Higgs cross sections for European Strategy studies in 2012


1. LHC acclerarator benchmark scenario

LHC √s Luminosity
before upgrades 14 TeV 300 fb-1
High Luminosity 14 TeV 3000 fb-1
Energy Upgrade 33 TeV 300 (3000) fb-1


2. Higgs cross sections and branching ratios for HL/HE-LHC

  • SM input parameters can be found here.
  • The default Higgs mass points for SM Higgs productions are MH=125 and 800 GeV. The 800 GeV point has been chosen to avoid the unitarity problem even in s→infinite case. For Higgs self-coupling study, MH=125 GeV only.

SM Higgs production cross sections at √s = 14 TeV (MH=125, 800 GeV)

  MH=125 GeV   MH=800 GeV
Process Cross section Scale uncertainty PDF+αs uncertainty   Cross section Scale uncertainty PDF+αs uncertainty
ggF a 50.35 pb +7.5% -8.0% +7.2% -6.0%   0.607 pb +5.3% -4.6% +8.2% -7.7%
VBF b 4.172 pb +0.4% -0.3% +1.9% -1.5%   0.2278 pb +0.3% -0.6% +2.6% -2.0%
WH c 1.504 pb +0.3% -0.6% +3.8% -3.8%   -        
ZH c 0.8830 pb +2.7% -1.8% +3.7% -3.7%   -        
ttH c 0.6113 pb +5.9% -9.3% +8.9% -8.9%   -        
PDF+αs uncertainties are according to PDF4LHC recipe.
a) Numbers in complex-pole-scheme with NNLO+NNLL QCD + NLO EW corrections (D. de Florian, G. Passarino) .
b) Higgs width zero-width approximation, same as CERN Report 1, with NNLO QCD + NLO EW corrections. (D. Rebuzzi)
c) Higgs width Zero-width approximation, with NNLO QCD + NLO EW (WH/ZH) and NLO QCD corrections (ttH). Numbers from CERN-2011-002, Table 39, and TWiki page summary.

SM Higgs production cross sections at √s = 33 TeV (MH=125, 800 GeV)

  MH=125 GeV   MH=800 GeV
Process Cross section Scale uncertainty PDF+αs uncertainty   Cross section Scale uncertainty PDF+αs uncertainty
ggF a 178.32 pb +7.8% -8.2% +7.4% -7.2%   4.855 pb +4.9% -4.4% +6.3% -6.2%
VBF b 15.47 pb +0.6% -0.6% +1.7% -1.4%   2.145 pb +0.3% -0.1% +2.3% -1.7%
WH c 4.272 pb +0.2% -0.7% +2.4% -2.4%   0.007390 pb +0.2% -0.5% +3.3% -3.3%
ZH c 2.780 pb +4.8% -3.2% +2.5% -2.5%   0.005776 pb +8.6% -5.7% +2.0% -2.0%
ttH d 4.377 pb +8.1% -8.9% +5.4% -5.4%   0.07658 pb +9.1% -10.9% +7.3% -7.3%
PDF+αs uncertainties are according to PDF4LHC recipe.
a) Numbers in complex-pole-scheme with NNLO+NNLL QCD + NLO EW corrections (D. de Florian, G. Passarino).
b) Higgs width zero-width approximation, same as CERN Report 1, with NNLO QCD + NLO EW corrections (D. Rebuzzi)
c) NNLO QCD + NLO EW corrections (R. Harlander).
d) NLO QCD. (M. Spira).

SM Higgs-pair (triple) production cross sections at √s = 14 and 33 TeV (MH=125GeV)

