LHCPhysics Web>LHCHXSWG>LHCHWGHH (2024-01-25, EnnioSalvioni)

LHC Higgs WG4 group (formerly LHC-HH sub group)

Group organization

Group conveners:

Mail	ATLAS	CMS	THEORY
Mail	Stefano Manzoni (10/2022)	Fabio Monti (10/2023)	Ludovic Scyboz (02/2024) / Javier Mazzitelli (06/2018) / Maggie Mühlleitner

Group mailing list: lhc-higgs-hh

Meetings

General documentation

CERN Yellow Reports: Handbook of LHC Higgs Cross Sections:

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

HH white paper: arXiv:1910.00012

References

Our recommendations for HH references:

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].

Combined (mtop + scale) uncertainties [8].

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[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.

[8] J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, J. Ronca, and M. Spira, Phys. Rev. D 103, 056002 (2021), arXiv:2008.11626.

Additional references:

Virtual corrections for NNLO in large-mt limit [9,10].

Differential NNLO in large-mt limit [11].

More on full NLO and cross checks [12-14].

Monte Carlo full NLO [15-17].

NNLL FTa [18].

N3LO in large-mt limit [19,20].

N3LL in large-mt limit [21].

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

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

[11] 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.

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

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

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

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

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

[17] G. Heinrich, S. P. Jones, M. Kerner, L. Scyboz, JHEP10 (2020) 021 arXiv:2006.16877

(supersedes JHEP06 (2019) 066, arXiv:1903.08137. )

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

[19] L. Chen, H. T. Li, H. Shao and J. Wang, Phys. Lett. B803 (2020) 135292, arXiv:1909.06808.

[20] L. Chen, H. T. Li, H. Shao and J. Wang, JHEP03 (2020) 072, arXiv:1912.13001.

[21] A.H. Ajjath and H. Shao, arXiv:2209.03914.

References for EFT

Full NLO [22].

NLO large-mt limit [23,24].

NNLO large-mt limit [25].

Approximate NNLO QCD [26].

SMEFT, full NLO [27].

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

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

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

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

[26] D. de Florian, I. Fabre, G. Heinrich, J. Mazzitelli, and L.Scyboz, JHEP 09 (2021) 161, arXiv:2106.14050.

[27] G. Heinrich, J. Lang, L. Scyboz, [update when published], arXiv:2204.13045.

References for other production modes

VBF NLO [28].

VBF NLO+PS [29].

VBF NNLO [30].

VBF differential NNLO [31].

VBF N3LO [32].

Associated production with vector bosons at NNLO [28].

Production of tthh and tjhh at NLO [29].

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

[29] 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.

[30] 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.

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

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

References for MC generation

It is important to refer also to the implementation of the process in Powheg and not only to the generic Powheg-box paper, in particular:

If the POWHEG generator ggHH is used (User-Processes-V2/ggHH) for SM predictions, ref.[15] should be cited.
If predictions within a non-linear EFT are considered, as well as κ_λ variations, ref.[17] should be cited.
If the ggHH_SMEFT generator is used (User-Processes-V2/ggHH_SMEFT), ref.[27] should be cited.

List of tasks (under construction)

Task	Contact person	Timescale	Status
ggF: top-quark mass renormalization scheme uncertainty	M. Mühlleitner and J. Mazzitelli	Completed	arXiv:2008.11626 Phys. Rev. D 103, 056002 (2021)
ggF: NLO EFT frameworks and new shape benchmarks, HEFT vs SMEFT	R. Gröber and L. Cadamuro	Completed	CDS record
ggF: combination of H and HH (in connection with WG2 activities)	R. Gröber and S. Manzoni and N. Lu	2023	discussions with WG2 ongoing
ggF: cross section / MC for gg -> H + bb	J. Mazzitelli and S. Manzoni	Completed	JHEP 09 (2023), 179 (arXiv:2307.09992)
ggF/VBF: updated cross sections for 13.6TeV, various mH values and new PDF sets	J. Mazzitelli	2023	In progress
VBF: fiducial cross-sections vs coupling modifiers	R. Gröber	2023	Need external inputs
VBF: cross-sections for ggF HH+2j at hard matrix-element	J. Mazzitelli and S. Manzoni and N. Lu	Spring 2023	Ongoing. MC studies @ at LHC HH link
Resonant: benchmarks for spin-0 HH, SH and SS to be probed with 100-300/fb, including interference with non-resonant HH	M. Mühlleitner	paper complete, decision needed	arXiV:2112.12515 J. High Energ. Phys. 11 (2022)
Compositeness models: covered by EFT?	R. Gröber and M. Mühlleitner	end 2023	started

Current recommendations for HH cross-sections

Latest recommendations for gluon fusion

1) Inclusive ggF cross sections for Higgs boson pair production are reported below for different centre-of-mass energies in NNLO FTapprox, for m_H = 125 GeV with the central scale μ0 = μR = μF = M_HH/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. Uncertainties arising from the choice of renormalization scheme and scale of the top-quark mass (mtop scheme+scale unc.) and their combination with μR and μF variations (comb. unc.) are based on https://arxiv.org/abs/2008.11626. PDF uncertainties are estimated within the Born-improved approximation and are based on the PDF4LHC15nnlomc set. The uncertainties related to missing NNLO finite top-quark mass effects within the FT approximation are also presented (mtop approx. unc.).

