NNLO QCD corrections to event shapes at the LHC

TL;DR

The paper delivers the first NNLO QCD calculation of jet-based event shapes at hadron colliders, addressing persistent discrepancies between data and NLO predictions. It employs sector-improved residue subtraction and leading-color approximations to compute NNLO corrections for multi-jet observables defined on reconstructed jets, including the TEEC. The results show substantial reductions in scale uncertainties (by factors of 2–4) and improved shape agreement with ATLAS data across most observables, while clearly signaling fixed-order limitations in narrow regions where resummation is required. The work also analyzes the sensitivity to the strong coupling constant ${\alpha_S}$, estimates non-perturbative corrections at the ${\sim}1\%$ level, and highlights the potential to extract $\alpha_S(m_Z)$ and its running to multi-TeV scales from LHC measurements.

Abstract

In this work we perform the first ever calculation of jet event shapes at hadron colliders at next-to-next-to leading order (NNLO) in QCD. The inclusion of higher order corrections removes the shape difference observed between data and next-to-leading order predictions. The theory uncertainty at NNLO is comparable to, or slightly larger than, existing measurements. Except for narrow kinematical ranges where all-order resummation becomes important, the NNLO predictions for the event shapes considered in the present work are reliable. As a prime application of the results derived in this work we provide a detailed investigation of the prospects for the precision determination of the strong coupling constant and its running through TeV scales from LHC data.

Figures (9)

• Figure 1: The transverse thrust $\tau_\perp$ (left) and the thrust minor $T_m$ (right) in three $H_{T,2}$ bins. The solid lines show fixed order LO (green), NLO (blue), and NNLO (red) predictions normalised to ATLAS data (black) ATLAS:2020vup. The coloured bands show the scale variation.
• Figure 2: As in fig. \ref{['fig:eventshapes-pQCD-1']} but for the transverse sphericity $S_{\perp}$ (left) and the aplanarity $A$ (right).
• Figure 3: As in fig. \ref{['fig:eventshapes-pQCD-1']} but for the variables $C$ (left) and $D$ (right).
• Figure 4: The TEEC variable in the inclusive $H_{T,2} \geq 1~\text{TeV}$ bin. The top panel shows the absolute differential distribution through LO (light green), NLO (blue) and NNLO (red) QCD. The coloured bands show the scale uncertainty estimates and vertical bars indicate statistical uncertainties. The second panel shows the ratio to the central NLO QCD prediction. The third panel shows the PDF uncertainty estimate from NNPDF30 at NLO QCD.
• Figure 5: The TEEC variable double differentially in $H_{T,2}$ bins. The panels show LO (light green), NLO (blue) and NNLO (red) QCD prediction as a ratio to the central NLO QCD prediction. The coloured bands show the scale uncertainty estimates and vertical bars indicate statistical uncertainties.