Indeed let us consider the case of small $p_{i\perp}$ of the outgoing protons. Then, from [(\[eq:rat4\])]{}, we see that $V_{h(0^+)} \sim Q_\perp^2$, whereas $V_{h(0^-)} \sim p_{3\perp}p_{4\perp}$ (since the linear contribution in $Q_\perp$ vanishes after the angular integration). Thus the $d^2Q_\perp/Q_\perp^4$ integration for $h(0^+)$ is replaced by $p_{3\perp}p_{4\perp} d^2Q_\perp/Q_\perp^6$ for $h(0^-)$, and now the Sudakov suppression is not enough to prevent a significant contribution from the $Q_\perp^2\lesim1~\GeV^2$ domain.

Uncertainties
-------------

To estimate the uncertainty in the predictions for the $h^\pm(0)$ exclusive diffractive cross sections we first quantify the above uncertainty arising from the infrared region, where the gluon distribution is not well known. Fig. 4 shows the $\phi$ dependence of $h(0^-)$ and $h(0^+)$ production at the LHC, for $m_h=120$ GeV and $\mu=m_h/2$, using different treatments of the infrared region.

The continuous and dashed curves are calculated using MRST99 [@MRST99] and CTEQ6M [@CTEQ] partons respectively with the very low $Q$ gluon frozen at its value at $Q_{3,4}=1.3$ GeV. Then we integrate down in $Q_\perp$ until $Q_{3,4}$ are close to $\Lambda_{\rm QCD}$, where the contribution vanishes due to the presence of the $T$-factor. This will slightly overestimate the cross sections as the gluon density decreases with decreasing $Q^2$ for $x\sim0.01$. A lower extreme 