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Higgs Cross Section Calculation at 7 and 8 TeV for RUN-1

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Blue led Standard Model input parameter

  • Input parameters for 8TeV calculations are the same as YR1.
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Gray led Higgs mass range and step:

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Higgs Cross Section Calculation at 7 and 8 TeV for RUN-1

Help This is the instruction for Higgs cross section calculations at centre-of-mass energy of 7 and 8 TeV.

Complete inclusive cross sections at LO, NLO and NNLO(+NNLL) should be calculated.

Aqua led Centre-of-mass Energy = 7 and 8 TeV

Blue led Standard Model input parameter

Gray led Higgs mass range and step:

  • MH=[80, 300]GeV for ggF, VBF, WH/ZH and ttH with the same method as YR1.
  • MH=[300, 1000]GeV for ggF and VBF with Passarino presciption as discussed in YR2 (Section 15).
  • Scanning points is defined by the LHC Higgs combination WG's note, ATL-PHYS-PUB-2011-11, CMS NOTE-2011/005, Table 1.
  • EXPs need numbers down to MH=80GeV as benchmark numbers for possible BSM physics.

Higgs Mass range step size # of points
[ 80,110] GeV 1 GeV 31 points
[110,140] GeV 0.5 GeV 60 points
[140,160] GeV 1 GeV 20 points
[160,290] GeV 2 GeV 65 points
[290,350] GeV 5 GeV 12 points
[350,400] GeV 10 GeV 5 points
[400,1000] GeV 20 GeV 30 points
+ 450, 550, 650, 750, 850, 950 GeV (6 points)
  • 229 points in total

Green led QCD scale uncertainty

  • It should be discussed in each subgroup how to estimate QCD scale uncertainty.
  • As these uncertainties change smoothly, it would be enough to do the coarse scan with following points.
  • Please carry out the interpolation with spline fit (or 3rd order polynomial fit) for other Higgs mass points.

* Scan example:

Higgs Mass range step size # of points
[80,200] GeV 5 GeV 25 points
[200,300] GeV 10 GeV 10 points
[300,1000] GeV 20 GeV 35 points
  • 70 points in total

  • 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)

Orange led PDF+αs uncertainty calculations (a la PDF4LHC prescription)

  • How to estimate PDF+αs uncertainty for 8TeV is under discussion by PDF experts.

PDF sets

  1. For NLO calculations, CTEQ6.6, MSTW2008 and NNPDF2.0 are the default sets. Others, e.g. HERAPDF, ABKM and (G)JR are optional, but we recommend to calculate with these PDF sets as well.
  2. For NNLO calculations, MSTW2008 is the defalut set. We also recommend to compare MSTW with ABKM and (G)JR at NNLO.

Yellow led Cross section central values

  1. For NLO, take the midpoint of CTEQ6.6, MSTW2008 and NNPDF2.0 envelope following the recommendation from PDF4LHC group.
  2. For NNLO, take MSTW2008 result.

Purple led PDF+αs uncertainties (PDF4LHC group recommendation)

  • Δαs=+-0.0012 for 68%C.L. and Δαs=+-0.0020 for 90%C.L.
  • If calculations only at 90% C.L. calculation exist (CTEQ), we shall translate (i.e., by dividing 90%C.L. error by 1.645).
  • PDF+αs uncertainties should be calculated both at 68% C.L. (priority) and at 90% C.L..

  1. The total PDF+αs uncertainty can be evaluated by adding the variations in PDFs due to αs uncertainty in quadrature with the fixed αs PDF uncertainty,
  2. For NNPDF, more efficiently taking a Gaussian distribution of PDF replicas corresponding to different values of αs.
  3. For MSTW, the PDF+ αs uncertainties should be evaluated using their prescription which better accounts for correlations between the PDF and αs uncertainties when using the MSTW dynamical tolerance procedure for uncertainties. Adding the αs uncertainty in quadrature for MSTW can be used as a simpli cation but generally gives slightly smaller uncertainties.

  1. For NLO, use the envelope provided by the central values and PDF+ αs errors from the MSTW08, CTEQ6.6 and NNPDF2.0 PDFs, using each group's prescriptions for combining the two types of errors. Take the symmetric error following the recommendation from PDF4LHC group.
  2. For NNLO, multiply the MSTW uncertainty at NNLO by the factor obtained by dividing the full PDF+αs uncertainty obtained from the envelope of MSTW, CTEQ and NNPDF results at NLO by the MSTW PDF+αs uncertainty at NLO (~ factor 2 at 7 TeV).

Red led Recipe from PDF4LHC

The official PDF4LHC recommendations on NLO/NNLO cross sections and PDF uncertainty estimations:

  1. Recommendation for LHC cross section calculations (June 22, 2010)

Practical guide on PDF+ αs error calculation

  1. Suggestions on calculating the PDF4LHC prescription (September 21, 2010)

  1. MSTW: Check the first two paragraphs of section 6 in arXiv:0905.3531.
    • However adding in quadrature is a pretty good approximation if one is attempting to be quicker.
  2. CTEQ: Check section III-B in arXiv:1004.4624.
  3. NNPDF: Check arXiv:1004.0962.

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Red led Recipe from PDF4LHC

We had been asking the PDF4LHC working group to provide us a prescription on PDF sets, including

  • QCD αs central value with the associated error to be used,
  • Definitions of PDF+αs uncertainties and their treatments.

We got the following recommendation from PDF4LHC group on May 19, 2010 :

"For estimates of PDF uncertainties, our recommendation would be for experimenters to use (at least) predictions from the three PDF fits that are truly global, i.e. that use results from the Tevatron and fixed target experiments as well as HERA: CTEQ, MSTW and NNPDF. The use of other PDFs for predictions is optional. The benchmarking exercises are useful to understand the αs dependence of LHC cross sections, and to understand what differences among the PDF groups result from assumptions of different values of αs. For the calculation of uncertainties at the LHC, the recommendation is to use the envelope provided by the central values and PDF+αs errors from the above three groups."

We finally got the official PDF4LHC recommendations on NLO/NNLO cross sections and PDF uncertainty estimations on June 22, 2010 :

Recommendation for LHC cross section calculations (Link to full recommendation)

"Recommendation for LHC cross section calculations: The LHC experiments are currently producing cross sections from the 7 TeV data, and thus need accurate predictions for these cross sections and their uncertainties at NLO and NNLO. Crucial to the predictions and their uncertainties are the parton distribution functions (PDFs) obtained from global fits to data from deep-inelastic scattering, Drell-Yan and jet data. A number of groups have produced publicly available PDFs using different data sets and analysis frameworks. Given the necessity of having an official recommendation from the PDF4LHC working group available on a short time frame, the prescription outlined at the the link below has been adopted. This is not intended to be an ideal or a final prescription, but is considered to be reasonably conservative and reasonably easy to implement. Further improvements and further standardizations are planned for future updates."

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-- ReiTanaka - 21-May-2010

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