Abstract
We find the exchange symmetry between left and right handed top quark in composite Higgs model with partial compositeness is efficient to soften the Higgs potential and reduce fine tuning. This symmetry can keep the Higgs potential in top sector invariant under trigonometric parity $\sin (h/f) \leftrightarrow \cos (h/f)$ and thus the Higgs quadratic divergences can be completely cancelled, resulting a UV insensitive Higgs potential. We explicitly construct the minimal left-right symmetric model based on coset space $SO(6)/SO(5)$ which is locally isomorphic to $SU(4)/Sp(4)$ and thus has well defined fermionic UV completion. This UV completion can automatically keep Higgs potential in gauge sector finite even the gauge sector breaks this discrete symmetry. We find that the vector mesons can be very heavy while the colored top partners are relatively light ($>1.5$ TeV) to obtain a light Higgs.
Highlights
With the discovery of Higgs boson at LHC [1,2], the Higgs mechanism [3,4,5,6] in the standard model (SM) is proven to successfully describe electroweak symmetry breaking (EWSB) at lower energy scale
We find that the minimal coset to realize this LR symmetry is SOð6Þ=SOð5Þ [28], which is locally isomorphic to SUð4Þ=Spð4Þ, and the latter has very well-defined pure fermionic UV completions based on the confining hypercolor gauge theory
In twin Higgs models (THM) [20,21,22,29,30,31], Higgs divergences are canceled by introducing a Z2 exchange symmetry between top and twin top to induce Higgs trigonometric parity [19] (TP) sinðh=fÞ ↔ cosðh=fÞ, which is very efficient to cancel the quadratic divergences of the ordinary top
Summary
With the discovery of Higgs boson at LHC [1,2], the Higgs mechanism [3,4,5,6] in the standard model (SM) is proven to successfully describe electroweak symmetry breaking (EWSB) at lower energy scale. One can achieve successful EWSB by introducing some new dynamics at some high energy scale, such as the TeV scale, to screen the quantum corrections from higher energy scales. Among these new physics theories, the composite Higgs model (CHM) [7,8,9] in which Higgs is a pseudoNambu-Goldstone boson (pNGB) of some strong dynamics can solve it in a tremendously simple way. We find that the exchange symmetry between left-handed (LH) and right-handed (RH) SM fermions, called left-right (LR) symmetry, can eliminate the ultraviolet (UV) divergences and double tuning in the Higgs potential if partial compositeness [24] is implemented. The Appendix contains the generators, specific form factors in effective Lagrangian and some comments on LR symmetric bottom sector
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