LHC Higgs Cross Section HH Sub-group (a.k.a LHC-HH)

Group organization

Group conveners:

Mail ATLAS CMS THEORY
Mail Arnaud Ferrari Luca Cadamuro Ramona Gröber / Javier Mazzitelli / Maggie Mühlleitner

Meetings

General documentation

CERN Yellow Reports: Handbook of LHC Higgs Cross Sections:

  1. Inclusive Observables: CERN-2011-002, arXiv:1101.0593
  2. Differential Distributions: CERN-2012-002, arXiv:1201.3084
  3. Higgs Properties: CERN-2013-004, arXiv:1307.1347
  4. Deciphering the Nature of the Higgs Sector: CERN-2017-002, arXiv:1610.07922

HH white paper: arXiv:1910.00012

References

A list of references for Higgs boson pair production is here. More details can be found below:

References for production via gluon fusion

Minimal set of references:

NLO in large-mt limit [1].

Full NLO [2,3].

NNLO in large-mt limit [4].

NNLL in large-mt limit [5,6]: please cite if YR4 predictions are used.

NNLO FTa [7].

[1] S. Dawson, S. Dittmaier, and M. Spira, Phys. Rev. D58 (1998) 115012, hep-ph/9805244.

[2] S. Borowka, N. Greiner, G. Heinrich, S. Jones, M. Kerner, J. Schlenk, U. Schubert, and T. Zirke, Phys. Rev. Lett. 117 (2016) 012001; erratum ibid 079901, arXiv:1604.06447.

[3] J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, M. Spira, and J. Streicher, Eur. Phys. J. C 79, arXiv:1811.05692.

[4] D. de Florian and J. Mazzitelli, Phys. Rev. Lett. 111 (2013) 201801, arXiv:1309.6594.

[5] D. Y. Shao, C. S. Li, H. T. Li, and J. Wang, JHEP07 (2013) 169, arXiv:1301.1245.

[6] D. de Florian and J. Mazzitelli, JHEP09 (2015) 053, arXiv:1505.07122.

[7] M. Grazzini, G. Heinrich, S. Jones, S. Kallweit, M. Kerner, J. M. Lindert, and J. Mazzitelli, JHEP05 (2018) 059, arXiv:1803.02463.

Additional references:

Virtual corrections for NNLO in large-mt limit [8,9].

Differential NNLO in large-mt limit [10].

More on full NLO and cross checks [11-13].

Monte Carlo full NLO [14-16].

NNLL FTa [17].

[8] D. de Florian and J. Mazzitelli, Phys. Lett. B724 (2013) 306, arXiv:1305.5206.

[9] J. Grigo, K. Melnikov, and M. Steinhauser, Nucl. Phys. B888 (2014) 17, arXiv:1408.2422.

[10] D. de Florian, M. Grazzini, C. Hanga, S. Kallweit, J. M. Lindert, P. Maierhöfer, J. Mazzitelli, and D. Rathlev, JHEP09 (2016) 151, arXiv:1606.09519.

[11] S. Borowka, N. Greiner, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk, and T. Zirke, JHEP10 (2016) 107, arXiv:1608.04798.

[12] F. Maltoni, E. Vryonidou, and M. Zaro, JHEP11 (2014) 079, arXiv:1408.6542.

[13] R. Bonciani, G. Degrassi, P. P. Giardino, and R. Gröber, Phys. Rev. Lett. 121 (2018), 162003, arXiv:1806.11564.

[14] G. Heinrich, S. P. Jones, M. Kerner, G. Luisoni, and E. Vryonidou, JHEP08 (2017) 088, arXiv:1703.09252.

[15] S. P. Jones and S. Kuttimalai, JHEP02 (2018) 176, arXiv:1711.03319.

[16] G. Heinrich, S. P. Jones, M. Kerner, G. Luisoni, L. Scyboz, JHEP06 (2019) 066, arXiv:1903.08137.

