Abstract
In original twin Higgs model, vacuum misalignment between electroweak and new physics scales is realized by adding explicit $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking term. Introducing additional twin Higgs could accommodate spontaneous $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking, which explains origin of this misalignment. We introduce a class of twin two Higgs doublet models with most general scalar potential, and discuss general conditions which trigger electroweak and $$ {\mathrm{\mathbb{Z}}}_2 $$ symmetry breaking. Various scenarios on realising the vacuum misalignment are systematically discussed in a natural composite two Higgs double model framework: explicit $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking, radiative $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking, tadpole-induced $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking, and quartic-induced $$ {\mathrm{\mathbb{Z}}}_2 $$ breaking. We investigate the Higgs mass spectra and Higgs phenomenology in these scenarios.
Highlights
Existence of fine-tuning between the tree-level Higgs mass parameter and loop-level Higgs mass corrections
In original twin Higgs model, vacuum misalignment between electroweak and new physics scales is realized by adding explicit Z2 breaking term
The radiative corrections calculated in the above section trigger spontaneous symmetry breaking, and induce VEVs for the h01 and h02 components in H1A,2A defined in eq (3.13)
Summary
We first briefly review the twin Higgs model [8, 9, 13,14,15,16] and how the vacuum misalignment is realized in this model. The global symmetry U(4) is explicitly broken once the SM and its mirror gauge group SMA × SMB are gauged, and the Yukawa interactions are introduced Both the gauge and Yukawa interactions give rise to radiative corrections to the quadratic part of the scalar potential. The sub-leading corrections proportional to g4 take the similar form with opposite sign Since both the squared mass and quartic coupling come from the same loopsuppressed corrections, the VEV is obtained to be at the scale f as mentioned in introduction. This fact can be seen if we write the scalar potential including the radiative corrections, to good approximation, as. For a TeV scale f , this corresponds to around 15% tuning
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