√s	7 TeV	8 TeV	13 TeV	13.6 TeV	14 TeV	27 TeV	100 TeV
σ_{NNLO FTapprox} [fb]	6.572	9.441	31.05	34.43	36.69	139.9	1224
PDF unc.	±3.5%	±3.1%	±2.1%	±2.1%	±2.1%	±1.7%	±1.7%
αS unc.	±2.6%	±2.4%	±2.1%	±2.1%	±2.1%	±1.8%	±1.7%
PDF+αS unc.	±4.3%	±3.9%	±3.0%	±3.0%	±3.0%	±2.5%	±2.4%
Scale unc.	_-6.5%^+3.0%	_-6.1%^+2.8%	_-5.0%^+2.2%	_-4.9%^+2.1%	_-4.9%^+2.1%	_-3.9%^+1.3%	_-3.2%^+0.9%
mtop unc.	-	-	_-18%^+4%	_-18%^+4%	_-18%^+4%	_-18%^+4%	_-18%^+3%
Scale+mtop unc.	-	-	_-23%^+6%	_-23%^+6%	_-23%^+6%	_-22%^+5%	_-21%^+4%
mtop approx. unc.	±2.2%	±2.3%	±2.6%	±2.7%	±2.7%	±3.4%	±4.6%

The recommended uncertainties to be considered are PDF, alphaS (combined "PDF+αS unc."), scale and mtop scheme (combined "Scale+mtop unc.").
The top mass approximation uncertainty reported in the last row should not be considered in analyses since it is expected to be covered by the larger mtop scheme uncertainty.

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

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

3) Inclusive ggF cross-sections for Higgs boson pair production at 13 TeV, for different values of the Higgs self-coupling modifier κ_λ, obtained for m_H = 125 GeV with the central scale μ0 = μR = μF = M_HH/2 at NNLO_NLO-i (rescaled to the NNLO FTapprox total cross section in the κ_λ = 1 limit). For more details, see https://arxiv.org/abs/2003.01700. The cross-section is found to be a quadratic function of κ_λ:

σ = 70.3874-50.4111*κ_λ+11.0595*κ_λ² in fb.

κ_λ	-10	-5	-1	0	1	2	2.4	3	5	10
σ [fb]	1680	598.9	131.9	70.38	31.05	13.81	13.10	18.67	94.82	672.2
Scale unc.	_-7.7%^+3.0%	_-7.5%^+2.7%	_-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%	_-8.5%^+4.2%
mtop unc.	_-6%^+10%	_-7%^+10%	_-9%^+8%	_-12%^+6%	_-18%^+4%	_-23%^+1%	_-22%^+4%	_-15%^+9%	_-4%^+13%	_-4%^+12%
Combined (Scale+mtop) unc.	_-14%^+13%	_-15%^+13%	_-16%^+11%	_-18%^+8%	_-23%^+6%	_-28%^+3%	_-27%^+6%	_-22%^+12%	_-13%^+18%	_-13%^+16%

In the table above, 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 those of the NNLO FTapprox SM prediction. The combined uncertainties are computed in https://arxiv.org/abs/2008.11626

, and should be used for the Run 2 results. The upper and lower scale uncertainty bands can be parameterized in a quite accurate way with the following functions:

upper_unc[κ_λ] = Max[ 76.6075 - 56.4818*κ_λ+ 12.635*κ_λ², 75.4617 - 56.3164*κ_λ + 12.7135*κ_λ²] in fb.

lower_unc[κ_λ] = Min[ 57.6809 - 42.9905*κ_λ+ 9.58474*κ_λ², 58.3769 - 43.9657*κ_λ+ 9.87094*κ_λ²] in fb.

Given the central prediction versus κ_λ, the percentage variation from scale uncertainties can then be computed for any given κ_λ.

As for the PDF uncertainties, they have been found not to vary significantly with κ_λ and are of the order of 3% over the whole range.

OLD recommendations for gluon fusion (from YR4)

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The table below shows NNLL-matched-to-NNLO cross-sections for gg → HH with the central scale μ0 = μR = μF = M_HH/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!

m_H	√s	σ′_NNLO+NNLL [fb]	scale unc. [%]	scale unc. [%]	th. unc. [%]	α_s 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.

m_H (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 = M_hhZ. 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%