  We perform a phenomenological study of $Z$ plus jet, Higgs plus jet and
di-jet production at the Large Hadron Collider. We investigate in particular
the dependence of the leading jet cross section on the jet radius as a function
of the jet transverse momentum. Theoretical predictions are obtained using
perturbative QCD calculations at the next-to and next-to-next-to-leading order,
using a range of renormalization and factorization scales. The fixed order
predictions are compared to results obtained from matching next-to-leading
order calculations to parton showers. A study of the scale dependence as a
function of the jet radius is used to provide a better estimate of the scale
uncertainty for small jet sizes. The non-perturbative corrections as a function
of jet radius are estimated from different generators.
