Jet Veto Resummation with Jet Rapidity Cuts

Jet vetoes are widely used in experimental analyses at the LHC to distinguish different hard-interaction processes. Experimental jet selections require a cut on the (pseudo)rapidity of reconstructed jets, $|\eta_{\rm jet}| \leq \eta_{\rm cut}$. We extend the standard jet-$p_T$ (jet-veto) resummation, which implicitly works in the limit $\eta_{\rm cut}\to\infty$, by incorporating a finite 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 of experimental relevance to avoid the increased pile-up contamination beyond the reach of the tracking detectors. We identify all relevant parametric regimes, discuss their factorization and resummation as well as the relations between them, and show that the phenomenologically relevant regimes are free of large nonglobal logarithms. The $\eta_{\rm cut}$ dependence of all resummation ingredients 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 the jet-veto resummation including a sharp cut or a step at $\eta_{\rm cut}$ to the same 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 find that a rapidity cut at high $\eta_{\rm cut} = 4.5$ is safe to use and has little effect on the cross section. A sharp cut at $\eta_{\rm cut} = 2.5$ can in some cases lead to a substantial increase in the perturbative uncertainties, which can be mitigated by instead using a step in the veto.