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Next-to-leading-logarithmic power corrections for $N$-jettiness subtraction in color-singlet production

Radja Boughezal, Andrea Isgrò, Frank Petriello

TL;DR

The paper derives next-to-leading-logarithmic (NLL) power corrections to the 0-jettiness factorization theorem for color-singlet production, performing a direct QCD calculation that matches and complements SCET results. It provides a complete LP and NLP ($\mathcal{O}(\mathcal{T})$) expansion, including explicit LL and NLL terms, and applies these corrections to Higgs production via gluon fusion using the $N$-jettiness subtraction method. Numerically, incorporating these power corrections markedly improves agreement with dipole-subtraction results and enhances computational efficiency, especially for the fixed-$\mathcal{T}$ definition. The work also maps the direct QCD results to SCET structures and lays groundwork for extending the approach to NNLO NLP corrections and jet production scenarios.

Abstract

We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable $\mathcal{T}$. Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small $\mathcal{T}$ at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections to a particular definition of 0-jettiness. We present a numerical study of the power corrections in the context of their application to the $N$-jettiness subtraction method for higher-order calculations, using gluon-fusion Higgs production as an example. The inclusion of the next-to-leading-logarithmic power corrections further improves the numerical efficiency of the approach beyond the improvement obtained from the leading-logarithmic power corrections.

Next-to-leading-logarithmic power corrections for $N$-jettiness subtraction in color-singlet production

TL;DR

The paper derives next-to-leading-logarithmic (NLL) power corrections to the 0-jettiness factorization theorem for color-singlet production, performing a direct QCD calculation that matches and complements SCET results. It provides a complete LP and NLP () expansion, including explicit LL and NLL terms, and applies these corrections to Higgs production via gluon fusion using the -jettiness subtraction method. Numerically, incorporating these power corrections markedly improves agreement with dipole-subtraction results and enhances computational efficiency, especially for the fixed- definition. The work also maps the direct QCD results to SCET structures and lays groundwork for extending the approach to NNLO NLP corrections and jet production scenarios.

Abstract

We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable . Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections to a particular definition of 0-jettiness. We present a numerical study of the power corrections in the context of their application to the -jettiness subtraction method for higher-order calculations, using gluon-fusion Higgs production as an example. The inclusion of the next-to-leading-logarithmic power corrections further improves the numerical efficiency of the approach beyond the improvement obtained from the leading-logarithmic power corrections.

Paper Structure

This paper contains 13 sections, 56 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation and $\mathcal{T}$ definitions
  3. Leading-power derivation using SCET
  4. Direct QCD derivation of leading and sub-leading power
  5. Factorization of the phase space
  6. Expansion of the matrix elements
  7. Derivation of the leading-power result
  8. Derivation of the subleading-power result
  9. Numerical results
  10. Conclusions
  11. $q\bar{q} \to Hg$
  12. $gq \to Hq$
  13. $qg \to Hq$

Figures (5)

  • Figure 1: Deviations of the NLO coefficient obtained using $N$-jettiness subtraction as a function of $\mathcal{T}^\text{cut}$ from the dipole-subtraction result for three different cases: no power corrections included, only the leading-logarithmic (LL) power corrections included, and the full NLL power corrections included.
  • Figure 2: Comparison of the fixed and hadronic $\mathcal{T}$ deviations from dipole subtraction for the total cross section. No power corrections are included.
  • Figure 3: Comparison of the fixed and hadronic $\mathcal{T}$ deviations from dipole subtraction for the total cross section. The full ${\cal O}(\mathcal{T})$ power corrections are included.
  • Figure 4: Deviations of the $qg+gq$ NLO coefficient obtained using $N$-jettiness subtraction as a function of $\mathcal{T}^\text{cut}$ from the dipole-subtraction result for three different cases: no power corrections included, only the leading-logarithmic (LL) power corrections included, and the full NLL power corrections included.
  • Figure 5: Deviations of the $q\bar{q}$ NLO coefficient obtained using $N$-jettiness subtraction as a function of $\mathcal{T}^\text{cut}$ from the dipole-subtraction result for three different cases: no power corrections included, only the leading-logarithmic (LL) power corrections included, and the full NLL power corrections included.