The Minimal Supersymmetric Fat Higgs Model

TL;DR

The Minimal Supersymmetric Fat Higgs model provides a UV-complete framework in which electroweak symmetry breaking is driven dynamically by a new strongly coupled SU(2) gauge sector, yielding composite Higgs mesons and a dynamical superpotential that sets the EW scale. By engineering a renormalizable low-energy theory with two Higgs doublets and a singlet, the model achieves a heavy Higgs mass in the range of roughly $200$–$450$ GeV, addressing the supersymmetric little hierarchy problem without fine-tuning. Fermion masses arise via conformally enhanced couplings and effective Yukawas after integrating out spectator fields, while gauge coupling unification is preserved with a minimal set of additional multiplets and a calculable high-scale threshold structure. The Fat Higgs predicts an unconventional Higgs spectrum with new scalar states, custodial SU(2) structure, and distinctive collider and cosmological implications, offering clear avenues for experimental tests at the LHC and future linear colliders.

Abstract

We present a calculable supersymmetric theory of a composite ``fat'' Higgs boson. Electroweak symmetry is broken dynamically through a new gauge interaction that becomes strong at an intermediate scale. The Higgs mass can easily be 200-450 GeV along with the superpartner masses, solving the supersymmetric little hierarchy problem. We explicitly verify that the model is consistent with precision electroweak data without fine-tuning. Gauge coupling unification can be maintained despite the inherently strong dynamics involved in electroweak symmetry breaking. Supersymmetrizing the Standard Model therefore does not imply a light Higgs mass, contrary to the lore in the literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum that is distinctly different from the Minimal Supersymmetric Standard Model.

Figures (5)

• Figure 1: The renormalization of the couplings in our Fat Higgs model. The model becomes strong and nearly conformal at the scale $\Lambda_4$, where $\alpha_{H}$ nears $4\pi$. The conformal invariance is broken by the mass of the extra doublet, $m'$, which makes the theory confine at $\Lambda_{H} \sim m'$. Below this scale the effective theory description becomes one of meson composites with a coupling $\lambda$ that quickly renormalizes down to ${\cal O}(1)$. When $4\pi v_0\ll \Lambda_{H}$ the mesons condense at weak coupling and the theory is calculable.
• Figure 2: Sample Higgs spectra in our Fat Higgs model. In Spectrum I the SM-like Higgs is dominantly $h^0$ (89%), whereas in Spectrum III the SM-like Higgs is purely $H^0$.
• Figure 3: Constraints on $S$ and $T$ parameters from precision electroweak data at 68% and 99% confidence levels. The plot assumes $U=0$. Contributions of the Fat Higgs model to $S$ and $T$ are shown along three trajectories where $\lambda$ is varied from 2 to 3 in the direction of the arrow. The endpoints are labeled with the mass (in GeV) of the lighter component of the SM-like Higgs. For comparison, the black line shows the contributions to $S$ and $T$ for the Standard Model with various Higgs masses between $100$ GeV and 1 TeV in increments of 100 GeV.
• Figure 4: Contribution of the stop-sbottom sector to the $T$-parameter.
• Figure 5: The compositeness scale is shown as a function of the Higgs mass, fixing $\tan\beta = 1$. This was determined by finding the scale $\Lambda_H$ where $\lambda=4\pi$, using one-loop renormalization group evolution.