Jet-mass in V/H+jet up to four-loops with $k_t$ clustering

We extend the work of [1] to the case in which final-state jets, produced in association with a Higgs or vector boson, are defined using the $k_t$ algorithm. We thereby compute the full distribution of the invariant mass squared of the leading, highest-$p_t$ jet, including both clustering and non-global logarithms, up to four-loops in perturbation theory. Our results are derived within the eikonal approximation under the assumption of strong ordering in the momenta of the final-state partons, and are consequently valid up to single-logarithmic accuracy. The final semi-analytical expressions retain the complete dependence on both colour and the jet radius. The broad features of $k_t$ clustering observed in $e^+ e^-$ processes persist in hadronic collisions, together with novel characteristics that are absent in the $e^+ e^-$ environment.