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We calculate the cross section for $p p \to W^{+} W^-$ in the recentlydeveloped $k_{\rm T}$-factorisation approach, including transverse momenta ofthe virtual photons. We focus on processes with single and double protondissociation. First we discuss the gap survival on the parton level as due tothe emission of extra jet. Both the role of valence and sea contributions isdiscussed. The hadronisation of proton remnants is performed with {PYTHIA 8}string fragmentation model, assuming a simple quark-diquark model for proton.Highly excited remnant systems hadronise producing particles that can be vetoedin the calorimeter. We calculate associated effective gap survival factors. Thegap survival factors depend on the process, mass of the remnant system andcollision energy. The rapidity gap survival factor due to remnant fragmentationfor double dissociative (DD) collisions ($S_{R,DD}$) is smaller than that forsingle dissociative (SD) process ($S_{R,SD}$). We observe the approximatefactorisation $S_{R,DD} \approx (S_{R,SD})^2$, however it is expected that thisproperty will be violated by soft rescattering effects not accounted for inthis letter.

physics letters b

Rapidity gap survival factors caused by remnant fragmentation for $W^+  W^-$ pair production via $\gamma^*\gamma^* \to W^+ W^-$ subprocess with  photon transverse momenta