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---+ Higgs Cross Section Calculation at 7 and 8 !TeV for RUN-1
 
%ICON{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.

%TOC%

---++ %ICON{led-aqua}% Centre-of-mass Energy = 7 and 8 !TeV

---++ %ICON{led-blue}% Standard Model input parameter
   * %RED% Input parameters for 8TeV calculations are the same as YR1.%ENDCOLOR%
   * https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWGSMInputParameter

---++ %ICON{led-gray}% Higgs mass range and step:

   * %RED%M<sub>H</sub>=[80, 300]GeV for ggF, !VBF, WH/ZH and ttH with the same method as YR1%ENDCOLOR%. 
   * %RED%M<sub>H</sub>=[300, 1000]GeV for ggF and !VBF with Passarino presciption as discussed in YR2 (Section 15)%ENDCOLOR%.
   * Scanning points is defined by the LHC Higgs combination WG's note, [[http://cdsweb.cern.ch/record/1375842/files/ATL-PHYS-PUB-2011-011.pdf][ATL-PHYS-PUB-2011-11, CMS NOTE-2011/005]], Table 1.
   * EXPs need numbers down to M<sub>H</sub>=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 

---++ %ICON{led-green}% QCD scale uncertainty

   * %RED%It should be discussed in each subgroup how to estimate QCD scale uncertainty.%ENDCOLOR%
   * 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.. 1/2M<sub>H</sub> < &mu;<sub>R</sub>, &mu;<sub>F</sub> < 2M<sub>H</sub>, do 2D scan with 1/2 < &mu;<sub>R</sub>/&mu;<sub>F</sub> < 2)

---++ %ICON{led-orange}% !PDF+&alpha;<sub>s</sub> uncertainty calculations (a la !PDF4LHC prescription)

   * %RED%How to estimate !PDF+&alpha;<sub>s</sub> uncertainty for 8TeV is under discussion by !PDF experts.%ENDCOLOR%

---+++  !PDF sets
   * !PDF sets: [[http://www.phys.psu.edu/~cteq/][CTEQ6.6]], [[http://projects.hepforge.org/mstwpdf/][MSTW2008]], [[http://sophia.ecm.ub.es/nnpdf/][NNPDF2.0]], [[https://www.desy.de/h1zeus/combined_results/benchmark/herapdf1.0.html][HERAPDF1.0]], [[https://mail.ihep.ru/~alekhin/abkm09/abkm09.html][ABKM09]], [[http://doom.physik.uni-dortmund.de/pdfserver/][GJR08/JR09]]. 
   * All these PDF sets are on [[http://projects.hepforge.org/lhapdf/][LHAPDF]].
   * !PDF prescriptions can be found [[LHCHXSWGPDF][here]].
   * QCD &alpha;<sub>s</sub>(M<sub>Z</sub>): Use [[LHCHXSWGSMInputParameter#QCD_s][default values of each !PDF set]].

   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. 
   1. For NNLO calculations, MSTW2008 is the defalut set. We also recommend to compare MSTW with ABKM and (G)JR at NNLO. 

---+++ %ICON{led-yellow}% Cross section central values

   1. For NLO, take the midpoint of CTEQ6.6, MSTW2008 and NNPDF2.0 envelope following the [[http://www.hep.ucl.ac.uk/pdf4lhc/PDF4LHCrecom.pdf][recommendation]] from [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]]  group.
   2. For NNLO, take MSTW2008 result. 

---+++ %ICON{led-purple}% !PDF+&alpha;<sub>s</sub> uncertainties ([[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]] group [[http://www.hep.ucl.ac.uk/pdf4lhc/PDF4LHCrecom.pdf][recommendation]])
	
   * &Delta;&alpha;<sub>s</sub>=+-0.0012 for 68%C.L. and &Delta;&alpha;<sub>s</sub>=+-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+&alpha;<sub>s</sub> uncertainties should be calculated both at 68% C.L. (priority) and at 90% C.L..

