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We discuss many new subleading processes for inclusive production of $W^+W^-$ pairs not included in the literature so far. We focus on photon-photoninduced processes. We include elastic-elastic, elastic-inelastic,inelastic-elastic and inelastic-inelastic contributions. The inelastic photondistributions in the proton are calculated in two different ways: naiveapproach used already in the literature and using photon distributions bysolving special evolution equation with photon being a parton in the proton.The results strongly depend on the approach used. We calculate alsocontributions with resolved photons. The diffractive components have similarcharacteristics as the photon-photon elastic-inelastic and inelastic-elasticmechanisms. The subleading contributions are compared with the well known $q\bar q$ and $g g$ as well as with double-parton scattering contributions.Predictions for the total cross section and differential distributions in $W$-boson rapidity and transverse momentum as well as $WW$ invariant mass arepresented. The $\gamma \gamma$ components constitute only about 1-2 % of theinclusive $W^+ W^-$ cross section but about 10 % at large $W^{\pm}$ transversemomenta, and are even comparable to the dominant $q \bar q$ component at large$M_{WW}$, i.e. are much larger than the often celebrated $g g \to W^+ W^-$component. Its size is comparable to double parton scattering contribution.Only elastic-elastic, elastic-inelastic and inelastic-elastic contributionscould be potentially measured to verify our predictions using forward protondetectors.

Subleading processes in production of $W^+ W^-$ pairs in proton-proton collisions