What Precision Electroweak Physics Says About the SU(6)/Sp(6) Little Higgs

TL;DR

The paper assesses precision electroweak constraints on the SU(6)/Sp(6) Little Higgs theory, identifying a near-oblique limit in which the heavy W' and B' gauge bosons decouple from light fermions and non-oblique corrections are suppressed. It computes oblique contributions from the gauge sector, non-linear sigma model, the two-Higgs-doublet sector, and the top sector, including finite one-loop top-induced corrections to the Higgs mass. The authors demonstrate that there exists parameter space with small $S$ and $T$ corrections and only mild Higgs-sector tuning, while allowing heavy states such as $W'$ at about $1.8$–$4.5$ TeV and a potentially light $B'$ (~a few hundred GeV) if its couplings to light fermions are suppressed. This work shows that naturalness and precision electroweak data can be compatible in this LH variant, with specific predictions for the Higgs spectrum and heavy-vector phenomenology relevant to collider searches.

Abstract

We study precision electroweak constraints on the close cousin of the Littlest Higgs, the SU(6)/Sp(6) model. We identify a near-oblique limit in which the heavy W' and B' decouple from the light fermions, and then calculate oblique corrections, including one-loop contributions from the extended top sector and the two Higgs doublets. We find regions of parameter space that give acceptably small precision electroweak corrections and only mild fine tuning in the Higgs potential, and also find that the mass of the lightest Higgs boson is relatively unconstrained by precision electroweak data. The fermions from the extended top sector can be as light as 1 TeV, and the W' can be as light as 1.8 TeV. We include an independent breaking scale for the B', which can still have a mass as low as a few hundred GeV.

Figures (12)

• Figure 1: Logarithmically divergent diagram to $T$ from quark doublets. The contractions of the $SU(2)_L$ indices are shown.
• Figure 2: $T$ as a function of $\delta m$ for $f=700 \text{ GeV}$, $\tan \beta=0.8$ and various values of $m_{q_H}$ as a function of $\delta m$. The plot on the right hand side shows T vs S for $f=700 \text{ GeV}$, $\tan \beta=0.8$ and $m_{q_H} = 2 \text{ TeV }$
• Figure 3: Dominant diagrams that contribute to $\mathcal{O}_{H q_3} ^L$ and $\mathcal{O}_{H q_3}^Y$ at tree level.
• Figure 4: Sketch of the parameter space that gives adequately small non-oblique corrections. The bounds on $f$ come from naturalness considerations (upper) and the requirement that the cutoff satisfies $\Lambda \,\hbox{$>$$\sim$}\, 10$ TeV (lower).
• Figure 5: Contributions to the $S$ and $T$ parameters for the reference parameter values of Sec. \ref{['Sec: Overview']}. The dashed ellipses are roughly the $1 \sigma$ and $2 \sigma$ limits in the $S-T$ plane.