Single-jet inclusive rates with exact color at $\mathcal{O}(α_s^4)$

TL;DR

The paper independently verifies that sub-leading color effects at O(αs^4) are negligible for single-jet inclusive double-differential cross sections within NNLO QCD, using a refined sector-improved residue subtraction with minimal subtraction terms. It introduces modifications to phase-space parameterisations and a four-dimensional formulation via 't Hooft-Veltman corrections, implemented in Stripper and validated against NNLOjet. The 13 TeV jet-rate results show agreement with existing NNLO predictions within uncertainties, justifying the leading-color treatment for practical PDFs fits and highlighting the method's potential for broader NNLO applications. The work also discusses computational costs, potential fast-grid integrations, and avenues to further optimize the subtraction scheme.

Abstract

Next-to-next-to-leading order QCD predictions for single-, double- and even triple-differential distributions of jet events in proton-proton collisions have recently been obtained using the NNLOjet framework based on antenna subtraction. These results are an important input for Parton Distribution Function fits to hadron-collider data. While these calculations include all of the partonic channels occurring at this order of the perturbative expansion, they are based on the leading-color approximation in the case of channels involving quarks and are only exact in color in the pure-gluon channel. In the present publication, we verify that the sub-leading color effects in the single-jet inclusive double-differential cross sections are indeed negligible as far as phenomenological applications are concerned. This is the first independent and complete calculation for this observable. We also take the opportunity to discuss the necessary modifications of the sector-improved residue subtraction scheme that made this work possible.

Figures (3)

• Figure 1: Decomposition tree of the triple-collinear sector unresolved phase space. The omitted right branch of the tree corresponds to a different ordering of the energies of the unresolved partons, and can be obtained by renaming the indices of the variables, $1 \leftrightarrow 2$. The function $\bar{\xi}_2$ is defined implicitly in Eq. (\ref{['eq:OneRefMomEnergies']}).
• Figure 2: Double-differential single jet inclusive cross-sections as measured by CMS Khachatryan:2016wdh and NNLO perturbative QCD predictions as a function of the jet $p_T$ in slices of rapidity, for anti-$k_T$ jets with R = 0.7 normalised to the NLO result. Both perturbative predictions, NLO and NNLO, have been obtained with the PDF4LHC15_nnlo PDF set and with $\mu_R = \mu_F = 2p_T$. The shaded bands represent the scale uncertainty obtained from differential distributions evaluated at $\mu_R = \mu_F = p_T$ and $\mu_R = \mu_F = 4p_T$.
• Figure 3: Comparison of the cross section ratios depicted in Fig. \ref{['fig:inclusive-jet-pTxY']} as obtained with NNLOjetCurrie:2018xkj (red line with scale variation error, leading-color approximation for channels involving quarks) and with Stripper (black points with Monte Carlo integration error bars, as given in Appendix \ref{['app:k-factors']}, exact in color). This figure has been obtained from Fig. 21 of Currie:2018xkj by removing the experimental data points as well as the scale variation band of the NLO calculation, followed by superimposing the results obtained in the present work.