Phenomenology of the Little Higgs Model

TL;DR

This work analyzes the littlest Higgs model as a concrete realization of the little Higgs mechanism, where the Higgs arises as a pseudo-Goldstone boson protected from one-loop quadratic divergences by a collective symmetry breaking pattern. It linearizes the theory, derives the spectrum and couplings of new states (heavy gauge bosons W_H, Z_H, A_H; a vector-like top partner T; and a scalar triplet Φ), and uses electroweak precision data to discuss custodial SU(2) breaking and potential model extensions that can alleviate constraints. The paper highlights robust collider signatures at the LHC, including multi-TeV heavy gauge bosons and the top partner T, as well as Higgs sector signatures like a doubly charged Φ^{++}, and it emphasizes the role of future linear colliders in probing triple gauge couplings and higher scales. It also provides detailed appendices with the linearized Lagrangian and Feynman rules to facilitate phenomenological studies. Collectively, the results indicate that while precision constraints push the symmetry-breaking scale f to several TeV, the LHC has strong prospects to test the core predictions of the littlest Higgs framework, with linear colliders offering complementary sensitivity to the underlying new physics.

Abstract

We study the low energy phenomenology of the little Higgs model. We first discuss the linearized effective theory of the "littlest Higgs model" and study the low energy constraints on the model parameters. We identify sources of the corrections to low energy observables, discuss model-dependent arbitrariness, and outline some possible directions of extensions of the model in order to evade the precision electroweak constraints. We then explore the characteristic signatures to test the model in the current and future collider experiments. We find that the LHC has great potential to discover the new SU(2) gauge bosons and the possible new U(1) gauge boson to the multi-TeV mass scale. Other states such as the colored vector-like quark T and doubly-charged Higgs boson Phi^{++} may also provide interesting signals. At a linear collider, precision measurements on the triple gauge boson couplings could be sensitive to the new physics scale of a few TeV. We provide a comprehensive list of the linearized interactions and vertices for the littlest Higgs model in the appendices.

Figures (6)

• Figure 1: Theoretical lower bounds on the heavy state masses versus the scale $f/v$ (bottom axis) or $f$ in TeV (top axis). For $M_\Phi$, we obtain the lower bound by assuming $m_H\ge 115$ GeV; the long-dashed curve is indistinguishable from that of $M_{W_H}$.
• Figure 2: (a) Total cross section for $Z_H$ production versus its mass $M_{Z_H}$ at the Tevatron (dashed) and the LHC (solid) for $\cot\theta=1$. The number of events expected per 300 fb$^{-1}$ luminosity is indicated on the right-hand axis. The scale $f$ corresponding to $\cot\theta=1$ is given on the top axis; (b) $Z_H$ decay branching fractions versus $\cot\theta$.
• Figure 3: (a) Total cross section for $A_H$ production versus its mass $M_{A_H}$ at the Tevatron (dashed) and the LHC (solid) for $\tan\theta' =1$. The number of events expected per 300 fb$^{-1}$ luminosity is indicated on the right-hand axis. The scale $f$ corresponding to $\tan\theta'=1$ is given on the top axis; (b) $A_H$ decay branching fractions versus $\tan\theta'$. The fermion hypercharge assignments are fixed by the anomaly-free condition.
• Figure 4: $A_H$ Decay branching fractions for $\tan\theta'=1$ (a) versus the charged lepton $U(1)$ hypercharge $y_e$ with fixed $y_u=-0.4$, and (b) versus up-quark hypercharge $y_u$ with fixed $y_e=0.6$. The vertical dotted lines indicate the hypercharge values determined by the anomaly-free condition.
• Figure 5: Total cross sections for $T\bar{T}$ production (dashed) and $T+$jet production (solid and dotted) via $t$-channel $W$-exchange versus mass $M_T$ at the LHC. The solid line is for the couplings $\lambda_1=\lambda_2$; the dotted are for $\lambda_1/\lambda_2=2$ (upper) and 1/2 (lower). The number of events expected per 300 fb$^{-1}$ luminosity is indicated on the right-hand axis. The scale $f$ corresponding to $\lambda_1=\lambda_2$ is given on the top axis.