Higgs Production Cross Section and Decay Branching Ratio Calculation for CERN Yellow Report 4

Help This is the instruction fo Higgs-boson production cross section and decay branching ratio calculations for RUN-2 (to be published in CERN Yellow Report 4).

  • See this link for previous instructions for 7 and 8 TeV in RUN-1.

Blue led Standard Model Input Parameter

Aqua led Lepton (PDG2014) &Quark Masses

e μ τ
0.510998928(11) MeV 105.6583715(35) MeV 1776.82(16) MeV
u c t
100 MeV 0.986 ± 0.026 GeV 172.5 ± 1.0 GeV
d s b
100 MeV 100 MeV 4.18 ± 0.03 GeV
  1. The top-quark mass is on-shell top-quark mass MtOS. Corresponding MS-bar mass is MtMS(Mt)=162.7±1.0 GeV.
  2. The bottom-quark mass is MS-bar bottom-quark mass MbMS(Mb). Corresponding on-shell mass is MbOS=4.92±0.13 GeV.
  3. The charm-quark mass is evaluated at Mc(3 GeV). On-shell charm-quark mass is McOS=1.51±0.13 GeV.

Green led Gauge Boson Masses and Widths (PDG2014)

W MW ΓW
  80.385(15) GeV 2.085(42) GeV
Z MZ ΓZ
  91.1876(21) GeV 2.4952(23) GeV


Red led 1. SM Higgs-boson production cross section and decay branching ratio calculation

Aqua led Mass scan: √s = 7 and 8 TeV (for updates) and 13 and 14 TeV

  • Full mass scan should be provided for major Higgs production processes:
    1. Major process: ggF, VBF, WH (also separate W+H and W-H), ZH (also gg→ZH)
    2. Associated Higgs with heavy quark: ttH, bbH
    3. Associated Higgs with single top-quark: tH (bq→tHq', bg→WtH, qq→btH)
  • Only at MH=[124.5, 125.0, 125.09, 125.5] GeV (4 points) for rare Higgs production processes (σ < O(100) fb) and rare Higgs decay channels:
    1. Associated Higgs with heavy quark: ccH
    2. Higgs pair/triple production: HH, ttHH, qqHH, tjHH, VHH, VVHH, HHH (V=W,Z)
    3. Associated Higgs with gauge boson: VVH (V=γ,W,Z)

  • Full mass scan should be provided for major Higgs decay channels.
  • Only at MH=[124.5, 125.0, 125.09, 125.5] GeV (4 points) for rare Higgs decay channels.

Mass range and step for SM-like Higgs boson:

Higgs Mass range step size # of points addendum
[120,124] GeV 0.5 GeV 9 points  
[124,126] GeV 0.1 GeV 20 points + MH=125.09 GeV
[126,130] GeV 0.5 GeV 8 points  
  • Total 38 points for MH=[120,130] GeV.
  • Empirical function of cross section as a function of Higgs-boson mass should be provided.

Aqua led Ecm scan: √s = [6,15] TeV with 0.5 TeV step (19 points)

  • Ecm scan should be provided for major Higgs production processes:
    1. Major process: ggF, VBF, WH (also separate W+H and W-H), ZH (also gg→ZH)
    2. Associated Higgs with heavy quark: ttH, bbH
    3. Associated Higgs with single top-quark: tH (bq→tHq', bg→WtH, qq→btH)
  • Should be scanned for both MH=125.0 and 125.09 GeV.


Red led 2. BSM Higgs-boson production cross section calculation and decay width

Aqua led Mass scan: √s = 7 and 8 TeV (for updates) and 13 and 14 TeV

  • Please check Proposal on how to provide reference "Higgs" cross sections for BSM applications
  • Full mass scan should be provided for major Higgs production processes:
    1. Major process: ggF, VBF, WH (also separate W+H and W-H), ZH (also gg→ZH)
    2. Associated Higgs with heavy quark: ttH, bbH
    3. Associated Higgs with single top-quark: tH (bq→tHq', bg→WtH, qq→btH) (only for 13 and 14 TeV)
  • Higgs width should be set to zero (NWA).
  • Separate electroweak correction should be provided.
  • For relevant processes, and if possible, the contributions proportional to different Higgs couplings should be given separately, together with the corresponding uncertainties.
  • All other external parameters should be chosen as in the corresponding best SM predictions as well as the evaluation of the uncertainties.
  • SM width: At each mass point, the corresponding Higgs widths calculated in the SM with the same characteristics above should be provided.
  • Examples on how to use these predictions in specific cases are provided.

