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.

- Input parameters for 8TeV calculations are the same as YR1.
- https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWGSMInputParameter

- 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, ATL-PHYS-PUB-2011-11, CMS NOTE-2011/005, 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 |

- 229 points in total

- 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.. 1/2M
_{H}< μ_{R}, μ_{F}< 2M_{H}, do 2D scan with 1/2 < μ_{R}/μ_{F}< 2)

- How to estimate PDF+α
_{s}uncertainty for 8TeV is under discussion by PDF experts.

- PDF sets: CTEQ6.6, MSTW2008, NNPDF2.0, HERAPDF1.0, ABKM09, GJR08/JR09.
- All these PDF sets are on LHAPDF.
- PDF prescriptions can be found here.
- QCD α
_{s}(M_{Z}): Use default values of each PDF set.

- 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.

- 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)

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

- Also please check PDF prescriptions.

- 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 III-B in arXiv:1004.4624.
- NNPDF: Check arXiv:1004.0962.

-- ReiTanaka - 21-May-2010

I | Attachment | History | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|---|

PDF4LHCrecom.pdf | r1 | manage | 55.5 K | 2015-11-19 - 16:19 | ReiTanaka | ||

PDF_error.pdf | r1 | manage | 45.3 K | 2015-11-19 - 16:19 | ReiTanaka |

This topic: LHCPhysics > LHCHXSWG > LHCHWGCrossSectionsCalc2014

Topic revision: r3 - 2016-12-13 - ReiTanaka

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