Light top partners and precision physics

TL;DR

This work develops a general EFT for minimal composite Higgs models with light top partners, focusing on electroweak precision observables. It uncovers a new logarithmically enhanced running of the $\widehat{S}$ parameter driven by non-linear Higgs dynamics in the presence of light fermionic resonances, and analyzes finite/finite-but-large $\widehat{T}$ corrections from top-partner loops, plus potential divergences in the $Z\overline b_L b_L$ vertex when 4-fermion operators are present. Through explicit models (singlet-only, 4-plet-only, and combined spectra) and both partially and completely composite $t_R$ scenarios, the study derives robust bounds on the sigma-model scale via $\xi = v^2/f^2$, typically $f \gtrsim 750$ GeV for light 4-plets, and highlights strong correlations between oblique parameters and top/bottom couplings. The results demonstrate that EW precision tests strongly constrain top-partner spectra and mixings, with notable implications for collider signatures and the viability of natural composite Higgs realizations.

Abstract

We analyze the corrections to the precision EW observables in minimal composite Higgs models by using a general effective parametrization which also includes the lightest fermionic resonances. A new, possibly large, logarithmically divergent contribution to S is identified, which comes purely from the strong dynamics. It can be interpreted as a running of S induced by the non-renormalizable Higgs interactions due to the non-linear sigma-model structure. As expected, the corrections to the T parameter coming from fermion loops are finite and dominated by the contributions of the lightest composite states. The fit of the oblique parameters suggests a rather stringent lower bound on the sigma-model scale f > 750GeV. The corrections to the Z bL bL vertex coming from the lowest-order operators in the effective Lagrangian are finite and somewhat correlated to the corrections to T. Large additional contributions are generated by contact interactions with 4 composite fermions. In this case a logarithmic divergence can be generated and the correlation with T is removed. We also analyze the tree-level corrections to the top couplings, which are expected to be large due to the sizable degree of compositeness of the third generation quarks. We find that for a moderate amount of tuning the deviation in Vtb can be of order 5% while the distortion of the Z tL tL vertex can be 10%.

Figures (18)

• Figure 1: Structure of the Feynman diagrams that generate $4$-fermions operator through the exchange of heavy gauge resonances. In the diagrams we represent the composite resonances with a double line.
• Figure 2: Constraints on the oblique EW parameters $\widehat{S}$ and $\widehat{T}$Baak:2012kk. The gray ellipses correspond to the $68\%$, $95\%$ and $99\%$ confidence level contours for $m_h = 126\ {\rm GeV}$ and $m_t = 173\ {\rm GeV}$. The red lines show the contributions that arise in composite Higgs models as explained in the main text. The IR contribution corresponds to the corrections due to non-linear Higgs dynamics, approximately given in eqs. (\ref{['eq:S_IR']}) and (\ref{['eq:T_IR']}), and is obtained fixing $m_* \sim 3\ {\rm TeV}$. The UV contribution is due to the EW gauge resonances (see eq. (\ref{['eq:S_UV']})).
• Figure 3: Upper bounds on $\xi$ in the $2$-site model ($c=0$) as a function of the $4$-plet mass parameter $m_4$ for different values of the cut-off $m_*$. The results have been obtained by considering the shift in $\widehat{S}$ given in eqs. (\ref{['eq:S_UV']}), (\ref{['eq:S_IR']}) and (\ref{['eq:S_div_explicit']}) and by marginalizing on $\widehat{T}$. The shaded regions correspond to the points compatible with the constraints at the $68\%$, $95\%$ and $99\%$ confidence level for $m_* = 3\ {\rm TeV}$. The dashed red curves show how the bounds are modified for $m_* = 5\ {\rm TeV}$.
• Figure 4: Diagrams with resonance loops that can contribute to the ${\cal O}_{W,B}$ operators.
• Figure 5: Schematic structure of a fermion loop diagram contributing to the $\widehat{T}$ parameter at leading order in the $y$ expansion.