SM Higgs production cross sections at √s = 7 TeV (update in CERN Report4 2016)

• Cross sections reported in CERN Report 4. See here and here here for previous numbers in CERN Report 3.
• Higgs cross sections and BRs in Spread sheet are available in xlsx format
• You can find figures at our gallery here.

Mass range and step for SM-like Higgs boson:

• Total 38 points for M_H=[120,130] GeV.

gluon-gluon Fusion Process

N3LO QCD cross sections supercede those of NNLO+NNLL QCD

N3LO

• Cross sections are calculated by Zürich group at N3LO QCD and NLO EW accuracies [Anastasiou:2016cez].
• QCD scales: μ=μ_F=μ_R=M_H/2 varied in the range of [M_H/4,M_H].
• Theory uncertainty:
  • "±Theory" uncertainty is interpreted as a flat 100% confidence level.
  • "TH Gaussian" uncertainty is interpreted as a one-sigma range. It is estimated by max{+TH,-TH}/sqrt{3} as discussed in CERN Report 4 ggF section.
  • "TH Gaussian" uncertainty should be used for the construction of the workspace in the current LHC-HCG prescription.
• PDF set: PDF4LHC15_nnlo_100

NNLO+NNLL

• Cross sections are calculated with dFG program at NNLO+NNLL QCD and NLO EW accuracies.
• Calculations are the same as CERN Report 3 (i.e. top, bottom and charm quark effects are taken into account), except it is in NWA (CPS in CERN Report 3).
• Program: dFG
• QCD scales: μ=μ_F=μ_R=M_H, uncertainty estimated in the range 1/2 < μ/M_H < 2 with 1/2 < μ_F/μ_R < 2 constraint.
  • No additional THU nor PU uncertainties assigned.
• PDF set: PDF4LHC15_nnlo_30

VBF Process

• Cross sections are calculated at (approx.) NNLO QCD and NLO EW accuracies.
• Calculations are the same as CERN Report 3, except it is in NWA (CPS in CERN Report 3).
• Program: NNLO QCD (VBF@NNLO) and NLO EW (HAWK).
• QCD scales: μ=μ_F=μ_R=M_W, uncertainty estimated in the range 1/2 < μ/M_W < 2 (keeping μ_F=μ_R).
  • No additional THU nor PU uncertainties assigned.
• PDF set: PDF4LHC15_nnlo_100 (QCD corrections) and NNPDF2.3QED (EW corrections + photon PDF)

WH Process

• Cross sections are calculated at NNLO QCD and NLO EW accuracies.
  • Calculations are the same as CERN Report 3, except photon-induced contribution (see below).
  • Total cross section is calculated from WH→lνH cross section by subtracting photon-induced cross section, and then scaled via BR(W→lν)=0.108535 in NLO EW accuracy.
• Program: NNLO QCD (VH@NNLO) and NLO EW (HAWK).
• QCD scales: μ=μ_F=μ_R=M_VH=(p_V+p_H)² for QCD part and μ=μ_F=μ_R=M_VH+M_H for EW part. Uncertainty is estimated in the range 1/3 < μ/M_VH < 3 (μ_F and μ_R are varied independently).
  • No additional THU nor PU uncertainties assigned.
• PDF set: PDF4LHC15_nnlo_mc (QCD part) and NNPDF2.3QED (EW part).
• Photon-induced contribution of O(5%)
  • NOT included for total cross section (agrees with CERN Report 3 numbers within 1%).
  • Included in cross sections for dedicated WH→lνH (l=e,μ or τ) process (we strongly recommend to use these numbers for dedicated analyses).

pp→WH Total Cross Section (with approximation)

WH→lνH (l=e,μ or τ) Process

ZH Process

• Cross sections are calculated at NNLO QCD and NLO EW accuracies.
  • Calculations are the same as CERN Report 3, except photon-induced contribution (see below).
  • Total cross section is calculated from ZH→llH,ννH cross sections by subtracting photon-induced cross section, and then scaled via BR(Z→ll)=0.0335962 and BR(Z→νν)=0.201030 in NLO EW accuracy.
  • gg→ZH (box-diagram) occurs as a part of NNLO QCD correction and included in the total cross section.
  • ZH cross section went up by +1~2%, due to +22~16% for √s = 7-14 TeV, due to increase in gg→ZH for NLO+NLL QCD corrections (NLO in CERN Report 3).
• Program: NNLO QCD (VH@NNLO) and NLO EW (HAWK).
• QCD scales: μ=μ_F=μ_R=M_VH=(p_V+p_H)² for QCD part and μ=μ_F=μ_R=M_VH+M_H for EW part. Uncertainty is estimated in the range 1/3 < μ/M_VH < 3 (μ_F and μ_R are varied independently).
  • No additional THU nor PU uncertainties assigned.
• PDF set: PDF4LHC15_nnlo_mc (QCD part) and NNPDF2.3QED (EW part).
• Photon-induced contribution of O(1%) or below
  • NOT included for total cross section (agrees with CERN Report 3 numbers).
  • Included in cross sections for dedicated ZH→llH,ννH (l=e,μ or τ) processes (we strongly recommend to use these numbers for dedicated analyses).

