One light composite Higgs boson facing electroweak precision tests

TL;DR

The paper addresses whether a minimal custodial composite Higgs model with an $SO(5)\to SO(4)$ symmetry breaking pattern and a pseudo-Goldstone Higgs can satisfy electroweak precision tests (EWPT). It employs a 4D two-site effective description with a single composite fermion multiplet $\chi$ mixing with the SM top via left/right compositeness parameters $\phi_L,\phi_R$ and a misalignment $\epsilon = v/f$, yielding a top mass $m_t = \frac{\epsilon}{\sqrt{2}} \sin\phi_L \sin\phi_R \ y^* f$. One-loop corrections to $S$, $T$, and the $Z\to b_L\bar b_L$ vertex are computed, including UV contributions from a vector resonance with $m_\rho = g_\rho f$ and IR Higgs corrections; the analysis identifies two viable parameter regions: a light singlet top partner $\tilde{T}$ or a largely composite left-handed top, each balancing $T$ and $\tau$ within the EWPT constraints. The results show that EWPT can be satisfied at the 2–3$\sigma$ level without extreme fine-tuning, though flavor constraints disfavor a fully composite $t_L$, and predict distinctive collider signatures, such as a relatively light charge-$5/3$ top partner, accessible at the LHC.

Abstract

We study analytically and numerically the bounds imposed by the electroweak precision tests on a minimal composite Higgs model. The model is based on spontaneous SO(5)/SO(4) breaking, so that an approximate custodial symmetry is preserved. The Higgs arises as a pseudo-Goldstone boson at a scale below the electroweak symmetry breaking scale. We show that one can satisfy the electroweak precision constraints without much fine-tuning. This is the case if the left-handed top quark is fully composite, which gives a mass spectrum within the reach of the LHC. However a composite top quark is strongly disfavoured by flavour physics. The alternative is to have a singlet top partner at a scale much lighter than the rest of the composite fermions. In this case the top partner would be light enough to be produced significantly at the LHC.

Figures (4)

• Figure 1: Left: allowed region in the plane $(\epsilon_3,\epsilon_1)$ fixing $\epsilon_2$ and $\epsilon_b$ to their SM values; the star corresponds to the Standard Model prediction, the black dot to our composite model. Right: same in the plane $(\epsilon_1,\epsilon_b)$ with $\epsilon_2$ and $\epsilon_3$ fixed to the SM values (dashed ellipses) and with the UV correction to $\epsilon_3$ turned on (solid ellipses). Here we have used $m_H=120$ GeV, $m_\rho=2.5$ TeV and $f=500$ GeV ($\epsilon^2 \approx 0.25$).
• Figure 2: Exact numerical computation of $\Delta T/T_\text{SM}^\text{top}$ and $\Delta \tau/\tau_\text{SM}^\text{top}$ for $f$ fixed to 2 TeV (left) and 500 GeV (right), and for four typical values of the ratio $\tilde{M}_0 / M_0$. The blue regions correspond to the analytical limits of equ. (\ref{['equ:TT']}-\ref{['equ:tauQX']}), in light blue where the corresponding composite states are below 500 GeV (mostly irrelevant). The electroweak precision constraints are given by the ellipses.
• Figure 3: Alloed mass of the fermions as a function of $\sin\phi_L$, with $f$ and the ratio $\tilde{M}_0/M_0$ fixed and $\phi_R$ varying freely. The green dots correspond to the charge $\frac{5}{3}$ quark $X^{5/3}$, the blue ones to the charge $\frac{2}{3}$ quarks $t$, $T$, $X^{2/3}$, $\tilde{T}$, and the red ones to the charge $-\frac{1}{3}$ quark $B$.
• Figure 4: Left: the maximal allowed value of $\epsilon^2$ as a function of $\sin \phi_L$, with $\sin \phi_R$ and $\tilde{M}_0/M_0$ varying freely. Right: regions of the plane $\sin \phi_L - \tilde{M}_0/M_0$ where $\epsilon^2$ can be larger than 0.15, 0.2 and 0.25 at 99% C.L.