1. Top mass measurements at the Tevatron and the standard model fits
Michael Wang, Fermilab
For the DØ and CDF collaborations
42nd Recontres de Moriond
March 17-24, 2007

2. Outline
Significance of top mass
3 decay channels used in measuring mass
Different measurement techniques
New results from DØ and CDF
Brand new world average and SM fits
Conclusions

3. Why measure the top mass?
Why is there so much interest in the top mass?
To see why, consider the mass of the W boson:
(1+r)
Radiative corrections
mt enters quadratically while mh enters logarithmically, so a precise knowledge of the W and Top masses will constrain the Higgs mass, providing a guide to the Higgs search.

4. Decay channel (1): All jetsW+ q b
All jets
44%
l+jets
29% t p q b W-
All jets
Largest branching fraction
High background levels:
QCD multijet
Benefits from in-situ jet energy calibration using hadronic W

5. Decay channel (2): Dileptonq
All jets
44%
dilepton 5% l  W+ b t p p t b W-
Dilepton
Low bkg levels:
diboson
Z+jets
Low branching fraction q  l

6. Decay channel (3): Lepton+jetsq
All jets
44%
dilepton 5% l 
l+jets
29%
Tau+X
22% W+ b t p p t
Lepton + jets
Reasonable branching fraction
Medium bkg levels:
W+jets
QCD multijet
Benefits from in-situ jet energy calibration using hadronic W
Has traditionally yielded the best results b W-  l

7. Measurement challenge
Jet 1
Jet 2
Jet 3
Jet 4
lepton
Missing ET t b W+ q
Primary interaction vertex p p t b W-  l
In general, don’t know which jet comes from which parton
In the l+jets case e.g., detector sees 4 jets, a lepton, missing ET, and an interaction vertex
No displaced vertices to isolate signal from background
Must try all permutations
No clean and sharp mass peaks

8. Probability density function → P(x;Mtop)
Template methods
Identify variable x sensitive to Mtop.
Using MC, generate distributions (templates) in x as a function of input Mtop.
Parameterize templates in terms of probability density function (p.d.f) in x, Mtop.
Construct likelihood L based on p.d.f’s:
Compare data x distributions with the MC templates using L
Maximize L (minimize -ln(L)) to extract top mass
Mtop=160 x
Mtop=170 x
Mtop=175 x
Mtop=180 x
Mtop=185 x
Probability density function → P(x;Mtop)
mtop

9. Matrix Element methods
In the M.E. method, probabilities are calculated directly for each event. For instance, with signal and background contributions:
Probabilities are taken to be the differential cross sections for the process in question. For example, the signal probability is given by:
where:

10. Matrix Element methods
To extract from a sample of events, probabilities are calculated for each individual event as a function of :
Event 1
Event 2
Event 3
Event n-1
Event n
From these we build
the likelihood function
The best estimate of the top mass is then determined
by minimizing:
And the statistical error can be
estimated from:
0.5

11. Ideogram method
Like the M.E. methods, the Ideogram method constructs an analytic likelihood for each event.
The portion of the signal probability that is sensitive to the top mass is of the form:
The main feature of this technique is the use of a constrained kinematic fit to extract the mass information xfit consisting of the fitted mass mi, estimated uncertainty σ2, and goodness of fit 2 (contained in wi).
This method which was first applied to the W mass at LEP aims to achieve similar statistical uncertainties as the M.E. method but without the burden of huge computational requirements.

12. 170.9 ± 2.2 (stat+JES) ± 1.4 (syst) GeV/c2
CDF lepton+jets
systematics
highlights
Matrix Element method
In-situ jet energy calibration
Current world best
Result:
170.9 ± 2.2 (stat+JES) ± 1.4 (syst) GeV/c2
0.94 fb-1

13. Only e+jets channel shown 170.5 ± 2.4 (stat+JES) ± 1.2 (syst) GeV/c2
DØ lepton+jets
Only e+jets channel shown
highlights
Matrix Element method
In-situ jet energy calibration
Result:
170.5 ± 2.4 (stat+JES) ± 1.2 (syst) GeV/c2
0.9 fb-1

14. 173.7 ± 4.4(stat.+JES)+2.1 -2.0(syst.) GeV/c2
DØ lepton+jets (ideogram)
highlights
Ideogram method
In-situ jet energy calibration
Result:
173.7 ± 4.4(stat.+JES) (syst.) GeV/c2
0.4 fb-1

15. CDF dilepton Result: 1 fb-1 164.5 ± 3.9 (stat.) ± 3.9 (syst.) GeV/c2
systematics
highlights
Matrix Element method
Best dilepton measurement
Result:
164.5 ± 3.9 (stat.) ± 3.9 (syst.) GeV/c2
1 fb-1

16. DØ dilepton Results: 1 fb-1 highlights
Expected error distribution
Mass calibration curve
highlights
Template method
 weighting technique
eμ, ee, and μμ channels
Results:
172.5 ± 5.8 (stat.) ± 5.5 (syst.) GeV/c2
1 fb-1

17. 171.1 ± 3.7 (stat+JES) ± 2.1 (syst) GeV/c2
CDF all jets
highlights
Matrix Element + Template
In-situ jet energy calibration
Result:
171.1 ± 3.7 (stat+JES) ± 2.1 (syst) GeV/c2
1 fb-1

18. New world average 170.9 ± 1.1 (stat) ± 1.5 (syst) GeV/c2
Combining the new results from the previous slides
shown above with past results from CDF and DØ
yields a NEW world average for the top mass:
170.9 ± 1.1 (stat) ± 1.5 (syst) GeV/c2
mtop now known to an uncertainty of 1.1% !

19. New SM fit Preferred value: mH = 76 GeV at minimum
March 2007, LEP EW WG
Preferred value: mH = 76 GeV at minimum
Upper limit: mH < 144 GeV

20. Summary and conclusions
Great interest in top mass due to the Higgs
Challenging measurement but various techniques make a precise measurement possible
New measurements from D0 and CDF yielding a new world average for the top mass with uncertainty of 1.1%
Using the new top mass in the SM fits yields new limits on the Higgs mass
The top mass measurements still dominated by the Lepton+jets results:
Best results in two other channels are very impressive, hope to see results competitive with l+jets in the future
Something to look forward to since different channels dominated by different systematics
By the end of Tevatron run (8fb-1), the statistical uncertainty of the top mass < 1 GeV and the total uncertainty dominated by the systematic uncertainty.

21. End

22. I have just described three measurement techniques to extract the top mass.
Although the three methods differ from each other substantially, they all share the common need for validation and calibration in order to determine that the extracted top mass corresponds to the true value and that the estimated errors are reliable
Since the procedure takes up a significant portion of any top mass analysis, I will briefly describe how it is done in the next slide
Although I will use the M.E. method as an example, the procedure should be very similar if not identical for the other two measurement techniques

23. Ensemble tests
From a large pool of M monte carlo events, we perform ensemble tests by randomly drawing n events N number of times to form N pseudo-experiments: M
A. The error is estimated for each experiment and entered into the “Mass Error” histogram
B. The mass at the minimum for each experiment is entered into the “Top Mass” histogram
C. The pulls are calculated for each experiment by dividing the deviation of the mass at the minimum from the mean of this mass for all experiments by the estimated error
Expt 1
Expt 2
Expt 3
Expt N-1
Expt N
min σ