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
Lepton+jet channel
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
mtop  166.165..13 (stat  syst )46..97 (theory)GeV

Dilepton channel
Dilepton channel
mtop  174.198..84 (stat  syst )46..20 (theory)GeV

In agreement with the central value from direct
measurement :
mtop = 172.6 ± 1.4 GeV. (see U.Heintz talk)
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March 11th , 2008
S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections
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
According to the factorization theorem, the
total cross section of t-tbar pair production
at the Tevatron is :

 tot ( pp  tt , S )    dxi dx j fi , p ( xi ,  F ) f j , p ( x j ,  F )
i, j
PDF
Experimental dependencies
The experimental cross section is
measured as :

 ( pp  tt ) 
 ˆ i , j (ij  tt ; sˆ  xi x j S ,  F ,  R , mtop )
Partonic cross section
Theoretical t-tbar cross section depends
on :
 the PDFs
 the factorization scale μ , the
F
renormalization scale μR

March 11th , 2008
N observed  N background
Atot  Ldt
Evaluated
by MC
Slight
dependance
with top mass
Experimental t-tbar cross section depends
on :
 systematics
 statistics

S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections
4
Combining uncertainties
Experimental
gaussian :
centered on
experimental
curve
p.d.f.
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 :



fexp(σ|mt)
cross section
Experimental uncertainty : taken gaussian
fexp(σ|mt)

p.d.f.
PDFs : taken gaussian and calculated
from CTEQ or MRST sets fth,PDF(σ|mt)
renormalization and factorization scales
fth,μ(σ|mt)
p.d.f.
fth,μ(σ|mt) )
p.d.f.
σ_min
σ σ_max
100%
Gaussian
probability due to
the PDFs
uncertainty
( fth,PDF(σ|mt)
Theoretical uncertainties :

x
x
p.d.f.
σ_min
1
cross section
σ σ_max
90%
2
σ σ_max
σ_min
60%
3
30%
10%
cross section
March 11th , 2008
δσ1
10%
δσ1 δσ2δσ2
cross section
δσ1
δσ1 δσ2δσ2
Different step
function for
the
probability
due to the
scale
uncertainty
cross section
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S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections
Results
Uncertainty +/- 7 GeV

Uncertainty +/- 10 GeV
Different choices for theoretical uncertainty have limited impact on mass extraction
(+/- 1 GeV for the central value and the error).
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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.

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March 11th , 2008
S. Chevalier-Thery, Moriond QCD – Top Mass from Cross Sections