Doubling down on naturalness with a supersymmetric twin Higgs

TL;DR

The paper presents a minimal supersymmetric completion of the mirror twin Higgs model, achieving double protection of the Higgs potential via both SUSY and a $\mathbf{Z}_2$-related twin sector. By embedding the Higgs into a $U(4)$ multiplet and exploiting a pseudo-Goldstone mechanism, the model preserves gauge coupling unification and keeps precision EW constraints under control while allowing stops around a few TeV and higgsinos near 1 TeV with percent-level tuning. The dominant naturalness signatures arise from Higgs portal effects: deviations in Higgs couplings, a modest invisible width, and novel Higgs states that can yield resonant di-Higgs production and invisible decays of a heavier Higgs, rather than conventional light superpartners. Precision Higgs coupling measurements, Higgs-width searches, and searches for the heavy Higgs $h_2$ and its decays provide the most promising tests at the LHC and future facilities. The framework also discusses UV completions for the singlet sector and the possibility of an emergent $\mathbf{Z}_2$ in the IR, with cosmological implications including mirror dark matter scenarios and constraints from $N_{ m eff}$.

Abstract

We show that naturalness of the weak scale can be comfortably reconciled with both LHC null results and observed Higgs properties provided the double protection of supersymmetry and the twin Higgs mechanism. This double protection radically alters conventional signs of naturalness at the LHC while respecting gauge coupling unification and precision electroweak limits. We find the measured Higgs mass, couplings, and percent-level naturalness of the weak scale are compatible with stops at ~3.5 TeV and higgsinos at ~1 TeV. The primary signs of naturalness in this scenario include modifications of Higgs couplings, a modest invisible Higgs width, resonant Higgs pair production, and an invisibly-decaying heavy Higgs.

Figures (8)

• Figure 1: The lightest Higgs mass in the SUSY twin Higgs model as a function of a common stop mass $m_{\tilde{t}_1} = m_{\tilde{t}_2} \equiv m_{\tilde{t}}$ and $\tan \beta$ with $\lambda = 1.4$, $f=3v$, and $m_A = 1.5 {\text{ TeV}}$. The green shaded region denotes $123 {\text{ GeV}} < m_{h} < 127 {\text{ GeV}}$.
• Figure 2: Tuning in the twin SUSY model with $\lambda = 1.4$, $f=3v$, $m_A = 1.5 {\text{ TeV}}$, and $m^2_S = (1 {\text{ TeV}})^2$. The left is the absolute tuning, and the right is the relative tuning compared to the NMSSM, $\Delta^{\rm NMSSM}/\Delta^{\rm twin}$, with the NMSSM parameters $\lambda = 0.6$, $m_A = 0.8 {\text{ TeV}}$, and $m^2_S = (1 {\text{ TeV}})^2$. At each point, $\tan\beta$ is determined independently for the twin and NMSSM models to obtain $m_h = 125 {\text{ GeV}}$.
• Figure 3: Tuning in the twin SUSY model with $\lambda = 1.4$, $f=3v$, $m_A = 1.5 {\text{ TeV}}$, $m^2_S = (1 {\text{ TeV}})^2$, $\mu = 0.5 {\text{ TeV}}$. The green shaded region is $123 {\text{ GeV}} < m_{h} < 127 {\text{ GeV}}$.
• Figure 4: Tuning in the twin SUSY model as a function of $\lambda$ and $m^2_S$ with $f=3v$, $m_A=1.5 {\text{ TeV}}$, $m_{\tilde{t}}=2.0 {\text{ TeV}}$, and $\mu = 0.5 {\text{ TeV}}$. At each point, $\tan\beta$ is determined to obtain $m_h = 125 {\text{ GeV}}$.
• Figure 5: Ratio of tuning for twin SUSY models with ($f=3v$, $m_A=1.5 {\text{ TeV}}$) versus ($f=5v$, $m_A=2.0{\text{ TeV}}$). For both models $\lambda=1.4$ and $m^2_S = (1 {\text{ TeV}})^2$. At each point, $\tan\beta$ is determined independently for each of the models to obtain $m_h = 125 {\text{ GeV}}$.