\left( \sum_{q} e^{2}_{q} \right)^{2} \left[ \int \frac{d\boldsymbol{k}^{2}}{\boldsymbol{k}^{6}} \; f_{g}(x,\boldsymbol{k}^{2}) \; {\cal{X}}(\boldsymbol{k}^{2},Q^{2}) \right]^{2}.\end{aligned}$$

An important feature considered by the Durham group is the suppression of the gluon emissions from the production vertex, i.e., gluons *bremsstrahlung* [@KMR-Rates]. The suppression probability $S$ for the emission of one gluon can be computed with the help of Sudakov form factors, such that $$\begin{aligned}
S(\boldsymbol{k}^{2},M^{2}_{H}) = \int^{M^{2}_{H}/4}_{\boldsymbol{k}^{2}} \frac{C_{A} \alpha_{s}(p^{2}_{T})}{\pi} \, \frac{dp^{2}_{T}}{p^{2}_{T}} \int^{M_{H}/2}_{p_{T}} \frac{dE}{E} = \frac{3 \alpha_{s}}{4 \pi} \ell n^{2} \left( \frac{M^{2}_{H}}{4\boldsymbol{k}^{2}} \right)
\label{sud-supress}\end{aligned}$$ where $E$ and $p_{T}$ are the energy and the transversal momentum of an emitted gluon in the rest-frame of the Higgs boson, respectively. The above result is obtained using a fixed strong coupling constant in the integration. The suppression of many emissions exponentiates, and an exponential term is introduced to the event rate $$\begin{aligned}
\left. \frac{d\sigma}{dy_{H}dt} \right|_{t,y_{_{H}} = 0} = \frac{1}{18 \pi^{3} b } \left( \frac{M^{2}_{H}}{N_{c}v} \right)^{2} \alpha_{s}^{4} \, \alpha^{2} \left( \sum_{q} e^{2}_{q} \right)^{2} \left[ \int_{\boldsymbol{k}^{2}_{0}}^{\infty} \frac{d\boldsymbol{k}^{2}}{\boldsymbol{k}^{6}} \; e^{-S(\boldsymbol{k}^{2},M^{2}_{H})} \; f_{g}(x,\boldsymbol{k}^{2}) \; {\cal{X}}(\boldsymbol{k}^{2},Q^{2}) \right]^{2},
\label{final-eq1}\end{aligned}$$ where a cutoff was included in the integration on the gluon momentum to avoid infrared divergences [@forshaw-KMR].

A last important aspect regarded to the diffractive process is the rapidity gaps present in the final state due to the 