[17] D. de Florian and J. Mazzitelli, JHEP08 (2018) 156, arXiv:1807.03704.

References for EFT

Full NLO [18].

NLO large-mt limit [19,20].

NNLO large-mt limit [21].

[18] G. Buchalla, M. Capozi, A. Celis, G. Heinrich, and L. Scyboz, JHEP09 (2018) 057, arXiv:1806.05162.

[19] R. Gröber, M. Mühlleitner, M. Spira, and J. Streicher, JHEP09 (2015) 092, arXiv:1504.06577.

[20] R. Gröber, M. Mühlleitner, and M. Spira, Nucl. Phys. B925 (2017) 1, arXiv:1705.05314.

[21] D. de Florian, I. Fabre, and J. Mazzitelli, JHEP10 (2017) 215, arXiv:1704.05700.

References for other production modes

VBF NLO [22].

VBF NLO+PS [23].

VBF NNLO [24].

VBF differential NNLO [25].

VBF N3LO [26].

Associated production with vector bosons at NNLO [22].

Production of tthh and tjhh at NLO [23].

[22] J. Baglio, A. Djouadi, R. Gröber, M. M. Mühlleitner, J. Quevillon, and M. Spira, JHEP04 (2013) 151, arXiv:1212.5581.

[23] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, P. Torrielli, E. Vryonidou, and M. Zaro, Phys. Lett. B732 (2014) 142, arXiv:1401.7340.

[24] L.-S. Ling, R.-Y. Zhang, W.-G. Ma, L. Guo, W.-H. Li, and X.-Z. Li, Phys. Rev. D89 (2014), 073001, arXiv:1401.7754.

[25] F. A. Dreyer and A. Karlberg, Phys. Rev. D99 (2019) 074028, arXiv:1811.07918.

[26] F. A. Dreyer and A. Karlberg, Phys. Rev. D98 (2018), 114016, arXiv:1811.07906.

List of tasks (under construction)

Task Contact person Timescale Status
ggF: top-quark mass renormalization scheme uncertainty M. Mühlleitner and J. Mazzitelli Summer 2020 In progress
ggF: NNLO FTapprox vs lambda J. Mazzitelli Summer 2020 In progress
ggF: NLO EFT frameworks and new shape benchmarks, HEFT vs SMEFT R. Gröber and A. Ferrari End 2020 Started
ggF: prescriptions for extracting κt and κλ from single- and double-Higgs-boson searches (in connection with WG2 activities) R. Gröber and A. Ferrari End 2020 In progress
ggF: cross section / MC for gg -> HH + bb Autumn 2020 To be started
VBF: prescriptions for the range of the Wilson coefficient, cross-sections vs coupling modifiers R. Gröber and L. Cadamuro Summer 2020 Started
VBF: cross-sections for ggF HH+2j at hard matrix-element J. Mazzitelli and L. Cadamuro Summer 2020 To be done
Resonant: benchmarks for spin-0 HH, SH and SS to be probed with 100-300/fb, including interference with non-resonant HH M. Mühlleitner, A. Ferrari, L. Cadamuro Summer 2020 Being collected
Compositeness models: MC development R. Gröber and M. Mühlleitner End 2020 To be started

Current recommendations for HH cross-sections

Latest recommendations for gluon fusion

Inclusive ggF cross sections for Higgs boson pair production are reported below for different centre-of-mass energies in NNLO FTapprox, for mH = 125 GeV with the central scale μ0 = μR = μF = MHH/2 (see https://arxiv.org/abs/1803.02463). Scale uncertainties are obtained by probing six relative variations of μR and μF on top of the central one, i.e. (0.5;0.5), (0.5;1), (2;1), (1;1), (1;2), (1;0.5), (2;2): they are reported as superscript/subscript below. PDF uncertainties are estimated within the Born-improved approximation and are based on the PDF4LHC15nnlomc set. The calculation is performed in the on-shell top-quark mass scheme. The uncertainties related to missing finite top-quark mass effects within this approximation are also presented (mtop unc.). The uncertainties related to the renormalization scheme and scale of the top-quark mass are not included for the moment, and studies aimed at estimating their size are in progress.

