Standard Model Input Parameters at LHC

Help These are the Standard Model input parameters agreed among ATLAS, CMS, LHCb and theory community for Higgs cross section calculations. The same parameters can be used for other SM and BSM processes at LHC.

Aqua led Lepton&Quark Masses

e μ τ
0.510998910(13) MeV 105.658367(4) MeV 1776.84(17) MeV
u c t
190 MeV 1.40 GeV 172.5 +- 2.5 GeV
d s b
190 MeV 190 MeV 4.75 GeV

* Note: The charm and bottom masses are the pole masses used in the MSTW2008 PDF set.

Light quark masses

Light quark masses as used in parton show Monte Carlos are in some cases (e.g.HERWIG) effective masses used to regulate the parton shower in the infrared region (HERWIG also uses massive gluons), and as such may be treated more as a semi-perturbative QCD model parameter specific to a given generator rather than a SM parameter.

Charm and Bottom quark masses

We propose a process dependent choice of the quark masses since this issue cannot be generalized. The best choice should be given depending on the process. The current best fits for the MSbar masses are (arXiv:1001.5173),
MSbar mass mc(mc) mb(mb)
  1.28 GeV 4.16 GeV
These MSbar masses are obtained from fits to the QCD sum rules in charmonium and bottomonium systems and should normally be considered as the primary input. One could start from the MSbar values and compute the needed mass. The pole masses obtained from the values above strongly depend on the order of the calculation:
pole mass mc mb
1-loop 1.41 GeV 4.49 GeV
2-loop 1.55 GeV 4.69 GeV
On the other hand if we are going to use MSTW2008 PDFs, we are forced to use 4.75 GeV as the bottom pole mass. This should correspond to the 1-loop pole mass. Whatever we do, we are always forced to make a compromise due to consistency, i.e. to use mass values fitted at the order at which your observable is calculated and to be consistent with the input, in particular with the PDFs.

(Comments from Michael Spira, February, 2010).

Green led Gauge Boson Masses

  80.398(25) GeV 2.141(41) GeV
  91.1876(21) GeV 2.4952(23) GeV

Orange led Electroweak Radiative Corrections

Gμ 1.16637(1)x10-5 GeV-2

For EW radiative corrections, it is more complicated than QCD because of renormalization and the treatment of unstable particles are complicated. For the treatment of resonances complex-mass scheme, fixed-width scheme and pole-mass scheme can be taken. Also for the renormalization scheme which defines relations between electroweak couplings and parameters beyond the leading order, various schemes exist such as α(0) scheme, α(MZ2) scheme and the GF scheme. For further detail, please refer to the Binoth Les Houches Accord arXiv:1001.1307, Section 5.1 - 5.3.. If we agree on, then this SM input parameter page could be extended.

(Comments from Giampiero Passarino, February, 2010).

Red led QCD αs

PDF4LHC recipe

We shall follow up the discussion at PDF4LHC working group for the consensus on an agreed value of QCD αs and procedure for associated error treatment.

The current agreement is to produce in the very short run some benchmarks for standard candles (typically, W, Z, Higgs and top cross sections) using different sets of PDFs, and both each group's favorite prescription, but also some common agreed prescription for:

  1. αs values and uncertainty;
  2. size of the error bars (90% CL vs 1σ/ 68% CL);
  3. perturbative order;
  4. electroweak parameters and order;
  5. anything else that will come up as source of disagreement.
These benchmarks may be the basis for a future agreement, and they should certainly allow us to get a picture of what to expect. The benchmarks should be available in a matter of weeks.

(Comments from Albert De Roeck, February 18, 2010).


In the mean time, we want to start the calculations for the Freiburg Workshop. Here is the TEMPORARY recipe suggested by Stefano Forte while we wait for the official recommendation by PDF4LHC group.

  1. Fix αs=0.119 with a 68% (1σ) error of (0.002/1.64485)=0.0012.
  2. Then take the 3 central sets of PDFs (CTEQ, MSTW and NNPDF with their built in preferred αs) and use the value αs=0.119 in all hard cross sections (even though strictly the three central PDFs correspond to slightly different αs values).
  3. Then vary αs by 0.0012 for 68% (1σ) error (keeping the same PDF).
  4. Then fix αs and vary the PDF by the 68% uncertainty using each group's recommended recipe for PDF variation.
  5. Sum in quadrature the differences.
  6. Compare results obtained using at least two different global PDF sets.

When doing an NNLO computation, I suggest to first do the NLO computation according to the above recipe. Then do both NLO and NNLO using MSTW2008 with the corresponding recommended values of αs. If it turns out that the PDF uncertainty on the NLO computation obtained from the recipe is much larger than the NLO-NNLO difference, consider the small NNLO uncertainty with due skepticism.

(Comments from Stefano Forte, February 19, 2010).

Default αs values

MSTW2008NLO 0.12018
NNPDF2.0 0.119
CTEQ6,6 0.118

MSTW2008LO 0.13939 0.254971
MSTW2008NLO 0.12018 0.255097
MSTW2008NNLO 0.11707 0.214634

Yellow led References

† C. Amsler et al. (Particle Data Group), Physics Letters B667 (2008) 1 and 2009 partial update for the 2010 edition.

-- ReiTanaka - 20-May-2010

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Topic revision: r7 - 2016-12-19 - ReiTanaka
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