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 May 2019 In progress
 ggF: NLO cross-sections with finite mtop effects and uncertainties vs κt and κλ G. Heinrich March 2019 Done
 ggF: prescriptions for the range of EFT coefficients, associated cross-sections R. Gröber and A. Ferrari Autumn 2019 Started
 ggF: prescriptions for extracting κt and κλ from single- and double-Higgs-boson searches R. Gröber and A. Ferrari Autumn 2019 Started
 VBF: prescriptions for the range of the Wilson coefficient, associated cross-sections R. Gröber and A. Ferrari Autumn 2019 Started
 VBF: cross-sections for ggF HH+2j at hard matrix-element J. Mazzitelli Autumn 2019 To be done
 HHV, HHtt, HHtj: add cross-sections at 27 TeV R. Gröber May 2019 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 Autumn 2019 Being collected
 Resonant: are spin-2 models still sensible for HH searches? M. Mühlleitner June 2019 Yes

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 Next-to-Leading-Order in QCD including the full top quark mass dependence, see https://arxiv.org/abs/1903.08137 for details. The NLO 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): they are reported as superscript/subscript below. PDF uncertainties have been found not to vary significantly with κλ and are of the order of 3% over the whole range.

When computing NNLO+FTapprox values of the cross-sections at non-SM values of κλ, the current recipe is to use the ratio NNLO+FTapprox / NLO at κλ=1, and use the scaling factor for all κλ values.

κλ -10 -5 -1 0 1 2 2.4 3 5 10
σNLO [fb] 1468.13 524.65 116.71 62.51 27.84 12.42 11.65 16.28 81.74 582.26
Scale unc. -14.9%+18.4% -14.7%+18.0% -14.3%+16.4% -13.7%+15.8% -12.9%+11.6% -12.0%+13.1% -12.7%+13.9% -15.3%+16.2% -15.6%+20.0% -15.4%+19.5%

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.

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