The Drell-Yan Process at NNLL$^\prime$+NNLO using Rapidity Dependent Jet Vetoes

We present results for the Drell-Yan process $pp \to Z/\gamma^* + X \to l^+l^- + X$ in the presence of the rapidity dependent jet vetoes $\mathcal{T}_{Bj}$ and $\mathcal{T}_{Cj}.$ These observables provide a tighter veto at central rapidities than at forward rapidities. Our predictions contain a resummation of large logarithms of the veto scale over the hard scale, matched to fixed order in perturbation theory; we present results at both NLL$^\prime$+NLO and NNLL$^\prime$+NNLO. Uncertainty estimates are provided that contain both resummation and fixed-order uncertainties; we find that using a standard profile scale variation procedure for the former seems to underestimate the uncertainty, particularly at NLL$^\prime$+NLO. Consequently, we modify the procedure to avoid cancellation of scale variations between partonic channels, and verify that the uncertainties from this method are reasonable using a simplified version of the Theory Nuisance Parameter (TNP) method. We then find that the uncertainty decreases going from the NLL$^\prime$+NLO to the NNLL$^\prime$+NNLO predictions, and obtain an uncertainty at the level of $1-3\%$ in the NNLL$^\prime$+NNLO predictions when the veto scale is of $\mathcal{O}(10 \text{ GeV})$.