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

Abstract

We present results for the Drell-Yan process $pp\to Z/{\gamma }^{\ast }+X\to l^{+}{l}^{-}+X$ 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 $\mathcal{O}(10\text{ GeV})$.

26 pages, 14 figures

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