Mass range and step for BSM Higgs boson:

Higgs Mass range step size # of points addendum
[10,150] GeV 5 GeV 29 points  
[150,500] GeV 10 GeV 35 points + MH=125.09 GeV
[500,3000] GeV 50 GeV 50 points  
  • Total 115 points for MH=[10,3000] GeV.
  • Lower mass limit might depend on stability of the code at low Bjorken-x. To be assessed.


Green led 3. QCD and EW corrections and uncertainties

  • Complete inclusive Higgs boson production cross sections and decay branching ratios should be estimated.
    • Highest-order QCD corrections should be included and associated uncertainties should be calculated as below.
    • Highest-order EW corrections should be included and associated uncertainties should be estimated.
  • It should be discussed and agreed in each subgroup how to estimate QCD and EW uncertainties.

  • For both Higgs cross section and decay branching ratio, theory uncertainties (THU) and parametric uncertainties (PU) should be separated.
  • Following i) QCD scale Uncertainty, ii) Theory Uncertainty (THU) and iii) Parametric Uncertainty (PU) should be calculated.

i) QCD Scale Uncertainty

  • The factorization and the renormalization scales are process dependent and should be defined by each subgroup.
  • The scale uncertainty should also be defined by each group, (e.g.. 1/2MH < μR, μF < 2MH, do 2D scan with 1/2 < μRF < 2).
  • As these uncertainties change smoothly, it would be enough to do the coarse scan.
    • Please carry out the interpolation with spline fit (or 3rd order polynomial fit) for other Higgs mass points.

ii) Theory Uncertainty (THU) (M. Spira's definition)

  • For all processes that are known up to certain QCD order exactly the scale dependence is sufficient. For any incomplete calculation as e.g. ggF or Higgs pairs there are additional missing higher-order mass effects. In addition in the context of elw. corrections the THUs will of course be estimated in a different way than just looking at the scale dependence. But this should be discussed by the corresponding subgroup contributions. In this way it makes sense to ask for additional THUs (for elw. stuff and missing mass effects).

iii) Parametric Uncertainty (PU)

  • PU should include the uncertainties due to quark-masses, αs, and they should be separated (to facilitate to combine results in different Higgs boson production and decay channels).

Orange led 4. PDF set and PDF+αs uncertainty calculations

  1. For highest precision in the case of SM Higgs (ex. ggF, VBF, etc.), PDF4LHC15_100 set should be used.
    • However in situations when computational speed is needed or a more limited number of error PDFs may be desirable, PDF4LHC15_30 set can be used.
    • Both PDF4LHC15_100 and PDF4LHC15_30 sets reproduce well the 900 replica (prior) PDF set for SM Higgs mass (See Figure 15 of PDF4LHC recommendations for LHC Run II).
  2. For BSM Higgs, PDF4LHC15_mc set can be used.

PDF set

Process SM Higgs BSM Higgs
NLO QCD NNLO QCD NLO QCD NNLO QCD
Central value PDF4LHC15_nlo_100 PDF4LHC15_nnlo_100 PDF4LHC15_nlo_mc PDF4LHC15_nnlo_mc
PDF4LHC15_nlo_30 PDF4LHC15_nnlo_30 - -
Uncertainties PDF4LHC15_nlo_100_pdfas PDF4LHC15_nnlo_100_pdfas PDF4LHC15_nlo_mc_pdfas PDF4LHC15_nnlo_mc_pdfas
PDF4LHC15_nlo_30_pdfas PDF4LHC15_nnlo_30_pdfas - -

  • 4FS PDF set should be used for corresponding processes.

  • For LO process combined PDFLHC set does not exist (yet). Either dedicated LO PDF set or combined PDF4LHC NLO PDF set can be used.
    • Warning: The theoretical uncertainty on LO is very large and dominant in general. If NLO PDFs are used in a LO computation, the nominal PDF uncertainty may not be representative of the actual PDF uncertainty.

PDF and QCD αs(MZ) uncertainties

  • QCD αs(MZ) should be set as 0.1180+-0.0015.
  • Separate PDF and αs uncertainties should be provided.
    • The total PDF+αs uncertainty is evaluated by adding the variations of PDFs and αs uncertainties in quadrature.
    • See Section 6.2 of new PDF4LHC recommendation for formulae of the uncertainty calculation.

Purple led 5. Numerical results

  • Results should be reported in the following format:
    • XS ±Scale Uncertainty [%] ±THU [%] ±PU(quark-mass) [%] ±PU(αs) [%] ±PDF Uncertainty [%]
    • BR ±THU [%] ±PU(quark-mass) [%] ±PU(αs) [%]
  • We recommend XS and BR numbers given in 4 significant digits (ex. 12.34 pb) and uncertainties should have 1 sub-digit in % (ex. ±1.2%).
  • PU(quark-mass) [%] should be the quadratic sum of uncertainties due to top, bottom and charm quarks.


-- ReiTanaka - 19-Nov-2015

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