Self-interacting scalar dark matter with local $Z_{3}$ symmetry

We construct a self-interacting scalar dark matter (DM) model with local discrete $Z_{3}$ symmetry that stabilizes a weak scale scalar dark matter $X$. The model assumes a hidden sector with a local $U(1)_X$ dark gauge symmetry, which is broken spontaneously into $Z_3$ subgroup by nonzero VEV of dark Higgs field $\phi_X$ ($ \langle \phi_X \rangle \neq 0$). Compared with global $Z_3$ DM models, the local $Z_3$ model has two new extra fields: a dark gauge field $Z^{'}$ and a dark Higgs field $\phi$ (a remnant of the $U(1)_X$ breaking). After imposing various constraints including the upper bounds on the spin-independent direct detection cross section and thermal relic density, we find that the scalar DM with mass less than $125$ GeV is allowed in the local $Z_3$ model, in contrary to the global $Z_3$ model. This is due to new channels in the DM pair annihilations open into $Z^{'}$ and $\phi$ in the local $Z_3$ model. Most parts of the newly open DM mass region can be probed by XENON1T and other similar future experiments. Also if $\phi$ is light enough (a few MeV $\lesssim m_\phi \lesssim$ O(100) MeV), it can generate a right size of DM self-interaction and explain the astrophysical small scale structure anomalies. This would lead to exotic decays of Higgs boson into a pair of dark Higgs bosons, which could be tested at LHC and ILC.