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

We discuss new subleading processes for inclusive production of $W^+ W^-$ pairs. We focus mainly on photon-photon induced processes. We include elastic-elastic, elastic-inelastic, inelastic-elastic and inelastic-inelastic contributions. The inelastic photon distributions in the proton are calculated in two different ways: naive approach used already in the literature and using photon distributions by solving special evolution equations with the photon being a parton in the proton. The results strongly depend on the approach used. The resolved photon contribution was calculated in addition and found to be small. We also calculate the cross section for single-diffractive production of $W^+ W^-$ pairs including pomeron and reggeon exchanges in the Ingelman-Schlein model. Finally we only mention here about double parton contribution which is interesting by itself.