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Jet vetoes are widely used in experimental analyses at the LHC to distinguishdifferent hard-interaction processes. Experimental jet selections require a cuton the (pseudo)rapidity of reconstructed jets, $|\eta_{\rm jet}| \leq \eta_{\rmcut}$. We extend the standard jet-$p_T$ (jet-veto) resummation, whichimplicitly works in the limit $\eta_{\rm cut}\to\infty$, by incorporating afinite jet rapidity cut. We also consider the case of a step in the required$p_T^{\rm cut}$ at an intermediate value of $|\eta| \simeq 2.5$, which is ofexperimental relevance to avoid the increased pile-up contamination beyond thereach of the tracking detectors. We identify all relevant parametric regimes,discuss their factorization and resummation as well as the relations betweenthem, and show that the phenomenologically relevant regimes are free of largenonglobal logarithms. The $\eta_{\rm cut}$ dependence of all resummationingredients is computed to the same order to which they are currently known for$\eta_{\rm cut}\to\infty$. Our results pave the way for carrying out thejet-veto resummation including a sharp cut or a step at $\eta_{\rm cut}$ to thesame order as is currently available in the $\eta_{\rm cut}\to\infty$ limit.The numerical impact of the jet rapidity cut is illustrated for benchmark$q\bar q$ and $gg$ initiated color-singlet processes at NLL$'+$NLO. We findthat a rapidity cut at high $\eta_{\rm cut} = 4.5$ is safe to use and haslittle effect on the cross section. A sharp cut at $\eta_{\rm cut} = 2.5$ canin some cases lead to a substantial increase in the perturbative uncertainties,which can be mitigated by instead using a step in the veto.

Jet Veto Resummation with Jet Rapidity Cuts