Twin Higgs with Exact $Z_2$

Understand

We present a novel mechanism for realistic electroweak symmetry breaking in Twin Higgs/neutral naturalness models where the $Z_2$ exchange symmetry can remain exactly unbroken.

• The exchange symmetry in the Yukawa sector will be implemented as an "N-trigonometric parity" $\sin N \frac{h}{f} \leftrightarrow \cos N \frac{h}{f}$.
• The Yukawa couplings will be suppressed leading to an N-suppressed Higgs quadratic term, without significantly affecting the quartic.
• We present a concrete implementation of this idea for general (odd) values of N using maximal symmetry, and a realistic benchmark model for $N=3$.