Implications of a Light Higgs in Composite Models

TL;DR

This work analyzes the Higgs mass in composite Higgs models with partial compositeness across two cosets, $SO(5)/SO(4)$ and $SO(6)/SO(5)$, using simplified 4D constructions with fermions in $SO(5)$ representations and an extra CP-odd singlet in the latter. The Higgs potential is generated by SM couplings that explicitly break global symmetries, with the top sector dominantly setting the Higgs mass and ensuring finiteness due to resonances; a natural Higgs mass around 125 GeV typically requires fermionic top partners below the TeV scale, while vector resonances remain heavier. The study finds a robust correlation between the lightest fermionic resonances and the Higgs mass across CHM$_5$, CHM$_{10}$, MFV scenarios, and the CHM$_6$ extension, indicating testable predictions for the LHC. CP properties are clarified, especially in $SO(6)/SO(5)$, where the top sector does not spontaneously or explicitly break CP, and a CP-odd singlet behaves as an additional, typically heavier state. Overall, the results support a naturalness-driven spectrum with accessible fermionic partners and provide concrete predictions for Higgs-singlet couplings and modified gluon couplings in these CHMs.

Abstract

We study the Higgs mass in composite Higgs models with partial compositeness, extending the results of Ref. [1] to different representations of the composite sector for SO(5)/SO(4) and to the coset SO(6)/SO(5). For a given tuning we find in general a strong correlation between the mass of the top partners and the Higgs mass, akin to the one in supersymmetry. If the theory is natural a Higgs mass of 125 GeV typically requires fermionic partners below TeV which might be within the reach of the present run of LHC. A discussion of CP properties of both cosets is also presented.

Figures (6)

• Figure 1: Masses of fermionic partners as a function of the Higgs mass for $f=800$ GeV in CHM$_5$. The six fermionic parameters are varied between $0.3$ and $4$ TeV and we require mixing elementary composite $\Delta_{t_L,t_R}/m_{T,\tilde{T}}<3$. The gauge contribution corresponds to $f_1=f_2=\sqrt{2}f$ and $g_\rho=3$. In the first plot mass of the lightest fermionic partner as a function of the Higgs mass. In the second plot mass of the fermionic excitations in the low mass region.
• Figure 2: Masses of fermionic partners as a function of the Higgs mass for $f=800$ GeV in CHM$_5$ with MFV. Same parameters as in Fig. \ref{['fig:SO5Higgs-all']} are chosen.
• Figure 3: Higgs and fermionic partners masses in CHM$_{10}$ for $f=800$ GeV. The mass parameters are chosen (in TeV): $1<\Delta_{t_L, t_R}<5$, $0.5<m_{T,\tilde{T}}<3$, $-2< m_{Y_T}< .5$ and $3<Y_T<6$.
• Figure 4: Masses of Higgs, singlet and fermionic partners in CHM$_6$ for $f=800$ GeV. The six fermionic parameters are varied between $0.3$ and $4$ TeV with the mixing elementary-composite $\Delta_{t_L,t_R}/m_{T,\tilde{T}}<3$. The gauge contribution corresponds to $f_1=f_2=\sqrt{2}f$ and $g_\rho=3$. Up left Figure: Higgs vs. lightest fermionic state. Up right Figure: Higgs vs. singlet mass. Below masses of lightest singlet, doublet and custodian in the low Higgs mass region.
• Figure 5: Coupling of the scalars to fermions including wave-function normalization effects. On the left Higgs coupling to the top vs. Higgs mass. On the right the Higgs vs. singlet coupling.