we list the mass-basis couplings in Appendix C for completeness.

               Vertex                                                                                                                                                                                      Strength
  -------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     $H_t\,t_{L}\bar{t}_R+h.c$                                                                                                                    $\frac{\lambda_t}{\sqrt{2}}\left[-1+\frac{(1+a^2)(x^2+2 \epsilon_{tR}^2)+4\sqrt{2}ax\, \epsilon_{tR}}{4(a^2-1)^2} \right]$
     $H_t\,T_{L}\bar{T}_R+h.c$                                                                                                                      $-\frac{\lambda_t}{\sqrt{2}}\left[\frac{a (x^2+2 \epsilon_{tR}^2)+\sqrt{2}(1+a^2)x\,\epsilon_{tR}}{2(a^2-1)^2} \right]$
     $H_t\,t_{L}\bar{T}_R+h.c$                                                                                                                                               $\lambda_t \left[\frac{a\,x+\sqrt{2}\epsilon_{tR}}{2(a^2-1)} \right]$
     $H_t\,t_{R}\bar{T}_L+h.c$                                                                                                                                               $\lambda_t \left[\frac{x+\sqrt{2}a\,\epsilon_{tR}}{2(a^2-1)} \right]$
    $\Pi_{t}^0\bar{t}_Lt_R-h.c.$                                $\frac{i\lambda_t}{\sqrt{2}}\left[-\textrm{cos}\,\omega + \frac{(a^2+\textrm{cos}2\omega)\textrm{sec}\,\omega(x^2+2\,\epsilon_{tR}^2)+\frac{2\sqrt{2}}{a}x\,\epsilon_{tR}\left[2a^2\textrm{cos}\,\omega+(a^2-1)\textrm{sin}\,\omega\,\textrm{tan}\,\omega \right]}{4\sqrt{2}(a^2-1)^2} \right]$
    $\Pi_{t}^0\bar{T}_LT_R-h.c.$                                                                  $\frac{i\lambda_t}{4\sqrt{2}}\left[\frac{ 2\sqrt{2}\,x\,\epsilon_{tR}(a^2+\textrm{cos}2\omega)+(2a^2\textrm{cos}\,\omega+(a^2-1)\textrm{sin}\,\omega\,\textrm{tan}\,\omega)\,(x^2+2\,\epsilon_{tR}^2)}{(a^2-1)^2} \right]$
    $\Pi_{t}^0\bar{t}_LT_R-h.c.$                                                                                              $\frac{i\lambda_t}{(a^2-1)}\left[\frac{x\textrm{sec}\,\omega(-1+3a^2+(1+a^2)\,\textrm{cos}2\omega)}{8a}+\frac{\epsilon_{tR}\textrm{cos}\,\omega}{\sqrt{2}} \right]$
    $\Pi_{t}^0\bar{T}_Lt_R-h.c.$                                                                                           $\frac{i\lambda_t}{(a^2-1)}\left[\frac{x\,\textrm{cos}\,\omega}{2}+\frac{\epsilon_{tR}\,\textrm{sec}\,\omega(-1+3a^2+(1+a^2)\,\textrm{cos}2\omega)}{4\sqrt{2}a} \right]$
   $\Pi_{t}^{-}t_R\bar{b}_L-h.c.$   $i\lambda_t\left[\textrm{cos}\,\omega-\frac{x^2\left(a^4+(a^4-2a^2+2)\,\textrm{cos}2\omega \right)\textrm{cos}\,\omega}{8(a^2-1)^2}-\frac{x\,\epsilon_{tR}\,\textrm{sec}\,\omega \left(-2+5a^2-a^4+(a^4-a^2+2)\,\textrm{cos}2\omega \right)\textrm{cos}\,\omega}{4\sqrt{2}a(a^2-1)^2}-\frac{\epsilon_{tR}^2\,\textrm{cos}\,\omega}{2(a^2-1)^2} \right]$
   $\Pi_{t}^{-}T_R\bar{B}_L-h.c.$                                                            $\frac{i\lambda_t\,\textrm{sec}\,\omega}{(a^2-1)}\left[-\frac{x^2\,(-1+3a^2+(1+a^2)\,\textrm{cos}2\omega)}{8a}-\frac{x\,\epsilon_{tR}(1+3\textrm{cos}2\omega)}{4\sqrt{2}a}+\frac{\textrm{sin}^2\omega\,\epsilon_{tR}^2}{2a} \right]$
   $\Pi_{t}^{-}T_R\bar{b}_L-h.c.$                                                                                         $-\frac{i\lambda_t}{(a^2-1)}\left[\frac{x\left(-1+3a^2+(1+a^2)\,\textrm{cos}2\omega \right)\,\textrm{sec}\,\omega}{4\sqrt{2}a}+\epsilon_{tR}\,\textrm{cos}\,\omega \right]$
   $\Pi_{t}^{-}t_R\bar{B}_L-h.c.$                                                                                                           $i\lambda_t\left[\frac{x\,\textrm{cos}\,\omega}{\sqrt{2}}-\frac{\epsilon_{tR}\,\textrm{sin}\,\omega\,\textrm{tan}\,\omega}{2a} \right]$

  : The couplings of the top-Higgs and top pions to third generation fermions and their heavy partners, calculated to $\mathcal{O}(x^{2},\epsilon_{tR}^2)$.

\[tab:H-fermion\]

Top-Higgs and top-pion phenomenology {#sec:pheno}
====================================

We are now prepared to investigate the phenomenology of the new states related to the top quark: the top-Higgs $(H_t)$, the top-pions $(\Pi_t)$, and the heavy vector fermion partner of the top quark $(T)$. First, we will show how existing Tevatron data can be applied to place limits on the top triangle moose model. Essentially, rescaling to take altered coupling values into account allows limits derived for other models to be transformed into limits on our model’s top-pions and top-Higgs. Next, we study top-Higgs and top-pion production at LHC. As indicated in Figure (\[fig:higgs\_prod\]) below, the new scalars can be produced either directly, through gluon fusion via a top 