Cross Section Prediction for Inclusive Production of Z Boson in $pp$ Collisions at $\sqrt{s}$$=14$ TeV: A Study of Systematic Uncertainty Due to Scale Dependence

Abstract: Prediction of $Z\rightarrow l^{+}l^{-}$ production cross section (where $l^{\pm} =e^{\pm},\mu^{\pm}$) in proton-proton collisions at $\sqrt{s}$=14 TeV is estimated up to next-to-next-to-leading order (NNLO) in perturbative QCD including next-to-leading order (NLO) electroweak (EW) corrections. The total inclusive Z boson production cross section times leptonic branching ratio, within the invariant mass window $66<m_{ll}<116$ GeV, is predicted using NNLO HERAPDF2.0 at NNLO QCD and NLO EW as $\sigma_{Z}^{Tot}$= 2111.69${-26.92}^{+26.31}$ (PDF) $\pm11$ ($\alpha{s}$) $\pm$17 (scale) $^{+57.41}_{-30.98}$ (parameterization and model). Theoretical prediction of the fiducial cross section is further computed with the latest modern PDF models (CT14, MMHT2014, NNPDF3.0, HERAPDF2.0 and ABM12) at NNLO for QCD and NLO for EW. The central values of the predictions are based on DYNNLO 1.5 program and the uncertainties are extracted using FEWZ 3.1 program. In addition, the cross section is also calculated as functions of $\mu_{R}$ and $\mu_{F}$ scales. The choice of $\mu_{R}$ and $\mu_{F}$ for scale variation uncertainty is further discussed in details.