   a. The total !PDF+&alpha;<sub>s</sub> uncertainty can be evaluated by adding the variations in !PDFs due to &alpha;<sub>s</sub> uncertainty in quadrature with the fixed &alpha;<sub>s</sub> !PDF uncertainty,  
   a. For NNPDF, more efficiently taking a Gaussian distribution of !PDF replicas corresponding to different values of &alpha;<sub>s</sub>. 
   a. For MSTW, the !PDF+&alpha;<sub>s</sub> uncertainties should be evaluated using their prescription which better accounts for correlations between the !PDF and &alpha;<sub>s</sub> uncertainties when using the MSTW dynamical tolerance procedure for uncertainties. Adding the &alpha;<sub>s</sub> uncertainty in quadrature for MSTW can be used as a simplication but generally gives slightly smaller uncertainties.

   1. For NLO, use the envelope provided by the central values and !PDF+&alpha;<sub>s</sub> 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 [[http://www.hep.ucl.ac.uk/pdf4lhc/PDF4LHCrecom.pdf][recommendation]] from [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]]  group.
   1. For NNLO, multiply the MSTW uncertainty at NNLO by the factor obtained by dividing the full !PDF+&alpha;<sub>s</sub> uncertainty obtained from the envelope of MSTW, CTEQ and NNPDF results at NLO by the MSTW !PDF+&alpha;<sub>s</sub> uncertainty at NLO (~ factor 2 at 7 !TeV).


---++ %ICON{led-red}% Recipe from [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]]

The official [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]] recommendations on NLO/NNLO cross sections and !PDF uncertainty estimations:

   1. [[%ATTACHURL%/PDF4LHCrecom.pdf][Recommendation for LHC cross section calculations]] (June 22, 2010)

---+++ Practical guide on !PDF+&alpha;<sub>s</sub> error calculation

   1. [[%ATTACHURL%/PDF_error.pdf][Suggestions on calculating the PDF4LHC prescription]] (September 21, 2010)
   * Also please check [[LHCHXSWGPDF][PDF prescriptions]].

   a. MSTW: Check the first two paragraphs of section 6 in [[http://arxiv.org/pdf/0905.3531][arXiv:0905.3531]]. 
      * However adding in quadrature is a pretty good approximation if one is attempting to be quicker. 
   a. CTEQ: Check section III-B in [[http://arxiv.org/pdf/1004.4624][arXiv:1004.4624]].
   a. NNPDF: Check [[http://arxiv.org/pdf/1004.0962][arXiv:1004.0962]].

<!-- comment out following

%ICON{led-red}% Recipe from [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]]

We had been asking the [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]] working group to provide us a prescription on !PDF sets, including
   * QCD &alpha;<sub>s</sub> central value with the associated error to be used,
   * Definitions of !PDF+&alpha;<sub>s</sub> uncertainties and their treatments.

We got the following recommendation from [[http://www.hep.ucl.ac.uk/pdf4lhc/][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 &alpha;<sub>s</sub> dependence of LHC cross sections, and to understand what differences among the !PDF groups result from assumptions of different values of &alpha;<sub>s</sub>. For the calculation of uncertainties at the LHC, the recommendation is to use the envelope provided by the central values and !PDF+&alpha;<sub>s</sub> errors from the above three groups."

We finally got the official [[http://www.hep.ucl.ac.uk/pdf4lhc/][PDF4LHC]] recommendations on NLO/NNLO cross sections and !PDF uncertainty estimations on June 22, 2010 :

[[http://www.hep.ucl.ac.uk/pdf4lhc/PDF4LHCrecom.pdf][Recommendation for LHC cross section calculations]] 
([[http://www.hep.ucl.ac.uk/pdf4lhc/PDF4LHCrecom.pdf][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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-- Main.ReiTanaka - 21-May-2010
Attachments
Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
pdf	PDF4LHCrecom.pdf	r1	manage	55.5 K	2015-11-19 - 16:19	ReiTanaka
pdf	PDF_error.pdf	r1	manage	45.3 K	2015-11-19 - 16:19	ReiTanaka
Topic revision: r2 - 2015-11-20 - ReiTanaka
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