwarf, Milky Way, and cluster) to calculate the cross section and here we plot the maximal one.

Figure 9

Feynman diagram of singlino DM annihilation to scalars in the GMSSM. The final state of $\varphi \varphi$ can be $hh$, $ha$, or $aa$.

Figure 10

Scatter plots of the parameter space in the DM self-interaction model [23] allowed by DM relic density plus dwarf scale structures (blue region), Milky Way size structures (red region), or cluster size structures (green region). We obtained these results by changing our Feynman rules to those in [23].

Figure 11

The scatter plots of the parameter space allowed by DM relic density and all three small scale structures (dwarf, Milky Way, cluster). The red ones are for the DM self-interaction model [23], while the green ones are for the GMSSM.

Figure 12

Same as Fig. 10, but showing the Sommerfeld enhancement factor. The left frame is for the DM self-interaction model [23], while the right frame is for the GMSSM.