flavor constraints tend to force $\epsilon_{tL} \simeq \epsilon_{L}$, so the value of this last parameter is set as well.

### Tevatron limits from Higgs searches {#sec:Higgs Limits}

The Tevatron experiments analyzed the channel $gg \to H \to WW$ and set upper bounds on the cross-section as a function of $M_H$ in Ref. [@Aaltonen:2010sv]. We can adapt this data to our model by appropriately rescaling the couplings involved in the following way: Because of the $\sin\omega$ factor in the denominator of Eq.  for $\lambda_t$ above, couplings of $H_t$ to top quarks are enhanced compared to those of the SM Higgs, particularly for small $\sin\omega$. This leads to an enhanced cross section for $H_t$ production in gluon fusion, scaling proportional to $(\lambda_t/\lambda_t^{\rm SM})^2$. Simultaneously, due to the absence of the decay mode $H_t \to b \bar b$ at low $H_t$ masses, the branching ratio for $H_t \to WW$ is larger than for the SM Higgs for masses below about 160 GeV. These two features lead to an enhancement of the predicted rate for $gg \to H_t \to WW$ compared to the corresponding SM process, which is already constrained by Tevatron data.

We can now translate the Tevatron bounds on the cross-section [@Aaltonen:2010sv] 