On the Tuning and the Mass of the Composite Higgs

TL;DR

This work analyzes fine-tuning in composite Higgs models with partial fermion compositeness, classifying models by the quantum numbers of top-partner fermions into three categories and deriving how the Higgs mass $m_h$ scales with the resonance scales. It shows that achieving $m_h\approx125$ GeV at moderate tuning generally requires light fermionic top partners around 1 TeV, with a necessary separation between fermionic and vector resonances—natural realizations can be constructed in 4D frameworks that decouple these scales. Explicit realizations (CHM$_5$ and CHM$_{14}$) confirm the parametric estimates and reveal that, while gauge contributions provide an irreducible tuning floor, light top partners remain a predictive hallmark of natural composite Higgs scenarios. The results imply that LHC top-partner searches probe the natural region, and non-observation would push models toward heavier spectra or additional tuning, akin to Natural SUSY.

Abstract

We analyze quantitatively the tuning of composite Higgs models with partial compositeness and its interplay with the predicted Higgs mass. In this respect we identify three classes of models, characterized by different quantum numbers of the fermionic colored resonances associated with the top quark, the so-called top partners. The main result of this classification is that in all models with moderate tuning a light Higgs, of 125 GeV mass, requires the presence of light top partners, around 1 TeV. The minimal tuning is comparable to the one of the most attractive supersymmetric models in particular the ones realizing Natural SUSY. This gives further support to an extensive program of top partners searches at the LHC that can already probe the natural region of composite Higgs models.

Figures (8)

• Figure 1: Schematic representation of the spectrum of the fermionic resonances.
• Figure 2: Scatter plots for the CHM$_5$ set-up corresponding to $\xi=0.1$ for large values of $g_\psi$. In the left panel we show the Higgs mass as a function of $g_\psi$ and in the right panel the amount of tuning as a function of the Higgs mass. The red lines correspond the general estimates given in eq. (\ref{['eq:mh_gpsi_5']}) and eq. (\ref{['tundt']}).
• Figure 3: Scatter plots for the CHM$_5$ set-up corresponding to $\xi=0.1$ for small $g_\psi$ (we restricted the top-partner mass parameters to the range $[-3 f, 3 f]$). In the left panel we show the Higgs mass as a function of $g_\psi$ and in the right panel the amount of tuning as a function of the Higgs mass for the same sample points. The red line in the left panel corresponds to the estimate given in eq. (\ref{['eq:mh_gpsi_5']}).
• Figure 4: Left panel: scatter plot of the Higgs mass as a function of $g_\psi$ for $\xi = 0.1$ in the CHM$_{14}$ set-up with composite $t_R$. Right panel: scatter plot showing the amount of tuning as a function of the Higgs mass for the same data set. The solid red lines show the estimates of the Higgs mass and the tuning with $y_L = y_t$, while the dot-dashed ones correspond to the choice $y_L = \sqrt{2/5}y_t$ and the dotted ones to $y_L = 4 y_t$. The black dots correspond to the points with $y_L \leq 1$, while the gray ones have $y_L > 1$.
• Figure 5: Scatter plots in the CHM$_{14}$ set-up with composite $t_R$ for $\xi = 0.1$ in the region of nearly degenerate $\bf 9$ and $\bf 4$ (we allow for a maximal $10\%$ split in the mass parameters). In the left panel we show the Higgs mass as a function of $g_\psi$ and in the right panel the mass of the lightest fermionic resonance as a function of the Higgs mass. For the colors of the points and the meaning of the red lines see the caption of fig. \ref{['fig:mh_gstar_14']}.