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Power Corrections in the N-jettiness Subtraction Scheme

Radja Boughezal, Xiaohui Liu, Frank Petriello

TL;DR

This work analyzes and computes leading-logarithmic power corrections (LL$_P$) in the N-jettiness subtraction scheme to improve NNLO QCD predictions for hadron colliders. It derives the NLO LL$_P$ for arbitrary $N$-jet processes and gives explicit NNLO LL$_P$ results for color-singlet production in both $q\bar{q}$ and $gg$ initial states, using SCET and the method of regions. The final results are compact analytic expressions that include PDF derivatives and soft-quark contributions, enabling larger $\tau_N^{cut}$ values and much faster numerical convergence in practical NNLO calculations (e.g., Drell–Yan and Higgs production at the LHC). The numerical studies confirm dramatic efficiency gains, and the authors discuss extensions to multi-jet final states and possible resummation approaches, highlighting the practical impact on precision collider phenomenology.

Abstract

We discuss the leading-logarithmic power corrections in the $N$-jettiness subtraction scheme for higher-order perturbative QCD calculations. We compute the next-to-leading order power corrections for an arbitrary $N$-jet process, and we explicitly calculate the power correction through next-to-next-to-leading order for color-singlet production for both $q\bar{q}$ and $gg$ initiated processes. Our results are compact and simple to implement numerically. Including the leading power correction in the $N$-jettiness subtraction scheme substantially improves its numerical efficiency. We discuss what features of our techniques extend to processes containing final-state jets.

Power Corrections in the N-jettiness Subtraction Scheme

TL;DR

This work analyzes and computes leading-logarithmic power corrections (LL) in the N-jettiness subtraction scheme to improve NNLO QCD predictions for hadron colliders. It derives the NLO LL for arbitrary -jet processes and gives explicit NNLO LL results for color-singlet production in both and initial states, using SCET and the method of regions. The final results are compact analytic expressions that include PDF derivatives and soft-quark contributions, enabling larger values and much faster numerical convergence in practical NNLO calculations (e.g., Drell–Yan and Higgs production at the LHC). The numerical studies confirm dramatic efficiency gains, and the authors discuss extensions to multi-jet final states and possible resummation approaches, highlighting the practical impact on precision collider phenomenology.

Abstract

We discuss the leading-logarithmic power corrections in the -jettiness subtraction scheme for higher-order perturbative QCD calculations. We compute the next-to-leading order power corrections for an arbitrary -jet process, and we explicitly calculate the power correction through next-to-next-to-leading order for color-singlet production for both and initiated processes. Our results are compact and simple to implement numerically. Including the leading power correction in the -jettiness subtraction scheme substantially improves its numerical efficiency. We discuss what features of our techniques extend to processes containing final-state jets.

Paper Structure

This paper contains 20 sections, 66 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Derivation of the NLO power correction
  3. Review of the leading-power factorization theorem
  4. Power corrections at NLO
  5. General features for LL$_P$ at NLO
  6. Beam contribution
  7. Jet contribution
  8. Summary of NLO results
  9. NLO power correction for DIS
  10. NLO power correction for hadronic production in $e^+e^-$ collisions
  11. NLO power correction for $ggH$ and Drell-Yan
  12. Derivation of the NNLO power correction
  13. Sketch of the RV calculation
  14. Sketch of the RR calculation
  15. NNLO power corrections for $ggH$ and Drell-Yan
  16. ...and 5 more sections

Figures (4)

  • Figure 1: A comparison of the fitted power corrections with the LL$_P$ calculated in this paper for inclusive $Z$-boson production (upper panel) and $W^+$-boson production with the indicated cuts on the final-state leptons (lower panel). We have normalized the ${\cal O}(\alpha_s^2)$ power corrections to the known ${\cal O}(\alpha_s^2)$ correction.
  • Figure 2: The difference between the NNLO coefficients for inclusive $Z$-boson and $W^+$-boson production at the LHC using $N$-jettiness subtraction with and without power corrections, normalized to the known NNLO coefficient. We have plotted the difference between the $N$-jettiness result for the ${\cal O}(\alpha_s^2)$ correction and the known result, and have normalized this difference to the known correction, for this and all other figures.
  • Figure 3: The difference between the NNLO coefficients for $Z$-boson and $W^+$-boson production with lepton and missing energy cuts at the LHC obtained using $N$-jettiness subtraction with and without power corrections, normalized to the exact NNLO coefficients.
  • Figure 4: A comparison of the NNLO coefficients for inclusive $ggH$ production at the LHC using $N$-jettiness subtraction with and without power corrections, normalized to the exact NNLO coefficient.