√s 7 TeV 8 TeV 13 TeV 14 TeV 27 TeV 100 TeV
σNNLO FTapprox [fb] 6.572 9.441 31.05 36.69 139.9 1224
Scale unc. -6.5%+3.0% -6.1%+2.8% -5.0%+2.2% -4.9%+2.1% -3.9%+1.3% -3.2%+0.9%
PDF unc. ±3.5% ±3.1% ±2.1% ±2.1% ±1.7% ±1.7%
αS unc. ±2.6% ±2.4% ±2.1% ±2.1% ±1.8% ±1.7%
PDF+αS unc. ±4.3% ±3.9% ±3.0% ±3.0% ±2.5% ±2.4%
mtop unc. ±2.2% ±2.3% ±2.6% ±2.7% ±3.4% ±4.6%

Inclusive ggF cross-sections for Higgs boson pair production at different values of mH were obtained from those at mH = 125 GeV after rescaling with the ratio σLO(mH)/σLO(125 GeV).

√s 7 TeV 8 TeV 13 TeV 14 TeV 27 TeV 100 TeV
σNNLO FTapprox at mH = 124.59 GeV [fb] 6.609 9.493 31.21 36.88 140.6 1229
σNNLO FTapprox at mH = 125.09 GeV [fb] 6.564 9.430 31.02 36.65 139.8 1223
σNNLO FTapprox at mH = 125.59 GeV [fb] 6.519 9.366 30.82 36.43 139.0 1217

Inclusive ggF cross-sections for Higgs boson pair production at 13 TeV, for different values of the Higgs self-coupling modifier κλ, obtained for mH = 125 GeV with the central scale μ0 = μR = μF = MHH/2 at NNLONLO-i (rescaled to the NNLO FTapprox total cross section in the κλ = 1 limit). For more details, see https://arxiv.org/abs/2003.01700. The cross-section is found to be a quadratic function of κλ. Scale uncertainties are obtained by probing three relative variations of μR=μF, i.e. (0.5;0.5), (1;1), (2;2) and they are adjusted by a normalization factor in order to match the ones of the NNLO FTapprox SM prediction. PDF uncertainties have been found not to vary significantly with κλ and are of the order of 3% over the whole range.

κλ -1 0 1 2 2.4 3 5
σ [fb] 131.9 70.38 31.05 13.81 13.10 18.67 94.82
Scale unc. -6.7%+2.5% -6.1%+2.4% -5.0%+2.2% -4.9%+2.1% -5.1%+2.3% -7.3%+2.7% -8.8%+4.9%

OLD recommendations for gluon fusion (from YR4)

The table below shows NNLL-matched-to-NNLO cross-sections for gg → HH with the central scale μ0 = μR = μF = MHH/2, including top-quark mass effects at NLO. Uncertainties are evaluated using the PDF4LHC recommendation and are based on the PDF4LHC15nnlomc set. The theoretical uncertainty of 5% is related to missing finite top-quark mass effects. Prior to r27 of this twiki page, the recommended cross-sections at 13 and 14 TeV were under-estimated by a few per-mille with respect to those published in the YR4.

These are only to be used for publications related to the 2015+2016 dataset... neither for end-of-Run-2 papers nor for projections!

mH √s σ′NNLO+NNLL [fb] scale unc. [%] scale unc. [%] th. unc. [%]
αs unc. [%] PDF unc. [%]
124.5 GeV 7 TeV 7.132 -5.7 +4.0 ±5 ±2.8 ±3.4
  8 TeV 10.24 -5.7 +4.1 ±5 ±2.6 ±3.0
  13 TeV 33.78 -6.0 +4.3 ±5 ±2.3 ±2.1
  14 TeV 39.93 -6.0 +4.4 ±5 ±2.2 ±2.1
               