  √s = 14 TeV   √s = 33 TeV
Process Cross section Scale uncertainty PDF+αs uncertainty   Cross section Scale uncertainty PDF+αs uncertainty
gg → HH1(λ=1) 33.86 fb +17.9% -14.9% +2.7% (+4.3%) -2.9% (-4.2%)   206.6 fb +15.1% -12.5% +2.0% (+2.9%) -2.3% (-3.1%)
(λ=0) 71.01 fb +17.9% -14.8% +2.6% (+4.1%) -2.8% (-4.0%)   413.8 fb +15.1% -12.4% +1.9% (+2.8%) -2.2% (-3.1%)
(λ=2) 15.85 fb +18.0% -15.0% +2.8% (+4.5%) -3.0% (-4.4%)   100.7 fb +15.3% -12.5% +1.8% (+2.8%) -2.5% (-3.4%)
gg → HHH2 0.044 fb +28% -21% +2.0% (+3.0%) -2.6% (-4.8%)   0.326 fb +20% -16% +1.5% (+2.7%) -1.3% ( -2.5%)
qq → qqHH3 1.807 fb +8.8% -7.7%       11.09 fb +4.6% -3.8%    
qq → WHH3 0.43 fb +1.1% -1.3% +1.2% (+2.6%) -1.5% (-3.4%)   1.58 fb +2.2% -3.1% +0.8% (+1.7%) -1.2% (-2.9%)
qq → ZHH3 0.27 fb +1.3% -1.4% +1.2% (+2.6%) -1.5% (-3.4%)   1.04 fb +2.1% -3.0% +0.8% (+1.7%) -1.2% (-2.9%)
  1. NLO QCD with MSTW2008NLO. The central scale is the invariant mass of the Higgs pair. The scale is varied by a factor 2 up and down. (M. Spira with HPAIR program)
  2. LO QCD with MSTW2008LO. The central scale is 3*MH=375 GeV, scale variation is by a factor 2 up and down. PDF+αs uncertainties are the envelope of the MSTW2008 PDF at 68% (90%) CL. (M. Rauch)
  3. LO QCD with MSTW2008LO. The central scale is MV in qqHH and MHHV in VHH. The scale is varied by a factor 2 up and down. WW-fusion makes up 70% and ZZ-fusion makes up 30% of the total qqHH cross section at 33 TeV. PDF+αs uncertainties are the envelope of the MSTW2008 PDF at 68% (90%) CL. (M. Mühlleitner, R. Gröber, J. Baglio)

SM Higgs decay branching ratio (MH=125GeV)

Process Branching ratio Uncertainty
H → bb 5.77 x 10-1 +3.2% -3.3%
H → ττ 6.32 x 10-2 +5.7% -5.7%
H → μμ 2.20 x 10-4 +6.0% -5.9%
H → cc 2.91 x 10-2 +12.2% -12.2%
H → gg 8.57 x 10-2 +10.2% -10.0%
H → γγ 2.28 x 10-3 +5.0% -4.9%
H → Zγ 1.54 x 10-3 +9.0% -8.8%
H → WW 2.15 x 10-1 +4.3% -4.2%
H → ZZ 2.64 x 10-2 +4.3% -4.2%
ΓH [GeV] 4.07 x 10-3 +4.0% -3.9%

Process Branching ratio Uncertainty   Process Branching ratio Uncertainty
H → 4l (l=e,μ,τ) 2.76 x 10-4 ±4.3%   H → 2l2q (l=e,μ,τ, q=udcsb) 3.70 x 10-3 ±4.3%
H → 4l (l=e,μ) 1.25 x 10-4 ±4.3%   H → 2l2q (l=e,μ, q=udcsb) 2.47 x 10-3 ±4.3%
H → eeee 3.27 x 10-5 ±4.3%   H → lνqq (l=e,μ, q=udcsb) 3.14 x 10-2 ±4.3%
H → eeμμ 5.93 x 10-5 ±4.3%   H → ννqq (ν=any, q=udcsb) 7.38 x 10-3 ±4.3%
H → 2l2ν (l=e,μ,τ, ν=any) 2.34 x 10-2 ±4.3%   H → 4q (q=udcsb) 1.10 x 10-1 ±4.3%
H → 2l2ν (l=e,μ, ν=any) 1.06 x 10-2 ±4.3%   H → 4f (f=any fefrmion) 2.40 x 10-1 ±4.3%
H → e+νe-ν 2.52 x 10-3 ±4.3%        
H → e+νμ-ν 2.52 x 10-3 ±4.3%        


3. Major SM background process cross sections

ttbar cross section at √s = 8, 14 and 33 TeV

  • The numbers have been obtained with the version 1.3 of the program HATHOR at approx. NNLO accuracy based on the theory input and with the latest improvements at NNLO. Please also note, that in addition to the scale uncertainty at LHC 14 and 33 TeV there is a uncertainty due to unknown terms at high energies at NNLO. (S.-O. Moch)
  • The numbers scan a pole mass for Mtop in the range of 170-175 GeV and use the MSTW2008 PDF set. The PDF uncertainties is given at 68% CL. The uncertainty due to the gluon luminosity is large.

