to scatter elastically on the proton. $b$ is the impact parameter of the overall collision while $Y=\ell n 1/x$ is the rapidity of the softest gluon with respect to the proton. In $lowest\ order,$ two-gluon exchange,

$$1-S \propto {x_PG(x_P,k_\perp^2)\over k_\perp^2}\eqno(3.7)$$

when $k_\perp$ is large and where an integration has been performed over impact parameter, $\b{b}.$ Using (3.6) and (3.7) in (3.5) one sees, dimensionally, that $k_\perp^2$ cannot be large and this is the logic that has led theorists to take $k_\perp \approx \mu$ and use soft pomeron exchange for the scattering amplitude, $1-S.$

However, if $S$ is near zero for $k_\perp = \mu$ and for $\b{b} =
0,$ and this is not unreasonable since the $S$ matrix is near zero for small impact parameter hadron-hadron collisions, then it is apparent from (3.5) and (3.6) that values of $k_\perp$ significantly larger than $\mu$ will be important. Indeed, the values of $k_\perp$ that will dominate large mass single diffractive production are those values where $S$ is near, but not too close to, one. This is the case since the probability in the $\gamma^*$ wavefunction is located in large $k_\perp-$ values. The situation here is quite different than for hadron-hadron collisions. In hadron-hadron 