125 GeV 7 TeV 7.078 -5.7 +4.0 ±5 ±2.8 ±3.4
  8 TeV 10.16 -5.7 +4.1 ±5 ±2.6 ±3.1
  13 TeV 33.53 -6.0 +4.3 ±5 ±2.3 ±2.1
  14 TeV 39.64 -6.0 +4.4 ±5 ±2.2 ±2.1
               
125.09 GeV 7 TeV 7.068 -5.7 +4.0 ±5 ±2.8 ±3.4
  8 TeV 10.15 -5.7 +4.1 ±5 ±2.6 ±3.1
  13 TeV 33.49 -6.0 +4.3 ±5 ±2.3 ±2.1
  14 TeV 39.59 -6.0 +4.4 ±5 ±2.2 ±2.1
               
125.5 GeV 7 TeV 7.023 -5.7 +4.0 ±5 ±2.8 ±3.4
  8 TeV 10.09 -5.7 +4.1 ±5 ±2.6 ±3.1
  13 TeV 33.29 -6.0 +4.3 ±5 ±2.3 ±2.1
  14 TeV 39.35 -5.9 +4.4 ±5 ±2.2 ±2.1

Sub-leading channels

HHjj (VBF)

The table below shows the cross-sections (in fb) for vector boson fusion (VBF) production of HHjj at N3LO QCD with the renormalization and factorization scales set to the individual virtualities of the t-channel vector bosons. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

mH (GeV) √s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
124.5 1.739 -0.04%+0.03% ±2.1% 2.071 -0.04%+0.03% ±2.1% 8.459 -0.04%+0.11% ±2.0% 83.25 -0.05%+0.15% ±2.1%
125 1.726 -0.04%+0.03% ±2.1% 2.055 -0.04%+0.03% ±2.1% 8.404 -0.04%+0.11% ±2.0% 82.84 -0.04%+0.13% ±2.1%
125.09 1.723 -0.04%+0.03% ±2.1% 2.052 -0.04%+0.03% ±2.1% 8.394 -0.04%+0.11% ±2.0% 82.77 -0.04%+0.11% ±2.1%
125.5 1.711 -0.04%+0.03% ±2.1% 2.038 -0.04%+0.03% ±2.1% 8.349 -0.04%+0.11% ±2.0% 82.44 -0.05%+0.14% ±2.1%
hhZ

Cross-section (in fb) vs centre-of-mass energy for hhZ production at NNLO QCD with the central scale μ0 = μR = μF = MhhZ. The Higgs boson mass is set to 125 GeV. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

√s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
0.363 -2.7%+3.4% ±1.9% 0.415 -2.7%+3.5% ±1.8% 1.23 -3.3%+4.1% ±1.5% 8.23 -4.6%+5.9% ±1.7%
At 13 and 14 TeV, the table below shows cross-section variations with the Higgs boson mass:

mh (GeV) √s = 13 TeV √s = 14 TeV
124.5 0.368-2.6%+3.5% ±1.9% 0.420-2.7%+3.6% ±1.8%
125 0.363-2.7%+3.4% ±1.9% 0.415-2.7%+3.5% ±1.8%
125.09 0.362-2.6%+3.4% ±1.9% 0.414-2.7%+3.5% ±1.8%
125.5 0.359-2.7%+3.5% ±1.9% 0.409-2.7%+3.5% ±1.9%
hhW+

Cross-section (in fb) vs centre-of-mass energy for hhW+ production at NNLO QCD with the central scale μ0 = μR = μF = MhhW. The Higgs boson mass is set to 125 GeV. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

