  In twin Higgs models, a discrete Z2 symmetry between the standard model Higgs
and the twin Higgs is introduced to address the hierarchy problem. In this
work, we propose another discrete symmetry in twin Higgs: the T parity, which
maps the twin Higgs quadruplet into its mirror copy. The T parity brings us a
whole group of T-odd particles, and leads to a promising dark matter candidate.
We present one realization of the T parity twin Higgs scenario by implementing
the $SU(2)_L \times SU(2)_R \times U(1)_1 \times U(1)_2$ gauge symmetry in twin
Higgs model. In this specific setup, the T-odd U(1) gauge boson could be the
dark matter candidate, and the T-odd particles have very distinct and
interesting phenomenology.