gg→ZH Cross Section

• ZH production has two distinct sources of gg→ZH:
  1. a genuine NNLO contribution to what called “Drell-Yan-like”, where ZH is accompanied by two-parton radiation, gg→HZ+qqbar.
  2. top- and bottom-loop induced contribution without any additional partons in the final state.
• What is usually meant by gg→HZ below is 2) above.
• The statement that “all but gg→HZ” is the same as “qq- and qg-initiated” is correct only through NLO QCD.
• For separate cross sections and associated QCD scale uncertainties in qq/qg→ZH(+gg→HZ+qqbar) and gg→ZH for NLO/LO MC normalization, use
  • σ(all but gg→ZH) = σ(pp→ZH)@(NNLO QCD + NLO EW, NLO+NLL QCD gg→ZH) - σ(gg→ZH)@(NLO+NLL QCD),
  • Separate QCD scale uncertainties are σ(all but gg→ZH) or on σ(gg→ZH) are calculated with VH@NNLO program.
• For M_H=125.0 GeV and at √s=7 TeV,

pp→ZH Total Cross Section (with approximation)

ZH→llH, ννH (l=e,μ or τ) Process

ttH Process

• Cross sections are calculated at NLO QCD and NLO EW accuracies.
  • Calculations are the same as CERN Report 3, except NLO EW corrections are adopted now.
• Program: MadGraph5_aMC@NLO (Sherpa+OpenLoops as cross ceck)
• QCD scales: μ=μ_F=μ_R=M_top+M_H/2, uncertainty estimated in the range 1/2 < μ/(M_top+M_H/2) < 2 (with 1/2 < μ_F/μ_R < 2 constraint).
  • No additional THU nor PU uncertainties assigned.
• PDF set: PDF4LHC15_nlo_30_pdfas

bbH Process

• The cross sections are the Santander matched numbers with 5FS (NNLO) and 4FS (NLO). No EW corrections.
• Program: SusHi for 5FS and dedicated version of MadGraph5_aMC@NLO for 4FS.
• QCD scales:
  • 5FS: μ_F=M_H/4, μ_R=M_H,
  • 4FS: μ_F=μ_R=(M_H+2M_b)/4,
  • scale with 7-point variation by a factor of 2 in both cases.
• Uncertainties
  • 5FS: Linearly added scale + (PDF⊕α_s) + M_b + μ_b (PDF and α_s uncertainties are added in quadrature).
  • 4FS: Only scale uncertainties (as they are the dominant ones) and no PDF uncertainties are included.
• PDF set
  • 5FS: Dedicated sets produced with APFEL are used which are generated from the PDF4LHC15_nnlo_100 sets taken below the M_b-threshold and evolved upwards, while generating a b-PDF set at high scale.
  • 4FS: PDF4LHC15_nlo_nf4_100

tH Process

t-ch (qb→tHq)

• Cross sections are calculated at NLO QCD accuracy (no NLO EW correction) in 5FS.
• Program: MadGraph5_aMC@NLO
• QCD scales: μ=μ_F=μ_R=(M_top+M_H)/4, uncertainty estimated in the range 1/2 < μ/{(M_top+M_H)/4} < 2 (with 1/2 < μ_F/μ_R < 2 constraint).
  • Flavour scheme (FS) dependence (4FS - 5FS envelope) included in the scale uncertainty. No PU uncertainty assigned.
• PDF set:
  • PDF4LHC15_nlo_30_pdfas (5FS)
  • PDF4LHC15_nlo_nf4_100 (4FS central set), used to compute the combined scale+FS uncertainty in tH t-channel.

s-ch (qq→tHb)

• Cross sections are calculated at NLO QCD accuracy (no NLO EW correction) in 5FS.
• Program: MadGraph5_aMC@NLO
• QCD scales: μ=μ_F=μ_R=(M_top+M_H)/2, uncertainty estimated in the range 1/2 < μ/{(M_top+M_H)/2} < 2 (with 1/2 < μ_F/μ_R < 2 constraint).
  • No additional THU nor PU uncertainties assigned.
• PDF set:
  • PDF4LHC15_nlo_30_pdfas (5FS)

W-associated (gb→tHW)

• Cross sections are calculated at NLO QCD accuracy (no NLO EW correction) in 5FS
  • With DR2 (Diagram Removal plus interference) described in [Demartin:2016axk]
  • σ(tHW^-) = σ(tbarHW⁺) = (σ(tHW^-)+σ(tbarHW⁺))/2
• Program: MadGraph5_aMC@NLO
• QCD scales: μ=μ_F=μ_R=(M_top+M_H+M_W)/2, uncertainty estimated in the range 1/2 < μ/{(M_top+M_H+M_W)/2} < 2 (with 1/2 < μ_F/μ_R < 2 constraint).
• PDF set:
  • PDF4LHC15_nlo_30_pdfas (5FS)

-- ReiTanaka - 2016-03-01