√s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
0.329 -0.41%+0.32% ±2.2% 0.369 -0.39%+0.33% ±2.1% 0.941 -0.53%+0.52% ±1.8% 4.70 -0.96%+0.90% ±1.8%
At 13 and 14 TeV, the table below shows cross-section variations with the Higgs boson mass:

mh (GeV) √s = 13 TeV √s = 14 TeV
124.5 0.333-0.41%+0.32% ±2.2% 0.373-0.39%+0.33% ±2.1%
125 0.329-0.41%+0.32% ±2.2% 0.369-0.39%+0.33% ±2.1%
125.09 0.329-0.41%+0.32% ±2.2% 0.368-0.39%+0.33% ±2.1%
125.5 0.326-0.41%+0.32% ±2.2% 0.365-0.39%+0.33% ±2.1%
hhW-

Cross-section (in fb) vs centre-of-mass energy for hhW- production at NNLO QCD with the central scale μ0 = μR = μF = MhhW. The Higgs boson mass is set to 125 GeV. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

√s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
0.173 -1.3%+1.2% ±2.8% 0.198 -1.3%+1.2% ±2.7% 0.568 -2.0%+1.9% ±2.1% 3.30 -4.3%+3.5% ±1.9%
At 13 and 14 TeV, the table below shows cross-section variations with the Higgs boson mass:

mh (GeV) √s = 13 TeV √s = 14 TeV
124.5 0.176-1.3%+1.2% ±2.8% 0.200-1.3%+1.2% ±2.7%
125 0.173-1.3%+1.2% ±2.8% 0.198-1.3%+1.2% ±2.7%
125.09 0.173-1.3%+1.2% ±2.8% 0.197-1.3%+1.2% ±2.7%
125.5 0.171-1.3%+1.2% ±2.8% 0.195-1.3%+1.2% ±2.7%
tthh

Cross-section (in fb) vs centre-of-mass energy for tthh production at NLO QCD with the central scale μ0 = μR = μF = Mhh/2. The Higgs boson mass is set to 125 GeV. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

√s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
0.775 -4.3%+1.5% ±3.2% 0.949 -4.5%+1.7% ±3.1% 5.24 -6.4%+2.9% ±2.5% 82.1 -7.4%+7.9% ±1.6%
At 13 and 14 TeV, the table below shows cross-section variations with the Higgs boson mass:

mh (GeV) √s = 13 TeV √s = 14 TeV
124.5 0.786-4.5%+1.3% ±3.2% 0.968-4.6%+1.7% ±3.1%
125 0.775-4.3%+1.5% ±3.2% 0.949-4.5%+1.7% ±3.1%
125.09 0.772-4.5%+1.7% ±3.2% 0.949-4.8%+1.8% ±3.1%
125.5 0.762-4.5%+1.3% ±3.2% 0.937-4.5%+1.5% ±3.1%
hhtj

Cross-section (in fb) vs centre-of-mass energy for hhtj production at NLO QCD with the central scale μ0 = μR = μF = Mhh/2. The Higgs boson mass is set to 125 GeV. The first uncertainty is the scale uncertainty and the second is the PDF + αs uncertainty based on the PDF4LHC15nnlomc set.

√s = 13 TeV √s = 14 TeV √s = 27 TeV √s = 100 TeV
0.0289 -3.6%+5.5% ±4.7% 0.0367 -1.8%+4.2% ±4.6% 0.254 -2.8%+3.8% ±3.6% 4.44 -2.8%+2.2% ±2.4%
At 13 and 14 TeV, the table below shows cross-section variations with the Higgs boson mass:

mh (GeV) √s = 13 TeV √s = 14 TeV
124.5 0.0289-3.4%+5.4% ±4.6% 0.0365-1.6%+4.4% ±4.7%
125 0.0289-3.6%+5.5% ±4.7% 0.0367-1.8%+4.2% ±4.6%
125.09 0.0281-3.2%+5.2% ±4.5% 0.0364-1.3%+3.7% ±4.7%
125.5 0.0279-4.6%+6.1% ±6.4% 0.0359-1.6%+3.8% ±4.7%

BSM predictions

Additional information about the EFT BSM parametrisation of HH can be found in the LHCHXSWG-INT-2016-001 internal note.

Topic attachments
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