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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Top Mass from Cross Sections

Solene Chevalier-Thery

LPTHE, CEA-IRFU/SPP D0 collaboration

Work in collaboration with :

- U.Bassler (SPP CEA Saclay)

- M.Cacciari (LPTHE Paris)

- F.Deliot (SPP CEA Saclay)

- U.Heintz (Boston University)

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Why extracting top mass from cross sections ?

Direct measurement already exists and is more precise.

However :

which mass do we really extract from Pythia :

LO, NLO, which renormalization scheme…?

Alternative :

extract mass from NLO+NLL cross section measurement

this gives a mass in a well-defined renormalization scheme

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

First approach

Both experimental and theoretical cross sections depend on top mass : their intersection gives the top mass.

Both cross sections have uncertainties : the intersection of the uncertainty bands gives the uncertainty on the top mass.

Extracted top mass (D0 note 5459) :

Lepton+jet channel

Dilepton channel

In agreement with the central value from direct measurement :

mtop = 172.6 ± 1.4 GeV. (see U.Heintz talk)

GeVtheorysyststatmtop )()(1.166 9.47.6

1.63.5

GeVtheorysyststatmtop )()(1.174 2.40.6

8.94.8

Dilepton channel

Lepton+jet channel

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Second approach : use of probabilities

Theoretical t-tbar cross section depends on :

the PDFs the factorization scale μF, the

renormalization scale μR

According to the factorization theorem, the total cross section of t-tbar pair production at the Tevatron is :

),(),(),( ,,

, Fjpjji

Fipijitot xfxfdxdxSttpp PDF

Partonic cross section

The theoretical and experimental cross sections suffer from uncertainties.

If you know the shape of these uncertainties, you can combine them according to probability rules to obtain the probability of having a given top mass.

Theoretical dependencies

),,,ˆ;(ˆ , topRFjiji mSxxsttij

Experimental dependencies

The experimental cross section is measured as :

LdtA

NNttpp

tot

backgroundobserved)(

Evaluated by MC

Slight dependance with top mass

Experimental t-tbar cross section depends on :

systematics statistics

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Combining uncertainties We want to determine the probability density function (p.d.f) for the top mass f(mt). So we have to know the different p.d.f.s for all the sources of uncertainties :

Experimental uncertainty : taken gaussian fexp(σ|mt)

Theoretical uncertainties : PDFs : taken gaussian and calculated

from CTEQ or MRST sets fth,PDF(σ|mt) renormalization and factorization scales

fth,μ(σ|mt)

Experimental gaussian : centered on experimental curve

cross section

p.d.f.

p.d.f.

cross section

Gaussian probability due to the PDFs uncertainty

f(mt) =

fexp(σ|mt)

x

( fth,PDF(σ|mt)

fth,μ(σ|mt) )

σσ_min σ_max

100%

cross section

p.d.f.

σσ_min σ_max

90%

cross section

p.d.f.

10%

δσ1 δσ1 δσ2δσ2

σ

σ_min

σ_max

60%

cross section

p.d.f.

10%

δσ1 δσ1 δσ2δσ2

30%

x

Different step function for the probability due to the scale uncertainty

1 2 3

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Results

Different choices for theoretical uncertainty have limited impact on mass extraction (+/- 1 GeV for the central value and the error).

Uncertainty +/- 7 GeV Uncertainty +/- 10 GeV

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March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

Conclusions

We can extract a value for top quark mass, in good agreement with the direct measurement but with greater uncertainty.

The uncertainties could be reduced using :

New data sets (more precise)

New PDFs sets with smaller uncertainties

Better higher order calculation (NNLO?)

This extraction depends on the choice for the shape of the p.d.f. due to the scales uncertainties. Work in progress.