√s = 8 TeV   √s = 14 TeV   √s = 33 TeV
Mtop σ scale uncertainty PDF uncert.   Mtop σ scale uncertainty PDF uncert.   Mtop σ scale uncertainty PDF uncert.
[GeV] [pb] [pb] [pb] [pb] [pb]   [GeV] [pb] [pb] [pb] [pb] [pb]   [GeV] [pb] [pb] [pb] [pb] [pb]
170.0 272.1 +14.7 -19.5 +6.7 -6.8   170.0 1046. +45.0 -64.6 +17.3 -18.8   170.0 5891. +168. -281. +56.4 -78.0
170.5 268.1 +14.5 -19.2 +6.6 -6.7   170.5 1032. +44.5 -63.7 +17.1 -18.7   170.5 5819. +166. -277. +55.2 -77.7
171.0 264.1 +14.3 -19.0 +6.5 -6.6   171.0 1018. +43.9 -62.8 +16.8 -18.5   171.0 5748. +164. -274. +54.6 -76.7
171.5 260.2 +14.1 -18.7 +6.4 -6.6   171.5 1005. +43.3 -62.0 +16.6 -18.3   171.5 5679. +163. -270. +53.6 -76.0
172.0 256.4 +13.8 -18.4 +6.3 -6.5   172.0 991.0 +42.7 -61.2 +16.5 -18.0   172.0 5610. +161. -267. +53.4 -74.9
172.5 252.6 +13.6 -18.1 +6.2 -6.4   172.5 977.7 +42.2 -60.3 +16.2 -17.9   172.5 5542. +159. -264. +52.7 -74.2
173.0 248.9 +13.5 -17.9 +6.2 -6.3   173.0 964.6 +41.6 -59.5 +16.1 -17.6   173.0 5476. +157. -261. +52.0 -73.2
173.5 245.3 +13.3 -17.6 +6.1 -6.2   173.5 951.7 +41.1 -58.8 +15.9 -17.4   173.5 5410. +155. -258. +51.7 -72.1
174.0 241.7 +13.1 -17.4 +6.0 -6.1   174.0 939.0 +40.5 -58.0 +15.7 -17.2   174.0 5346. +153. -255. +50.9 -71.5
174.5 238.2 +12.9 -17.1 +5.9 -6.1   174.5 926.5 +40.0 -57.2 +15.5 -17.1   174.5 5282. +152. -252. +50.3 -70.9
175.0 234.8 +12.7 -16.8 +5.8 -6.0   175.0 914.2 +39.5 -56.4 +15.4 -16.8   175.0 5219. +150. -249. +50.1 -69.7


4. Higgs cross sections for HE-LHC

SM Higgs production cross sections at √s = 14, 33, 40, 60, 80 and 100 TeV (MH=125 GeV)

Process √s = 14 TeV √s = 33 TeV √s = 40 TeV √s = 60 TeV √s = 80 TeV √s = 100 TeV
ggF a 50.35 pb 178.3 pb (3.5) 231.9 pb (4.6) 394.4 pb (7.8) 565.1 pb (11.2) 740.3 pb (14.7)
VBF b 4.40 pb 16.5 pb (3.8) 23.1 pb (5.2) 40.8 pb (9.3) 60.0 pb (13.6) 82.0 pb (18.6)
WH c 1.63 pb 4.71 pb (2.9) 5.88 pb (3.6) 9.23 pb (5.7) 12.60 pb (7.7) 15.90 pb (9.7)
ZH c 0.904 pb 2.97 pb (3.3) 3.78 pb (4.2) 6.19 pb (6.8) 8.71 pb (9.6) 11.26 pb (12.5)
ttH d 0.623 pb 4.56 pb (7.3) 6.79 pb (11) 15.0 pb (24) 25.5 pb (41) 37.9 pb (61)
gg → HHe(λ=1) 33.8 fb 207 fb (6.1) 298 fb (8.8) 609 fb (18) 980 fb (29) 1.42 pb (42)
PDF is NNLO(NLO) MSTW2008 set. Numbers in () parentheses are the cross-section ratio wrt 14 TeV.
a) NNLO+NNLL QCD + NLO EW corrections. QCD scale and PDF+αs uncertainties remain constant about +-8% for both (D. de Florian).
b) NNLO QCD only with VBF@NNLO (M. Zaro).
c) NNLO QCD only with VH@NNLO (R. Harlander).
d) NLO QCD. (M. Spira).
e) NLO QCD with HPAIR. The central scale is the invariant mass of the Higgs pair. The scale is varied by a factor 2 up and down. (M. Spira).

