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Dark matter protohalos in MSSM-9 and implications for direct and indirect detection

We study how the kinetic decoupling of dark matter (DM) within a minimal supersymmetric extension of the standard model, by adopting nine independent parameters (MSSM-9), could improve our knowledge of the properties of the DM protohalos. We show that the most probable neutralino mass regions, which satisfy the relic density and the Higgs mass contraints, are those with the lightest supersymmetric neutralino mass around 1 TeV and 3 TeV, corresponding to Higgsino-like and Wino-like neutralino, respectively. The kinetic decoupling temperature in the MSSM-9 scenario leads to a most probable protohalo mass in a range of $M_{\mathrm{ph}}\sim 10^{-12}-10^{-7}\,M_\odot$. The part of the region closer to 2 TeV gives also important contributions from the neutralino-stau co-annihilation, reducing the effective annihilation rate in the early Universe. We also study how the size of the smallest DM substructures correlates to experimental signatures, such as the spin-dependent and spin-independent scattering cross sections, relevant for direct detection of DM. Improvements on the spin-independent sensitivity might reduce the most probable range of the protohalo mass between $\sim$10$^{-9}\,M_\odot$ and $\sim$10$^{-7}\,M_\odot$, while the expected spin-dependent sensitivity provides weaker constraints. We show how the boost of the luminosity due to DM annihilation increases, depending on the protohalo mass. In the Higgsino case, the protohalo mass is lower than the canonical value often used in the literature ($\sim$10$^{-6}\,M_\odot$), while $\langleσv\rangle$ does not deviate from $\langleσv\rangle\sim 10^{-26}$ cm$^3$ s$^{-1}$; there is no significant enhancement of the luminosity. On the contrary, in the Wino case, the protohalo mass is even lighter, and $\langleσv\rangle$ is two orders of magnitude larger; as its consequence, we see a substantial enhancement of the luminosity.