1. Top mass measurements at the Tevatron
Michael Wang, Fermilab
For the DØ and CDF collaborations
Heavy Quarks and Leptons
Melbourne, Australia
June 5-9, 2008

2. Outline
Significance of top mass
3 decay channels used in measuring mass
Different measurement techniques
Latest results from DØ and CDF
Winter top mass combinations
Conclusions

3. A whale of a quark Top is most massive of all quarks and leptons
~20x
Top is most massive of
all quarks and leptons
Large coupling to the
Higgs boson
Special role in EW
symmetry breaking
~35x

4. Narrowing down on the Higgs
Current interest in the top mass primarily driven by Higgs search.
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.

5. 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

6. 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

7. 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

8. Challenging measurement
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

9. 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

10. Matrix Element methods
The M.E. method is based on the calculation of event probability densities which are taken to be the sum of all contributing ( and assumed to be non-interfering ) processes. For example, in the case of two major processes:
Probabilities are taken to be the differential cross sections for the process in question. For example, the signal probability is given by:
where:

11. 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

12. 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.

13. DØ lepton+jets Result: 2.1 fb-1 172.2 ± 1.1 (stat) ± 1.6 (syst) GeV/c2
highlights
Sytematics
Matrix Element method
In-situ jet energy calibration
Source
GeV/c2
Signal mod
0.40
Background mod
0.08
W+jets HF factor
0.07
B fragmentation
0.10
PDF
0.24
Residual JES
0.03
b JES
0.82
b tagging
0.16
Trigger efficiency
0.09
Jet energy reso
0.30
QCD background
0.20
MC calibration
0.14
Total systematic
1.0
Result shown here is for 2nd 1fb-1: ± 1.9(stat+JES)±1.0(syst) GeV/c2
Not shown is result for 1st 1fb-1 : ± 2.5(stat+JES)±1.4(syst) GeV/c2
Combining both results give the result below:
Result:
172.2 ± 1.1 (stat) ± 1.6 (syst) GeV/c2
2.1 fb-1

14. 171.4 ± 1.5 (stat+JES) ± 1.0 (syst) GeV/c2
CDF lepton+jets
highlights
Matrix Element method
In-situ jet energy calibration
Neural network based signal to background discrimination
Angular resolution of jets taken into account
Result:
171.4 ± 1.5 (stat+JES) ± 1.0 (syst) GeV/c2
1.9 fb-1

15. DØ dilepton Results: 1.0 fb-1 173.7 ± 5.4 (stat.) ± 3.4 (syst.) GeV/c2
WT
Sytematic uncertainty
Template based
eμ, ee, and μμ channels
 solutions weighted by:
Source
GeV/c2
JES
2.46
B-JES
1.87
Temp stat
0.90
Background
0.64
PDF
0.57
Jet reso
0.48
Muon reso
0.22
Und. Evt.
0.20
Gluon rad.
0.12
Total syst
3.4
MWT
Template
eμ, ee, and μμ channels
 sol. weighted by:
Results:
173.7 ± 5.4 (stat.) ± 3.4 (syst.) GeV/c2
1.0 fb-1

16. CDF dilepton Result: 1.9 fb-1 171.2 ± 2.7 (stat.) ± 2.9 (syst.) GeV/c2
highlights
Matrix Element method
Neural network based selection optimized for precision
Result:
171.2 ± 2.7 (stat.) ± 2.9 (syst.) GeV/c2
1.9 fb-1

17. 177.0 ± 3.7 (stat+JES) ± 1.6 (syst) GeV/c2
CDF all jets
Source
GeV/c2
Residual bias
0.31
2D calibration
0.04
Generator
0.34
ISR
FSR
0.33
Bkg templates
1.03
Sig templates
0.26
B-jets energy scale
0.11
SF ET dependence
0.35
Residual JES
0.80
PDF
0.41
mt/mW correlations
0.21
Total
1.60
highlights
Template based method
Background shapes determined from data
In-situ jet energy calibration
Result:
177.0 ± 3.7 (stat+JES) ± 1.6 (syst) GeV/c2
1.9 fb-1

18. DØ cross section Results: 1 fb-1 highlights 170 ± 7 GeV/c2
Mass is determined by comparing measured ttbar cross section with best theoretical calculations
Unlike direct measurements of the mass based on kinematic information, does not rely on precise modeling of MC ttbar signal events to extract mass
MC events only used to determine efficiencies
Complementary to direct measurements and provides a valuable cross-check
Result is consistent with world average
Results:
170 ± 7 GeV/c2
1 fb-1

19. 180.7 +15.5-13.4 (stat) ± 8.6 (syst) GeV/c2
CDF b decay length
Assuming top produced nearly at rest:
highlights
Boost imparted to b is a function of top mass
Average velocity of b quark/hadron and hence decay length is strongly correlated to top mass
This dependence is parameterized using MC events and used to extract top mass from data
Depends only on tracking and is largely insensitive to jet energy scale uncertainties that dominate other methods
Result:
(stat) ± 8.6 (syst) GeV/c2
0.7 fb-1

20. World average top mass (Winter 2008)
**CDF-II l+jets result in combination is previous version
***D0 xsec mass measurement not included

21. Summary and conclusions
Large mass of the top quark is interesting in itself. Also much interest due to the constraint on the Higgs mass.
Challenging measurement but sophisticated techniques make a precise measurement possible.
Measurements in different channels sensitive to different systematics and backgrounds. Important to check consistency between these channels.
New novel techniques, while still dominated by large uncertainties, seem very promising and are complementary to direct measurements
Uncertainty of world average top mass fast approaching 1 GeV. Must continue striving to improve techniques, understanding biases, and addressing systematic uncertainties.

22. End