Section 4. Here it suffices to say, from the analysis [@KMRsoft] of all soft $pp$ data, that a conservative error on the values of $S^2$ is $\pm50\%$.

Combining together all these sources of error we find that the prediction for the $0^+$ cross section is uncertain to a factor of almost 2.5, that is up to almost 2.5, and down almost to $1/2.5$, times the default value.[^6] On the other hand, $0^-$ production is uncertain by this factor just from the first (infrared) source of error, with the remaining errors contributing almost another factor of 2.5. Although the rate of $h(0^-)$ production is very sensitive to the infrared contribution, and could indicate the presence of a significant non-perturbative contribution, we find that the form of the $\phi$ dependence is not. We discuss this point in Section \[sec:5\].

Note that the non-local structure of the amplitude leads to an extra angular dependence coming from the correlations between $\vec Q_\perp$ and the $\vec p_{i\perp}$ in the integral in [(\[eq:rat3\])]{}. In fact, expanding the gluon propagators gives corrections of the type Q\_p\_[3]{} / Q\_\^2,Q\_p\_[4]{} / Q\_\^2, \[eq:rat7\] which lead to an additional contribution of the form $-\vec p_{3\perp}\cdot \vec p_{4\perp}/Q_\perp^2$. This reflects the 