Factorisation of soft gluons in multiparton scattering

We show that soft gluons exchanged between the two colliding protons in multiparton scattering processes can be decoupled, such that their effects are described by the vacuum expectation values of Wilson lines. Our argument relies on nonabelian Ward identities and generalises the proof of factorisation for single Drell-Yan production given by Collins, Soper and Sterman.