Higgs Low-Energy Theorem (and its corrections) in Composite Models

TL;DR

This work extends the Higgs Low-Energy Theorem to composite Higgs scenarios, detailing how nonlinear Higgs interactions and heavy fermionic resonances alter Higgs couplings to gluons and photons. It shows that, in single-Higgs production, LET predictions are accurate and largely spectrum-independent due to cancellations, while double-Higgs production via gluon fusion is highly sensitive to the top-partner spectrum and can deviate by up to ~50% from LET estimates. The authors perform a full one-loop calculation in the minimal composite Higgs model MCHM5, including all fermionic resonances, and analyze constraints from electroweak precision data, flavor, and direct LHC searches. They find that top partners reduce the strong-dynamics-driven enhancement of gg→hh and that the cross section remains highly spectrum-dependent, offering an indirect probe of the top sector in addition to direct searches.

Abstract

The Higgs low-energy theorem gives a simple and elegant way to estimate the couplings of the Higgs boson to massless gluons and photons induced by loops of heavy particles. We extend this theorem to take into account possible nonlinear Higgs interactions resulting from a strong dynamics at the origin of the breaking of the electroweak symmetry. We show that, while it approximates with an accuracy of order a few percents single Higgs production, it receives corrections of order 50% for double Higgs production. A full one-loop computation of the gg->hh cross section is explicitly performed in MCHM5, the minimal composite Higgs model based on the SO(5)/SO(4) coset with the Standard Model fermions embedded into the fundamental representation of SO(5). In particular we take into account the contributions of all fermionic resonances, which give sizeable (negative) corrections to the result obtained considering only the Higgs nonlinearities. Constraints from electroweak precision and flavor data on the top partners are analyzed in detail, as well as direct searches at the LHC for these new fermions called to play a crucial role in the electroweak symmetry breaking dynamics.

Figures (12)

• Figure 1: Generic diagram contributing to Higgs production in gluon fusion. In the SM case we have $Q\equiv t,b$. In composite Higgs models with additional heavy fermionic resonances these add to the particles $Q$ running in the loop.
• Figure 2: Generic diagrams contributing to double Higgs production via gluon fusion in composite Higgs models with $n_f$ novel fermionic resonances of mass $m_{i}$ ($i=1,...,n_f$). The index $j$ is introduced to indicate that different fermions can contribute to each box diagram.
• Figure 3: (Left panel) The $pp\to hh$ cross section for $m_h=125$ GeV at LHC14, computed using the LET, normalized to the SM cross section also computed in the $m_{t}\to \infty$ limit. MHCM5 is discussed in detail in the text, whereas the $gg\to hh$ amplitudes for MCHM4 and for the Littlest Higgs model are given in App. \ref{['LH and\n MCHM4']}. (Right panel) Square of the function $C(m_{hh}^2)$, which was defined in Eq. \ref{['gghh ampl']} and is proportional to the LET $gg\to hh$ amplitude, in the three models under consideration (for $\xi = 0.25$) and in the SM, as a function of $m_{hh}=\sqrt{\hat{s}}$.
• Figure 4: A sample of parameters passing the $\chi^2$-test of electroweak precision observables, displaying the compositeness of the left-handed top versus the mass of the lightest top partner, for $\xi = 0.25$ (left) and $\xi = 0.1$ (right). The points in light gray do not pass the direct collider constraints. Points in orange/medium gray pass the present constraints but will be tested by the LHC running at 8 TeV with an integrated luminosity of $15 \,\mathrm{fb}^{-1}$, see Section \ref{['sec:searches']}.
• Figure 5: Physical mass spectrum of the composite fermions for a sample of points passing the electroweak precision tests, as a function of the left-handed top compositeness for $\xi=0.25$ (left) and $\xi=0.1$ (right). The blue/dark gray points are top-like fermions (charge $+2/3$), the green/fair gray points bottom-like (charge $-1/3$), and the red/medium gray ones correspond to the exotic $X$ (charge $+5/3$). Light gray points are excluded by present collider constraints, see Section \ref{['sec:searches']}.