Spontaneous twin symmetry breaking

Abstract

We consider a twin Higgs model where the Z2 twin symmetry is broken spontaneously, not explicitly. We show that introducing an exact copy of the standard model with a renormalizable Higgs portal potential is enough to realize such a scenario. In this scenario, the SU(4) breaking scale f is determined by the scale where the Higgs self-quartic coupling flips its sign, whose standard model prediction is O(1010 GeV). For the misalignment of nonzero vacuum expectation values of the twin Higgs fields, it is explicitly shown that parameter tuning of O(mh2/f2) is required, so we conclude that minimal setup does not solve the hierarchy problem. We point out that the tuning can be significantly reduced (f∼2.7 TeV) if there are twin vectorlike leptons with a large Yukawa coupling.