Higgs cross sections for HL-LHC and HE-LHC

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1. LHC acclerarator benchmark scenario

LHC	√s	Luminosity
before upgrades	14 TeV	300 fb-1
High Luminosity (HL-LHC)	14 TeV	3000 fb-1
Energy Upgrade	33 TeV	300 (3000) fb-1
High Energy (FCC/FHC)	80-100 TeV

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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 M_H=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, M_H=125 GeV only.

SM Higgs production cross sections at √s = 14 TeV (M_H=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%		-
bbH d	0.5805 pb	+13.0%	-24.0%	+6.1%	-6.1%		-

PDF+α_s 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.
d) The cross section is the Santander matched numbers with 5FS (NNLO, R. Harlander) and 4FS (NLO, M. Spira) (see Section 12.2.2 in CERN Report 2).

SM Higgs production cross sections at √s = 33 TeV (M_H=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%
bbH e	2.132 pb	+7.0%	-34.0%	+5.9%	-5.9%		-

PDF+α_s 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).
e) NNLO QCD in 5FS (R. Harlander).

SM Higgs-pair (triple) production cross sections at √s = 7 and 8 TeV (M_H=125GeV)

	√s = 7 TeV						√s = 8 TeV
Process	Cross section	Scale uncertainty		PDF+αs uncertainty			Cross section	Scale uncertainty		PDF+αs uncertainty
gg → HH1(λ=1)	5.582 fb	+20.9%	-17.2%	+2.6% (+6.0%)	-1.8% (-5.1%)		8.152 fb	+20.3%	-16.7%	+2.7% (+6.0%)	-1.8% (-5.1%)

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)

SM Higgs-pair (triple) production cross sections at √s = 14 and 33 TeV (M_H=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%	+2.5% (+5.8%)	-1.8% (-5.1%)		206.6 fb	+15.1%	-12.5%	+2.5% (+5.8%)	-1.7% (-5.0%)
(λ=0)	71.01 fb	+17.9%	-14.8%	+2.6% (+6.0%)	-1.9% (-5.2%)		413.8 fb	+15.1%	-12.4%	+2.7% (+6.0%)	-1.8% (-5.1%)
(λ=2)	15.85 fb	+18.0%	-15.0%	+2.8% (+6.1%)	-1.7% (-5.0%)		100.7 fb	+15.3%	-12.5%	+2.7% (+6.0%)	-1.8% (-5.0%)
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*M_H=375 GeV, scale variation is by a factor 2 up and down. PDF+α_s uncertainties are the envelope of the MSTW2008 PDF at 68% (90%) CL. (M. Rauch)
3. LO QCD with MSTW2008LO. The central scale is M_V in qqHH and M_HHV 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+α_s uncertainties are the envelope of the MSTW2008 PDF at 68% (90%) CL. (M. Mühlleitner, R. Gröber, J. Baglio)

SM Higgs decay branching ratio (M_H=125GeV)

• For latest numbers, please always refer to BR TWiki page.

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%

• Reference: CERN-2012-002, Tables A1-A20.

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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 M_top 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

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4. Higgs cross sections for HE-LHC

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

Process	√s = 14 TeV	√s = 33 TeV	√s = 40 TeV	√s = 60 TeV	√s = 80 TeV	√s = 100 TeV
bbH e	0.581 pb	2.13 pb (3.7)	2.77 pb (4.8)	4.69 pb (8.1)	6.65 pb (11)	8.64 pb (15)
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)
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)
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)
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)
gg → HHf(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+α_s 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) NNLO QCD in 5FS (R. Harlander).
f) 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 μ_R = M_top + M_H/2 (F. Cascioli, J. Thompson).

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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)

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6. Plots

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6. References

1. LHC Physics Review
   • F. Gianotti, M.L. Mangano, T. Virdee (conveners), Eur. Phys. J. C39 (2005) 293–333.
   • A. De Roeck, et al., Eur. Phys. J. C66 (2010) 525–583.
2. Higgs Trilinear Coupling
   • E.W.N. Glover, J.J. van der Bij, Physics Letters B219 (1989) 488–492.
   • S. Dawson, S. Dittmaier and M. Spira, Phys. Rev. D58 (1998) 115012.
   • A. Djouadi, W. Kilian, M. Mühlleitner and P.M. Zerwas, Eur. Phys. J. C10 (1999) 45–49 .
   • U. Baur,T. Plehn, and D. Rainwater, Phys. Rev. Lett. 89 (2002) 151801, Phys. Rev. D67 (2003) 033003, Phys. Rev. D68 (2003) 033001, Phys. Rev. D69 (2004) 053004 .
   • T. Binoth, S. Karg, N. Kauer, and R. Rückl, Phys. Rev. D74 (2006) 113008.
   • M.J. Dolan,C. Englert, and M. Spannowsky, arXiv:1206.5001.
3. Higgs Quartic Coupling
   • T. Plehn and M. Rauch, Phys. Rev. D72 (2005) 053008.
4. BSM interpretation
   • M. Moretti, et al., JHEP 02 (2005)024.
   • A. Noble and M. Perelstein, Phys. Rev. D78 (2008) 063518.
   • R. Gröber and M. Mühlleitner, JHEP 06 (2011) 020.
     + many.

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-- ReiTanaka - 19 Dec 2013