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Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD

Daniel de Florian, Javier Mazzitelli

TL;DR

The paper tackles the precision prediction of Higgs boson pair production in the Standard Model by computing the full NNLO QCD corrections in the large-$M_t$ limit and normalizing to the exact LO mass dependence. It presents a detailed separation of contributions, including soft-virtual and real-emission parts, with a robust subtraction scheme, and provides analytic $K$-factors as functions of the Higgs-pair invariant mass. At the LHC (14 TeV), the NNLO corrections yield a ~20% increase over NLO and substantially reduce scale uncertainties, with a NNLO $K$-factor around 2.3 and high agreement with the soft-virtual approximation. The results extend to 8–100 TeV colliders, offering precise cross sections and compact fits for energy-dependent $K$-factors, thereby enhancing theoretical precision for probing the Higgs self-coupling.

Abstract

We compute the next-to-next-to-leading order QCD corrections for Standard Model Higgs boson pair production inclusive cross section at hadron colliders within the large top-mass approximation. We provide numerical results for the LHC, finding that the corrections are large, resulting in an increase of ${\cal O}(20%)$ with respect to the next-to-leading order result at c.m. energy $\sqrt{s_H}=14\,\text{TeV}$. We observe a substantial reduction in the scale dependence, with overlap between the current and previous order prediction. All our results are normalized using the full top- and bottom-mass dependence at leading order. We also provide analytical expressions for the K factors as a function of $s_H$.

Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD

TL;DR

The paper tackles the precision prediction of Higgs boson pair production in the Standard Model by computing the full NNLO QCD corrections in the large- limit and normalizing to the exact LO mass dependence. It presents a detailed separation of contributions, including soft-virtual and real-emission parts, with a robust subtraction scheme, and provides analytic -factors as functions of the Higgs-pair invariant mass. At the LHC (14 TeV), the NNLO corrections yield a ~20% increase over NLO and substantially reduce scale uncertainties, with a NNLO -factor around 2.3 and high agreement with the soft-virtual approximation. The results extend to 8–100 TeV colliders, offering precise cross sections and compact fits for energy-dependent -factors, thereby enhancing theoretical precision for probing the Higgs self-coupling.

Abstract

We compute the next-to-next-to-leading order QCD corrections for Standard Model Higgs boson pair production inclusive cross section at hadron colliders within the large top-mass approximation. We provide numerical results for the LHC, finding that the corrections are large, resulting in an increase of with respect to the next-to-leading order result at c.m. energy . We observe a substantial reduction in the scale dependence, with overlap between the current and previous order prediction. All our results are normalized using the full top- and bottom-mass dependence at leading order. We also provide analytical expressions for the K factors as a function of .

Paper Structure

This paper contains 4 sections, 36 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Results
  3. Phenomenology
  4. One-loop real corrections

Figures (3)

  • Figure 1: Example of Feynman diagrams needed for the NNLO calculation for $gg\rightarrow HHg$ (top) and $qg\rightarrow HHq$ (bottom) subprocesses. Other parton subprocesses can be obtained from crossings.
  • Figure 2: Higgs pair invariant mass distribution at LO (dotted blue), NLO (dashed red) and NNLO (solid black) for the LHC at c.m. energy $E_{cm}=14\,\text{TeV}$. The bands are obtained by varying $\mu_F$ and $\mu_R$ in the range $0.5\,Q\leq \mu_F,\mu_R \leq 2\,Q$ with the constraint $0.5\leq \mu_F/\mu_R \leq 2$.
  • Figure 3: Total cross section as a function of the c.m. energy $E_{cm}$ for the LO (dotted blue), NLO (dashed red) and NNLO (solid black) prediction. The bands are obtained by varying $\mu_F$ and $\mu_R$ as indicated in the main text. The inset plot shows the corresponding $K$ factors.