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Finite top-mass effects in gluon-induced Higgs production with a jet-veto at NNLO

Tobias Neumann, Marius Wiesemann

TL;DR

This work validates the heavy-top EFT for Higgs production with a jet veto at NNLO by examining finite top-mass corrections through a $1/m_t$ expansion up to several orders. It shows that the jet-veto cross section is highly stable against mass effects, remaining at the permille to few-percent level for realistic veto cuts, while inclusive Higgs+jet rates require a high-energy matching to avoid unphysical high-$p_T$ tails. The study also finds that differential $K$-factors for the hardest jet are only mildly sensitive to the top mass for moderate jet transverse momenta, enabling accurate predictions using EFT-based corrections. Overall, the results support using the heavy-top EFT for jet-veto observables at NNLO and provide practical guidance on when mass effects must be reintroduced through matching or reweighting.

Abstract

Effects from a finite top quark mass on the H+n-jet cross section through gluon fusion are studied for $n=0/n\ge 1$ at NNLO/NLO QCD. For this purpose, sub-leading terms in $1/m_t$ are calculated. We show that the asymptotic expansion of the jet-vetoed cross section at NNLO is very well behaved and that the heavy-top approximation is valid at the five permille level up to jet-veto cuts of 300 GeV. For the inclusive Higgs+jet rate, we introduce a matching procedure that allows for a reliable prediction of the top-mass effects using the expansion in $1/m_t$. The quality of the effective field theory to evaluate differential K-factors for the distribution of the hardest jet is found to be better than 1-2% as long as the transverse momentum of the jet is integrated out or remains below about 150 GeV.

Finite top-mass effects in gluon-induced Higgs production with a jet-veto at NNLO

TL;DR

This work validates the heavy-top EFT for Higgs production with a jet veto at NNLO by examining finite top-mass corrections through a expansion up to several orders. It shows that the jet-veto cross section is highly stable against mass effects, remaining at the permille to few-percent level for realistic veto cuts, while inclusive Higgs+jet rates require a high-energy matching to avoid unphysical high- tails. The study also finds that differential -factors for the hardest jet are only mildly sensitive to the top mass for moderate jet transverse momenta, enabling accurate predictions using EFT-based corrections. Overall, the results support using the heavy-top EFT for jet-veto observables at NNLO and provide practical guidance on when mass effects must be reintroduced through matching or reweighting.

Abstract

Effects from a finite top quark mass on the H+n-jet cross section through gluon fusion are studied for at NNLO/NLO QCD. For this purpose, sub-leading terms in are calculated. We show that the asymptotic expansion of the jet-vetoed cross section at NNLO is very well behaved and that the heavy-top approximation is valid at the five permille level up to jet-veto cuts of 300 GeV. For the inclusive Higgs+jet rate, we introduce a matching procedure that allows for a reliable prediction of the top-mass effects using the expansion in . The quality of the effective field theory to evaluate differential K-factors for the distribution of the hardest jet is found to be better than 1-2% as long as the transverse momentum of the jet is integrated out or remains below about 150 GeV.

Paper Structure

This paper contains 12 sections, 4 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Outline of the calculation
  3. Results
  4. Input parameters
  5. Notation
  6. Lower order results
  7. Jet-veto at .9 NNLO
  8. Inclusive Higgs+jet rate at $\text{\scalefont{.9} NLO}{}$
  9. Distributions of the hardest jet
  10. Conclusions
  11. Acknowledgements.
  12. Higgs $p_T{}$ distribution

Figures (14)

  • Figure 1: A sample of Feynman diagrams contributing at $p_T = 0$. (a) .9 LO (one-loop); (b) .9 NLO (2-loop); (c) .9 NNLO (3-loop). The graphical notation for the lines is: thick straight $\hat{=}$ top quark; spiraled $\hat{=}$ gluon; dashed $\hat{=}$ Higgs boson.
  • Figure 2: A sample of Feynman diagrams contributing at $p_T >0$. (a-c) single-real; (e-f) mixed real-virtual. The graphical notation for the lines is: thick straight $\hat{=}$ top quark; thin straight $\hat{=}$ light quark $q\in\{u,d,c,s,b\}$; spiraled $\hat{=}$ gluon; dashed $\hat{=}$ Higgs boson.
  • Figure 3: Same as Fig. \ref{['fig:real']} but double real emission diagrams.
  • Figure 4: Higgs+$0$-jet cross section at .9 NLO including terms up to $1/m_t^k$ as a function of $m_{H}$ for $p_{T,\text{veto}}^{\text{jet}}=30$ GeV. Dotted/dashed/dash-dotted: $k = 0/2/4$. (a) absolute; (b) normalized to $k=0$.
  • Figure 5: Higgs+$0$-jet cross section at .9 NLO including terms up to $1/m_t^k$ as a function of $p_{T,\text{veto}}^{\text{jet}}{}$. Dotted/dashed/dash-dotted: $k = 0/2/4$. (a) absolute; (b) normalized to $k=0$.
  • ...and 9 more figures