  The left-right twin Higgs model predicts a light stable scalar \hat{S}, which
is a candidate for WIMP dark matter. We study its scattering on nucleon and
find that the cross section is below the CDMS II upper bound but can reach the
SuperCDMS sensitivity. Then we study the Higgs phenomenology by paying special
attention to the decay h -> \hat{S} \hat{S} which is strongly correlated with
the dark matter scattering on nucleon. We find that such an invisible decay can
be sizable, which can severely suppress the conventional decay modes like h->VV
(V=W,Z) and h->b\bar{b}. On the other hand, compared to the SM prediction, the
rates of Higgs boson productions at the LHC via gluon-gluon fusion, weak boson
fusion or in association with top quark pairs are all reduced significantly,
e.g., the gluon-gluon fusion channel can be suppressed by about 30%.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena;High Energy Physics - Experiment