Correlated theoretical uncertainties for the one-jet inclusive cross section

TL;DR

The paper develops a defensible framework to quantify correlated theoretical uncertainties in NLO QCD predictions for the one-jet inclusive cross section in hadron collisions. By expressing the prediction as a central NLO value multiplied by a sum of smooth, partially correlated error functions f_J with Gaussian coefficients, the authors separate perturbative and non-perturbative contributions and provide explicit forms for Tevatron and LHC kinematics. They validate the approach via scale-dependence analyses, contour mappings, and threshold-log considerations, and they quantify non-perturbative corrections from underlying event and hadronization, translating these into cross-section shifts. The resulting 7-function decomposition enables practical inclusion of theory errors in fits to jet data and PDFs, facilitating robust comparisons between SM predictions and experimental results at both the Tevatron and LHC.

Abstract

We discuss the correlated systematic theoretical uncertainties that may be ascribed to the next-to-leading order QCD theory used to predict the one-jet inclusive cross section in hadron collisions. We estimate the magnitude of these errors as functions of the jet transverse momentum and rapidity. The total theoretical error is decomposed into a set of functions of transverse momentum and rapidity that give a model for statistically independent contributions to the error. This representation can be used to include the systematic theoretical errors in fits to the experimental data.

Figures (12)

• Figure 1: illustration of (a) uncorrelated and (b) correlated theoretical errors. In (a), the total error is about 10% for all $P_{T}$, but the error at any $P_{T}$ is not correlated with the error at nearby points. In (b), there are just three functions $f_{J}(P_{T})$ giving, again, about a 10% total error at any one $P_{T}$. Because the $f_{J}(P_{T})$ are smooth functions, the theoretical error at a given $P_{T}$ will be smoothly related to the error at other $P_{T}$ values.
• Figure 2: Contour plot of the jet cross section in the $\{x_{1},x_{2}\}$ plane for the Tevatron ($\sqrt{s}=1960$ GeV) with $P_{T}=100$ GeV and a) central rapidity $y=0$ and b) forward rapidity $y=2$. We plot the ratio of the cross section compared to the central value at $\{x_{1},x_{2}\}=\{0,0\}$. Contour lines are drawn at intervals of 0.10. The (red) circle is at radius $|x|=2$.
• Figure 3: The cross section for Higgs production at the LHC for LO, NLO, and NNLO calculations as taken from Ref. Anastasiou:2007mz. The computed cross section vetos jets ($P_{T}^{\rm jet}>P_{T}^{\rm veto}$) in the central region $|\eta|<2.5$.
• Figure 4: The estimate of the uncertainty ${\cal E}(P_T,y) = {\cal E}_{\rm scale}$ due to the scale variation as given in Eq. (\ref{['eq:Escaleresult']}) for the Tevatron ($\sqrt{s}=1960$ GeV) with $y=\{0,1,2\}$. The calculation from the jet code is represented by the (blue) points, and the fit based on Eq. (\ref{['eq:neterror']}) is shown with the solid (red) curve.
• Figure 5: The estimate of the uncertainty ${\cal E}_{\rm scale}$ due to the scale variation as given in Eq. (\ref{['eq:Escaleresult']}) for the Tevatron ($\sqrt{s}=1960$ GeV) with $y=\{0,1,2\}$. The combined uncertainty ${\cal E}_{\rm scale}$ is shown as the upper thick (red) curve, and the individual functions $f_{J}(P_{T},y)$ are indicated below.