Single jet inclusive production for the individual jet $p_{T}$ scale choice at the LHC

TL;DR

The paper delivers NNLO QCD predictions for the fully differential single jet inclusive cross section using the NNLOJET framework with antenna subtraction. It compares two scale choices—individual jet $p_T$ ($\mu_R=\mu_F=p_T$) and leading-jet $p_T$ ($\mu_R=\mu_F=p_{T1}$)—and studies their impact against ATLAS 7 TeV data with $R=0.4$ jets. The results show that NNLO corrections can improve agreement with data in some regions, but the optimal scale choice remains ambiguous, with significant differences at low $p_T$ and converging behavior at high $p_T$, highlighting the need for further exploration of scale definitions. The findings emphasize the ongoing scale ambiguity in jet production and motivate exploration of non-standard scales to maximize the phenomenological impact of jet data on PDFs and $\alpha_s$ determinations.

Abstract

We study the single jet inclusive cross section up to next-to-next-to leading order in perturbative QCD, implemented in the parton-level event generator NNLOJET . Our results are fully differential in the jet transverse momentum and rapidity and we apply fiducial cuts for comparison with the available ATLAS 7 TeV 4.5 fb$^{-1}$ data for jet radius $R=0.4$. For the theoretical calculation we employ the antenna subtraction method to reliably cancel all infrared divergences present at intermediate stages of the calculation. We present all results using the individual jet transverse momentum $μ_{R}=μ_{F}\sim p_{T}$ as the renormalization and factorization scale for each jet's contribution to the single jet inclusive cross section. Finally, we consider the differences between our predictions using this scale choice to those for the leading jet transverse momentum scale choice, $μ_{R}=μ_{F}\sim p_{T_{1}}$, used in [14], with reference to the ATLAS data.

Figures (6)

• Figure 1: The fraction of jets associated with a given initial-state for inclusive jet production calculated at LO for the LHC at 7 TeV. The different bands denote different initial-states: $gg$ (green), $qg$ (blue), $qq$ (red). The relative size of the contributions goes from $gg>qg>qq$ at low $p_{T}$ to an inverted hierarchy $qq>qg>gg$ at high $p_{T}$.
• Figure 2: NLO/LO (green), NNLO/NLO (red) and NNLO/LO (blue) $K$-factors for jet production at $\sqrt{s}=7$ TeV. The lines correspond to the double differential $K$-factors (ratios of perturbative predictions in the perturbative expansion) for $p_T > 100$ GeV and across six rapidity $|y|$ slices. Lines correspond to theoretical predictions evaluated with NNLO PDFs from NNPDF3.0 and central scale choice $\mu_{R}=\mu_{F}=p_{T}$.
• Figure 3: The scale variation of the cross section at LO (green), NLO (blue) and NNLO (red) for central rapidity and three different $p_{T}$ bins: (a) 100 GeV$<p_{T}<$116 GeV, (b) 290 GeV$<p_{T}<$318 GeV, (c) 642 GeV$<p_{T}<$688 GeV.
• Figure 4: The NLO (green), NNLO (blue) and ATLAS data normalized to the NLO prediction for the individual jet $p_{T}$ scale choice. The bands correspond to the variation of $\mu=\mu_{R}=\mu_{F}$ by factors of 0.5 and 2 about the central scale choice. Electroweak correction are applied multiplicatively and separately represented as a dashed red line.
• Figure 5: The NLO predictions normalized to data for two different scale choices, individual jet $p_{T}$ (red) and leading jet $p_{T}$ (green). The bands correspond to the variation of $\mu=\mu_{R}=\mu_{F}$ by factors of 0.5 and 2 about the central scale choice.