March 11 th , 2008

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

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

3. Lepton+jet channel 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) Dilepton channel March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

4. Second approach : use of probabilities • 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 Experimental dependencies • According to the factorization theorem, the total cross section of t-tbar pair production at the Tevatron is : • The experimental cross section is measured as : Evaluated by MC Slight dependance with top mass PDF Partonic cross section • Experimental t-tbar cross section depends on : • systematics • statistics • Theoretical t-tbar cross section depends on : • the PDFs • the factorization scale μF, the renormalization scale μR March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

5. p.d.f. p.d.f. cross section cross section p.d.f. p.d.f. σ σ_min p.d.f. σ_max σ σ_max σ σ_min σ_max 1 σ_min 2 60% 90% 3 100% 30% 10% 10% cross section cross section δσ1 δσ1 δσ2 δσ2 δσ1 δσ1 δσ2 δσ2 cross section Combining uncertainties Experimental gaussian : centered on experimental curve f(mt) = • 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) • fexp(σ|mt) x x Gaussian probability due to the PDFs uncertainty • ( fth,PDF(σ|mt) fth,μ(σ|mt) ) Different step function for the probability due to the scale uncertainty March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

6. Results Uncertainty +/- 10 GeV Uncertainty +/- 7 GeV • Different choices for theoretical uncertainty have limited impact on mass extraction (+/- 1 GeV for the central value and the error). March 11th , 2008 S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections

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