$V/H$+Jet Production with the Cambridge/Aachen Algorithm

We present fixed-order perturbative calculations up to four-loop order for a generic non-global QCD observable in hadron-hadron collisions. Specifically, we study the invariant-mass distribution of the highest-$p_t$ jet produced in association with a vector boson or a Higgs boson, where jets are defined using the Cambridge/Aachen sequential recombination algorithm. This work is part of a series of papers~\cite{Khelifa-Kerfa:2015mma, Khelifa-Kerfa:2024hwx, Khelifa-Kerfa:2024dut, Khelifa-Kerfa:2025cdn, Khelifa-Kerfa:2024udm, Khelifa-Kerfa:2025jev} examining the impact of various jet algorithms on the perturbative structure of non-global observables across different collision environments. We find that at fixed order the Cambridge/Aachen algorithm suppresses the large non-global logarithms more effectively than the anti-$k_t$ and $k_t$ algorithms, while at all orders it performs comparably to the $k_t$ algorithm. Furthermore, comparisons of all-orders resummed form factors reveal that finite-$N_c$ corrections remain at the percent level, consistent with previous findings.