| Summary: | We begin by reviewing the basic theory and phenomenology of twin Higgs models. In these theories, the Higgs arises as a pseudo-Nambu-Goldstone boson of a spontaneously broken global symmetry. A discrete symmetry restricts the form of the radiatively generated Higgs potential such that dimensionful terms respect this global symmetry. The Higgs mass is then protected from receiving quadratically divergent contributions, allowing natural electroweak symmetry breaking up to a cutoff scale of about 10 TeV. We then show how to incorporate a tree level quartic into the left-right twin Higgs. The addition of such a term results in a substantial reduction in the fine tuning compared to that of the original twin Higgs. We do this by extending the symmetry of the theory to include two Z₂ symmetries, each of which is sufficient to protect Higgs mass from receiving quadratically divergent corrections. Although both parities are broken explicitly, the symmetries that the protect Higgs mass from getting a quadratically divergent mass are broken only collectively. Therefore, the Higgs mass parameter is free from quadratic divergences to one loop. Finally, we consider the collider signatures of the left-right twin Higgs in the limit that the right-handed neutrino mass is less than the right-handed gauge boson mass. In this limit, which has not been considered previously, new leptonic decay channels open up. This allows the discovery of the right-handed gauge boson WR and the heavy top partner T(H), which are responsible for canceling the one-loop quadratic divergences of the Higgs mass. Half of these events contain same-sign leptons without missing energy, which have no SM background. These signals may be used to complement other collider searches, and in certain regions of parameter space, may be the only way to observe the particles responsible for natural electroweak symmetry breaking in the left-right twin Higgs.
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