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.
