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Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme

Julien Baglio, Francisco Campanario, Seraina Glaus, Margarete Mühlleitner, Michael Spira, Juraj Streicher

TL;DR

This work delivers the first independent full NLO QCD calculation of Higgs-boson pair production via gluon fusion with exact top-mass dependence in both virtual and real corrections. The authors employ direct numerical integration of the complete two-loop virtual diagrams, stabilized by integration-by-parts and Richardson extrapolation to the narrow-width limit, and supplement with HTL-based real corrections to obtain the full mass effects. They present differential and total cross sections at the 14 TeV LHC, demonstrating negative mass effects up to ~-30% at large Higgs-pair invariant masses and a total NLO reduction of about -15% relative to HTL, while exposing significant uncertainties from scale choice and top-mass schemes. The results enhance the precision of Higgs self-coupling studies and underline the importance of top-mass-scheme uncertainties, with planned extensions to beyond-the-Standard-Model scenarios like 2HDM and MSSM.

Abstract

We present the calculation of the full next-to-leading order (NLO) QCD corrections to Higgs boson pair production via gluon fusion at the LHC, including the exact top-mass dependence in the two-loop virtual and one-loop real corrections. This is the first independent cross-check of the NLO QCD corrections presented in the literature before. Our calculation relies on numerical integrations of Feynman integrals, stabilised with integration-by-parts and a Richardson extrapolation to the narrow width approximation. We present results for the total cross section as well as for the invariant Higgs-pair-mass distribution at the LHC, including for the first time a study of the uncertainty due to the scheme and scale choice for the top mass in the loops.

Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme

TL;DR

This work delivers the first independent full NLO QCD calculation of Higgs-boson pair production via gluon fusion with exact top-mass dependence in both virtual and real corrections. The authors employ direct numerical integration of the complete two-loop virtual diagrams, stabilized by integration-by-parts and Richardson extrapolation to the narrow-width limit, and supplement with HTL-based real corrections to obtain the full mass effects. They present differential and total cross sections at the 14 TeV LHC, demonstrating negative mass effects up to ~-30% at large Higgs-pair invariant masses and a total NLO reduction of about -15% relative to HTL, while exposing significant uncertainties from scale choice and top-mass schemes. The results enhance the precision of Higgs self-coupling studies and underline the importance of top-mass-scheme uncertainties, with planned extensions to beyond-the-Standard-Model scenarios like 2HDM and MSSM.

Abstract

We present the calculation of the full next-to-leading order (NLO) QCD corrections to Higgs boson pair production via gluon fusion at the LHC, including the exact top-mass dependence in the two-loop virtual and one-loop real corrections. This is the first independent cross-check of the NLO QCD corrections presented in the literature before. Our calculation relies on numerical integrations of Feynman integrals, stabilised with integration-by-parts and a Richardson extrapolation to the narrow width approximation. We present results for the total cross section as well as for the invariant Higgs-pair-mass distribution at the LHC, including for the first time a study of the uncertainty due to the scheme and scale choice for the top mass in the loops.

Paper Structure

This paper contains 10 sections, 20 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Calculation
  3. Partonic leading order cross section
  4. Hadronic cross section
  5. Virtual corrections
  6. Real corrections
  7. Numerical results
  8. Factorisation and renormalisation scale dependence
  9. Uncertainties due to the top mass scheme
  10. Conclusions

Figures (2)

  • Figure 1: Typical two-loop diagrams contributing to Higgs-boson pair production via gluon fusion: (a) triangle diagram, (b) one-particle reducible diagram, (c) box diagram.
  • Figure 2: Invariant Higgs-pair-mass distributions for Higgs boson pair production via gluon fusion at the 14 TeV LHC as a function of $Q=m_{HH}$. LO results (in black), HTL results (in blue), HTL results including the full real corrections (in yellow), HTL results including the full virtual corrections (in green, including the numerical error), and the full NLO QCD results (in red, including the numerical error). Left: Results with the MMHT2014 PDF set, the insert below displays the $K$-factors for the different results. Right: Results with the PDF4LHC15 PDF set, the insert below displays the ratio to the NLO HTL result for the different calculations. The red band indicates the renormalisation and factorisation scale uncertainties for results including the full NLO QCD corrections.