Twin Higgs with Exact $Z_2$

TL;DR

This paper introduces a new mechanism in Twin Higgs models where an exact $Z_2$ symmetry is maintained, leading to suppressed Higgs quadratic terms and distinctive collider signatures, with minimal tuning and testable predictions.

Contribution

It proposes an N-trigonometric parity mechanism for exact $Z_2$ symmetry in Twin Higgs models, providing a concrete implementation and benchmark with reduced tuning and unique collider predictions.

Findings

Negligible tuning in Higgs potential.

Two-loop gauge contributions are sufficiently small.

Distinct Higgs couplings offer testable collider signatures.

Abstract

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 $N=3$. We find that the tuning in the resulting Higgs potential is negligible, and also show that two-loop N-suppression violating gauge contributions can be sufficiently small. The Higgs potential and its couplings in top sector are different from other neutral naturalness models, which are the main predictions of our model and can be tested in colliders.