  Many experimental analyses separate events into exclusive jet bins, using a
jet algorithm to cluster the final state and then veto on jets. Jet clustering
induces logarithmic dependence on the jet radius R in the cross section for
exclusive jet bins, a dependence that is poorly controlled due to the
non-global nature of the clustering. At jet radii of experimental interest, the
leading order (LO) clustering effects are numerically significant, but the
higher order effects are currently unknown. We rectify this situation by
calculating the most important part of the next-to-leading order (NLO)
clustering logarithms of R for any 0-jet process, which enter as
$O(\alpha_s^3)$ corrections to the cross section. The calculation blends
subtraction methods for NLO calculations with factorization properties of QCD
and soft-collinear effective theory (SCET). We compare the size of the known LO
and new NLO clustering logarithms and find that the impact of the NLO terms on
the 0-jet cross section in Higgs production is small. This brings clustering
effects under better control and may be used to improve uncertainty estimates
on cross sections with a jet veto.
