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Higgs Cross Section Calculation at 7 and 8 TeV for RUN1
This is the instruction for Higgs cross section calculations at centreofmass energy of 7 and 8 TeV.
Complete inclusive cross sections at LO, NLO and NNLO(+NNLL) should be calculated.
Centreofmass Energy = 7 and 8 TeV
Standard Model input parameter
Higgs mass range and step:
 M_{H}=[80, 300]GeV for ggF, VBF, WH/ZH and ttH with the same method as YR1.
 M_{H}=[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, ATLPHYSPUB201111, CMS NOTE2011/005, Table 1.
 EXPs need numbers down to M_{H}=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)
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:
 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)
PDF+α_{s} uncertainty calculations (a la PDF4LHC prescription)
 How to estimate PDF+α_{s} uncertainty for 8TeV is under discussion by PDF experts.
PDF sets
 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.
 For NNLO calculations, MSTW2008 is the defalut set. We also recommend to compare MSTW with ABKM and (G)JR at NNLO.
Cross section central values
 For NLO, take the midpoint of CTEQ6.6, MSTW2008 and NNPDF2.0 envelope following the recommendation from PDF4LHC group.
 For NNLO, take MSTW2008 result.
 Δα_{s}=+0.0012 for 68%C.L. and Δα_{s}=+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+α_{s} uncertainties should be calculated both at 68% C.L. (priority) and at 90% C.L..
 The total PDF+α_{s} uncertainty can be evaluated by adding the variations in PDFs due to α_{s} uncertainty in quadrature with the fixed α_{s} PDF uncertainty,
 For NNPDF, more efficiently taking a Gaussian distribution of PDF replicas corresponding to different values of α_{s}.
 For MSTW, the PDF+α_{s} uncertainties should be evaluated using their prescription which better accounts for correlations between the PDF and α_{s} uncertainties when using the MSTW dynamical tolerance procedure for uncertainties. Adding the α_{s} uncertainty in quadrature for MSTW can be used as a simplication but generally gives slightly smaller uncertainties.
 For NLO, use the envelope provided by the central values and PDF+α_{s} 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.
 For NNLO, multiply the MSTW uncertainty at NNLO by the factor obtained by dividing the full PDF+α_{s} uncertainty obtained from the envelope of MSTW, CTEQ and NNPDF results at NLO by the MSTW PDF+α_{s} uncertainty at NLO (~ factor 2 at 7 TeV).
The official PDF4LHC recommendations on NLO/NNLO cross sections and PDF uncertainty estimations:
 Recommendation for LHC cross section calculations (June 22, 2010)
Practical guide on PDF+α_{s} error calculation
 Suggestions on calculating the PDF4LHC prescription (September 21, 2010)
 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.
 CTEQ: Check section IIIB in arXiv:1004.4624.
 NNPDF: Check arXiv:1004.0962.
<! comment out following
Recipe from PDF4LHC
We had been asking the PDF4LHC working group to provide us a prescription on PDF sets, including
 QCD α_{s} central value with the associated error to be used,
 Definitions of PDF+α_{s} 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 α_{s} dependence of LHC cross sections, and to understand what differences among the PDF groups result from assumptions of different values of α_{s}. For the calculation of uncertainties at the LHC, the recommendation is to use the envelope provided by the central values and PDF+α_{s} 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 deepinelastic scattering, DrellYan 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  21May2010
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