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

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.

Standard Model Input Parameter

• Please check INT note Standard Model input parameters for Higgs physics (LHCHXSWG-INT-2015-006)

Lepton (PDG2014) &Quark Masses

1. The top-quark mass is on-shell top-quark mass M_t^OS. Corresponding MS-bar mass is M_t^MS(M_t)=162.7±1.0 GeV.
2. The bottom-quark mass is MS-bar bottom-quark mass M_b^MS(M_b). Corresponding on-shell mass is M_b^OS=4.92±0.13 GeV.
3. The charm-quark mass is evaluated at M_c(3 GeV). On-shell charm-quark mass is M_c^OS=1.51±0.13 GeV.

Gauge Boson Masses and Widths (PDG2014)

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

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 M_H=[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 M_H=[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:

• Total 38 points for M_H=[120,130] GeV.
• Empirical function of cross section as a function of Higgs-boson mass should be provided.

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 M_H=125.0 and 125.09 GeV.

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

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:

• Total 115 points for M_H=[10,3000] GeV.
• Lower mass limit might depend on stability of the code at low Bjorken-x. To be assessed.

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.. 1/2M_H < μ_R, μ_F < 2M_H, do 2D scan with 1/2 < μ_R/μ_F < 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, α_s, and they should be separated (to facilitate to combine results in different Higgs boson production and decay channels).

4. PDF set and PDF+α_s uncertainty calculations

• Please follow the new PDF4LHC recommendations for LHC Run II. Please read Section 6 in particular for calculation prescription.
• All these PDF sets are on Hepforge LHAPDF.

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.
   • PDF4LHC15_mc set reproduces well the 900 replica (prior) PDF set for whole M_H=[10,3000] GeV range (See Figure 14 of PDF4LHC recommendations for LHC Run II).

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 α_s(M_Z) uncertainties

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

5. Numerical results

• Results should be reported in the following format:
  • XS ±Scale Uncertainty [%] ±THU [%] ±PU(quark-mass) [%] ±PU(α_s) [%] ±PDF Uncertainty [%]
  • BR ±THU [%] ±PU(quark-mass) [%] ±PU(α_s) [%]
• 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