Constructing all-order corrections to multi-jet rates

We discuss the universal behaviour of scattering cross sections in the limit of infinite rapidity separation between all produced particles, and illustrate the behaviour explicitly for the production of n jets, W + n jets, Z + n jets for n = 2, 3, 4, and for H + 2, 3 jets. We give a set of rules for constructing scattering cross sections, which are exact in the given limit, and order-by-order reproduce well the full fixed order results when applied to LHC phenomenology. The approximation includes both real and virtual corrections, and is sufficiently simple to allow for the regulated all-order perturbative sum to be explicitly constructed. We test the expected accuracy by comparing results orderby-order with full fixed-order perturbation theory for the processes mentioned above.