Modelling the underlying event in photon-initiated processes

Modelling the underlying event in high-energy hadronic collisions is important for physics at colliders. This includes lepton colliders, where low-virtuality photons accompanying the lepton beam(s) may develop hadronic structure. Similarly, photon-induced collisions also occur in proton or heavy-ion beam experiments. While the underlying event in proton-proton collisions has been the subject of much study at the LHC, studies of hadronic-photon-induced underlying event are now of increasing interest in light of planned future lepton and lepton-hadron colliders, as well as the photon-induced processes in ultra-peripheral collisions at the LHC. Here we present an investigation of the underlying event in photon-initiated processes, starting from the Pythia models used to describe LHC and Tevatron data, and revisiting HERA and LEP2 data. While no single tune describes all the data with different beam configurations, we find that a good agreement can still be found within the same model by adjusting the relevant parameters separately for \gamma\gammaγγ, \gamma pγp and pppp. This suggests that the basic model of multiparton interaction implemented in Pythia can be applied for different beam configurations. Furthermore, we find that a reasonable agreement for \gamma\gammaγγ and \gamma pγp data, and for pppp data at an LHC reference energy, can be found within a single parametrization, but pppp collisions would prefer a stronger energy dependence, leading to too many multiparton interactions in lower energy photon-induced collisions. On this basis, we make some recommendations for simulations of photon-induced processes, such as \gamma \gammaγγ events at the LHC or FCC and epep or eAeA collisions at the EIC, and suggest possibilities for improvements in the modelling.