  We present a new framework for calculating multi-jet observables. The
framework is based on the factorisation of scattering amplitudes in the
kinematical limit of large invariant mass between all particles. We show that
by constraining the analyticity of scattering amplitudes away from this limits,
we get good agreement order by order with the full, fixed order perturbative
calculation at the low orders where these are available, and therefore get firm
predictions on the all-order behaviour. As an example, we study Higgs boson
production through gluon fusion in association with at least two jets at the
LHC.
