Fig. \[fig:limit-sin.pdf\] - as can clearly be seen, the scaling of the Yukawa enhances the production cross-section in our model. As we move to larger $M_{H_t}$ values, $\sigma\, \cdot\, \text{BR}$ declines toward zero as the parton distribution function of the gluon falls rapidly.

![Constraints on $\sigma\cdot BR$ for top-Higgs production at the Tevatron as a function of $M_{H_t}$ and $\sin\omega$. One can clearly see how $\sin\omega < 1$ enhances the production cross-section. For a given value of $\sin\omega$, the range of masses for which the corresponding curve lies above the “Tevatron upper limit" curve is excluded. Each curve for fixed $\sin\omega$ falls off at small $M_{H_t}$ due to a decline in $BR(H_t \to WW)$ and drops off at high $M_{H_t}$ because the falling gluon pdf reduces the production cross-section $\sigma(gg \to H_t)$.[]{data-label="fig:limit-sin.pdf"}](limit-sin.pdf)

Turning to the top-pion, we find that there are more important constraints on the $\Pi_t$ masses than those derived from the Tevatron Higgs search limit. These constraints come from limits on rare top decays, from $Zb\bar{b}$ couplings, and from B-physics. We discuss these in turn below.

### Lower bound on the top-pion mass

If the charged top-pion $\Pi_t^+$ is lighter than the top quark, it can appear in 