  We present a twin Higgs model based on left-right symmetry with a tree level
quartic. This is made possible by extending the symmetry of the model to
include two Z_2 parities, each of which is sufficient to protect the Higgs from
getting a quadratically divergent mass squared. Although both parities are
broken explicitly, the symmetries that protect the Higgs from getting a
quadratically divergent mass are broken only collectively. The quadratic
divergences of the Higgs mass are thus still protected at one loop. We find
that the fine tuning in this model is reduced substantially compared to the
original left-right twin Higgs model. This mechanism can also be applied to the
mirror twin Higgs model to get a significant reduction of the fine tuning,
while keeping the mirror photon massless.