Process √s = 14 TeV √s = 33 TeV √s = 40 TeV √s = 60 TeV √s = 80 TeV √s = 100 TeV
W+H a 0.963 pb 2.65 pb (2.7) 3.27 pb (3.4) 5.08 pb (5.3) 6.88 pb (7.1) 8.66 pb (9.0)
W-H a 0.624 pb 1.92 pb (3.1) 2.43 pb (3.9) 3.93 pb (6.3) 5.42 pb (8.7) 6.93 pb (11.1)
ZH a 0.861 pb 2.55 pb (3.0) 3.21 pb (3.7) 5.12 pb (5.9) 7.06 pb (8.2) 9.02 pb (10.5)
ttH b 0.625 pb 4.55 pb (7.3) 6.81 pb (11) 15.0 pb (24) 25.5 pb (41) 37.9 pb (61)
PDF is NLO MSTW2008 set. Numbers in () parentheses are the cross-section ratio wrt 14 TeV.
a) OpenLoops+Sherpa, NLO QCD corrections only, with dynamical renormalization scale set to the virtuality of the intermediate vector boson. gg → ZH is not included (F. Cascioli, J. Thompson).
b) OpenLoops+Sherpa, NLO QCD corrections only, with μR = Mtop + MH/2 (F. Cascioli, J. Thompson).


Figure : Parton luminosity and ratio for Ecms=14, 40, 60, 80 and 100 TeV. (J. Stirling, see also here).

5. Tools

Monte Carlo

  • HPAIR: program for gg→HH. (M. Spira)

  • MadGraph 5: all processes gg→HH, HHH, qq→qqHH and qq→VHH are available at tree-level. MadGraph 4 contains gg→HH. (F. Maltoni)


6. Plots

Figure 1: Standard Model process cross sections at hadron colliders as a function of centre-of-mass energy (left), cross sections for SM and BSM particles as a function of mass at √s = 7 TeV (right). More plots for 8 and 33 TeV to come. (J. Stirling, see also here).



Figure 2: The ratio of parton luminosities between 7, 8, 14 and 33 TeV. (J. Stirling, see also here).

Figure 3: Higgs-boson production cross sections as a function of centre-of-mass energies.

Figure 4: Higgs-boson pair production cross section in gg→HH as a function of Higgs-boson mass at centre-of-mass energies at 14 and 33 TeV (M. Spira).


6. References

  1. LHC Physics Review
  2. Higgs Trilinear Coupling
  3. Higgs Quartic Coupling
  4. BSM interpretation


-- ReiTanaka - 08-May-2012

Topic attachments
I Attachment History Action Size Date Who Comment
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PDFpdf Higgs_XS_7-100TeV.pdf r1 manage 14.3 K 2013-11-13 - 14:00 ReiTanaka Higgs Cross Sections
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PDFpdf Stirling_crosssections2012HE.pdf r1 manage 27.2 K 2012-05-30 - 12:14 ReiTanaka pp Cross Sections (J. Striling)
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PDFpdf Stirling_lhclumi71433_2012_v0.pdf r1 manage 66.5 K 2012-05-30 - 12:16 ReiTanaka Parton Luminosities (J. Striling)
PNGpng Stirling_lhclumi71433_2012_v0.png r1 manage 40.0 K 2012-05-30 - 12:16 ReiTanaka Parton Luminosities (J. Striling)
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PNGpng Stirling_lhclumi7813_2013_v1.png r1 manage 66.9 K 2013-08-30 - 12:13 ReiTanaka Parton Luminosities (J. Striling)
JPEGjpg Stirling_lhclumi78_linear_2012.jpg r1 manage 645.1 K 2012-06-27 - 19:50 ReiTanaka Parton Luminosities (J. Striling)
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PDFpdf Stirling_lhclumi81433_2012_v0.pdf r1 manage 69.1 K 2013-08-30 - 12:13 ReiTanaka Parton Luminosities (J. Striling)
PNGpng Stirling_lhclumi81433_2012_v0.png r1 manage 75.5 K 2013-08-30 - 12:13 ReiTanaka Parton Luminosities (J. Striling)
JPEGjpg hpair.jpg r1 manage 689.7 K 2012-06-27 - 17:55 ReiTanaka Higgs pair production cross section in gg->HH
Postscriptps hpair.ps r1 manage 13.6 K 2012-06-27 - 17:55 ReiTanaka Higgs pair production cross section in gg->HH
PDFpdf lumi_14to100_abs.pdf r1 manage 213.6 K 2012-10-14 - 22:30 ReiTanaka Parton Luminosities (J. Striling)
PNGpng lumi_14to100_abs.png r1 manage 310.1 K 2012-10-14 - 22:32 ReiTanaka Parton Luminosities (J. Striling)
PDFpdf lumi_14to100_ratios.pdf r1 manage 159.4 K 2012-10-14 - 22:31 ReiTanaka Parton Luminosities (J. Striling)
PNGpng lumi_14to100_ratios.png r1 manage 243.0 K 2012-10-14 - 22:31 ReiTanaka Parton Luminosities (J. Striling)
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