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$gg \to ZH$ : updated predictions at NLO QCD

Benjamin Campillo Aveleira, Long Chen, Joshua Davies, Giuseppe Degrassi, Pier Paolo Giardino, Ramona Gröber, Gudrun Heinrich, Stephen Jones, Matthias Kerner, Johannes Schlenk, Matthias Steinhauser, Marco Vitti

TL;DR

This work delivers state-of-the-art NLO QCD predictions for the gluon-initiated process gg to ZH, using a hybrid virtual-correction strategy that combines forward and high-energy expansions with Padé improvements and exact real-emission corrections. The predictions achieve a reduced scale uncertainty of about 15% and include a conservative estimate of the top-quark mass renormalisation-scheme uncertainty, with the inclusive cross section enhanced by roughly a factor of 1.85 over LO. The study validates the analytic-approximation approach against full numerical calculations and finds compatibility with LHCHWG recommendations, while highlighting the top-mass scheme as a key source of remaining uncertainty and the potential for higher-order refinements toward ~1% precision for the HL-LHC. Overall, the work provides a robust, practical framework for precise hadronic predictions of gg-initiated ZH production, informing experimental analyses and global fits.

Abstract

We present state-of-the-art predictions for the inclusive cross section of gluon-initiated $ZH$ production, following the recommendations of the LHC Higgs Working Group. In particular, we include NLO QCD corrections, where the virtual corrections are obtained from the combination of a forward expansion and a high-energy expansion, and the real corrections are exact. The expanded results for the virtual corrections are compared in detail to full numerical results. The updated predictions show a reduction of the scale uncertainties to the level of 15%, and they include an estimate of the top-mass-scheme uncertainty.

$gg \to ZH$ : updated predictions at NLO QCD

TL;DR

This work delivers state-of-the-art NLO QCD predictions for the gluon-initiated process gg to ZH, using a hybrid virtual-correction strategy that combines forward and high-energy expansions with Padé improvements and exact real-emission corrections. The predictions achieve a reduced scale uncertainty of about 15% and include a conservative estimate of the top-quark mass renormalisation-scheme uncertainty, with the inclusive cross section enhanced by roughly a factor of 1.85 over LO. The study validates the analytic-approximation approach against full numerical calculations and finds compatibility with LHCHWG recommendations, while highlighting the top-mass scheme as a key source of remaining uncertainty and the potential for higher-order refinements toward ~1% precision for the HL-LHC. Overall, the work provides a robust, practical framework for precise hadronic predictions of gg-initiated ZH production, informing experimental analyses and global fits.

Abstract

We present state-of-the-art predictions for the inclusive cross section of gluon-initiated production, following the recommendations of the LHC Higgs Working Group. In particular, we include NLO QCD corrections, where the virtual corrections are obtained from the combination of a forward expansion and a high-energy expansion, and the real corrections are exact. The expanded results for the virtual corrections are compared in detail to full numerical results. The updated predictions show a reduction of the scale uncertainties to the level of 15%, and they include an estimate of the top-mass-scheme uncertainty.

Paper Structure

This paper contains 12 sections, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Calculation of NLO QCD corrections
  3. Virtual corrections
  4. Real emission contributions
  5. $Z$-boson radiation
  6. Assessment of top-mass scheme uncertainty
  7. Predictions
  8. Setup and numerical input
  9. Numerical Results
  10. Discussion of theoretical uncertainties
  11. Conclusion
  12. Funding information

Figures (3)

  • Figure 1: Comparison of the results for $\mathcal{V}_\text{fin}$ of Ref. Degrassi:2022mro and Ref. Chen:2020gae. The orange (purple) points denote the normalized difference defined in Eq. \ref{['eq:deltaVfin']}, where the $p_T$ (high-energy) expansion is used in $\mathcal{V}_\text{fin}^\text{Ref.~}Degrassi:2022mro$. The grey error bars indicate the relative uncertainty associated to the points from $\mathcal{V}_\text{fin}^\text{Ref.~}Chen:2020gae$. The figure is based on a comparison of 460 different phase space points $(\hat{s},\hat{t})$. The range of $\hat{t}$ values corresponds to $p_T < 670~\text{GeV}$.
  • Figure 2: Representative $Z$-radiation Feynman diagrams for the real-emission contributions in the $qg$ and $q\bar{q}$ channels.
  • Figure 3: The invariant mass distribution of the $Z$-Higgs-system for an energy of $\sqrt{S}=13.6~\mathrm{TeV}$ and a Higgs mass of $m_H=125.0~\mathrm{GeV}$. Presented are the NLO and LO distributions with the 7-points scale uncertainty.