Light Composite Higgs from Higher Representations versus Electroweak Precision Measurements -- Predictions for LHC

TL;DR

This work presents a dynamical electroweak symmetry-breaking framework built from technicolor theories with fermions in higher representations, focusing on two-index symmetric matter to achieve near-conformal (walking) dynamics with only two techniflavors. It shows that the two-color theory requires a new fourth lepton family to cancel the Witten anomaly and remains compatible with precision electroweak data when lepton mass splittings are tuned, while predicting a light composite Higgs with $M_H \lesssim 150$ GeV. The study also analyzes a three-color variant without anomaly-induced leptons, explores a range of hypercharge assignments, and discusses LHC signatures and a potential dark-matter candidate from the lepton sector. By linking the light Higgs to proximity to a quantum phase transition and to SYM in the large-$N$ limit, the paper provides lattice-testable, phenomenologically viable alternatives to elementary-Higgs scenarios with concrete experimental targets. Overall, it demonstrates that higher-representation technicolor can address the hierarchy problem while remaining consistent with precision data and offering distinctive collider and cosmological signatures.

Abstract

We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide useful constraints on the relative mass splitting of the new leptons needed to cure the Witten anomaly. In the case of a fourth family of leptons with ordinary lepton hypercharge the new heavy neutrino can be a natural candidate of cold dark matter. We also propose theories in which the critical number of flavors needed to enter the conformal window is higher than the one with fermions in the two-index symmetric representation, but lower than in the walking technicolor theories with fermions only in the fundamental representation of the gauge group. Due to the near conformal/chiral phase transition, we show that the composite Higgs is very light compared to the intrinsic scale of the technicolor theory. For the two technicolor theory we predict the composite Higgs mass not to exceed 150 GeV.

Figures (7)

• Figure 1: Left(Right) panel: Phase diagram as function of number of $N_{Tf}$ Dirac flavors and $N$ colors for fermions in the two-index symmetric (antisymmetric) representation, i.e. S(A)-types, of the gauge group.
• Figure 2: Left Panel: A standard running behavior of a coupling constant in a generic asymptotically free theory. Right Panel: The walking behavior of the coupling constant when the number of flavors is near a conformal fixed point. The associated beta function is plotted below the previous graph.
• Figure 3: Schematic diagram summarizing the particle content and gauge interactions of the new minimal standard model like technicolor theory. On the left we represent the standard model. The oriented lines linking the walls to the $SU(2)_{L/R}$ circles are the leptons. The lines connecting the $SU(2)_{L/R}$ circles to $SU(3)_c$ are quarks. The dashed line is the ordinary Higgs field. On the right we have the same schematic picture except that now the Higgs is replaced by new gauge dynamics. Note that the oriented arrows terminate in the new $SU(2)$ of technicolor with two legs representing the two-index symmetric representation of SU(2). We have also added another left and right leptonic line. The new leptons are needed to avoid the global $SU(2)_L$ Witten anomaly.
• Figure 4: Left Panel: The black shaded parabolic area corresponds to the accessible range of $S$ and $T$ for the extra neutrino and extra electron for masses from $m_Z$ to $10 m_Z$. The perturbative estimate for the contribution to $S$ from techniquarks equals $1/2\pi$. The ellipses are the $90$% confidence level contours for the global fit to the electroweak precision data with $U$ kept at $0$. The values of $U$ in our model lie typically between $0$ and $0.05$ whence they are consistent with these contours. The contours from bottom to top are for Higgs masses of $m_H = 117$, $340$, $1000$ GeV, respectively. Right Panel: We added non-perturbative corrections to the $S$ parameter in the technicolor sector of the theory.
• Figure 5: Left Panel: The black shaded parabolic area corresponds to the accessible range of $S$ and $T$ for the new singly and doubly charged leptons with masses from $m_Z$ to $10 m_Z$. The perturbative estimate for the contribution to S from the techniquarks is $1/2\pi$. The ellipses are the $90$% confidence level contours for the global fit to the electroweak precision data with $U$ kept at $0$. The values of $U$ in our model lie typically between $0$ and $0.05$ and hence they are consistent with these contours. The contours from bottom to top are for Higgs masses of $m_H = 117$, $340$, $1000$ GeV, respectively. Right Panel: We added non-perturbative corrections to the $S$ parameter in the technicolor sector of the theory.