1. APS 5-MAY-2009 G. Gutierrez, Fermilab Edward A. Bouchet Award Talk “ The top quark mass, a brief history and present status” Gaston Gutierrez Fermilab This talk is dedicated to the memory of Clicerio Avilez.

2. APS 5-MAY-2009 G. Gutierrez, Fermilab Concepts of maximum likelihood. A brief history of the top quark mass measured by calculating a probability density distribution for every event. The current status of the top mass measurements. Other application of M.E.M. Conclusion. Outline of the talk

3. APS 5-MAY-2009 G. Gutierrez, Fermilab If for an event characterized by a set of measurements one can calculate the probability density function: then given N events the optimal estimation of the set of parameters is obtained by maximizing General Maximum Likelihood technique

4. APS 5-MAY-2009 G. Gutierrez, Fermilab In general we have to sun over all states that can lead to the set of measurements the sum is over probabilities (amplitudes) if the states do not (do) interfere. For a perfect detector we have with Probability calculation

5. APS 5-MAY-2009 G. Gutierrez, Fermilab Probability calculation for real detectors Detector acceptance (e.g. cuts, trigger, …) partonic integral partonic variables mapping between partonic and measured variables measured variables parameters Integral over measured Variable (normalization)

6. APS 5-MAY-2009 G. Gutierrez, Fermilab Why apply the previous method to the top mass? The top mass is an important SM parameter. Together with the W mass it constrains the Higgs mass Top is a very isolated state, which makes for a cleaner calculation of the pdf. No matter which method we use we all need to model the relation between the top mass and the detector measurements.

7. APS 5-MAY-2009 G. Gutierrez, Fermilab Kunitaka Kondo J. Phys. Soc. Japan, 57, 4126 (1988) J. Phys. Soc. Japan, 60, 836 (1991) J. Phys. Soc. Japan, 62, 1177 (1993)

8. APS 5-MAY-2009 G. Gutierrez, Fermilab R.H. Dalitz and Gary R. Goldstein Phys. Rev. D45, 1541 (1992) Proc. Roy. Soc. Lond. A455, 2803 (1999) J. Mod. Phys. A9, 635 (1994) Phys. Lett. B287, 225 (1992) Phys. Rev. D47, 967 (1993)(with K. Sliwa)

9. APS 5-MAY-2009 G. Gutierrez, Fermilab D0 experiment Nature 429,638 (2004) First complete measurement, including: 1) all detector effects (e.g. reconstruction efficiencies, cuts, trigger, …), 2) correct normalization, 3) background probabilities, 4) MC tests of linearity, 5) pull calculations and 6) estimation of systematic effects.

10. APS 5-MAY-2009 G. Gutierrez, Fermilab Run I: Top probability for data events Left plot show -ln(P tt ) as a function of M t for 10 -9 <P bkg <10 -8 (red arrows in lower figure). x=-ln(P B ) x=18.5 x=20.4 x=20.0 x=19.4 x=19.2 x=20.5

11. APS 5-MAY-2009 G. Gutierrez, Fermilab Run I: Top probability for data events Left plots show -ln(P tt ) as a function of M t for 9.7x10 -13 <P bkg < 9.0x10 -12 (red arrows in lower figure). x=-ln(P B ) x=27.7 x=27.2 x=26.7 x=26.6 x=25.9 x=25.7

12. APS 5-MAY-2009 G. Gutierrez, Fermilab Run I: MC linearity after background selection Test of linearity of response with MC samples containing large numbers of events. The number of events in the plot are given before the background cut

13. APS 5-MAY-2009 G. Gutierrez, Fermilab Run I: Top mass measurement M t = 180.1  3.6 GeV (stat) This new technique improves the statistical error on M t from 5.6 GeV [ PRD 58 52001, (1998) ] to 3.6 GeV. This is equivalent to a factor of 2.4 in the number of events. The number of extracted signal events is: (11±3)/(0.71 x 0.70 x 0.87)=25 ±7 (a 0.5 GeV shift has been applied, from MC studies)

14. APS 5-MAY-2009 G. Gutierrez, Fermilab Run I: W mass check 80.9 ± 2.6 GeV The likelihood minimizes at = 79.4 GeV, with an error of 2.2 GeV. Studies at M top = 175 GeV show that there is a systematic shift in M W of 1.5 GeV and an under estimation of the error of 20%. Therefore

15. APS 5-MAY-2009 G. Gutierrez, Fermilab Tevatron Run II top quark mass results using M.E.M.

16. APS 5-MAY-2009 G. Gutierrez, Fermilab SM Top pair production

17. APS 5-MAY-2009 G. Gutierrez, Fermilab lepton+jets top event p p t b W q q W b t l

18. APS 5-MAY-2009 G. Gutierrez, Fermilab Top and W decay W lqlq ν q’-bar p = 40 GeV/c The decay to jets is 3 times more likely than to e and μ t b W p ~ 70 GeV/c Top decays to W+b essentially 100 % of the time M t = 172 GeV/c 2 M W = 80 GeV/c 2

19. APS 5-MAY-2009 G. Gutierrez, Fermilab Run II: Top mass at D0 There were many improvements in the probability calculations. But the main gain has been to: 1) include a Jet Energy Scale (JES) parameter in the minimization and 2) use a prior from the γ+jet energy calibration. lepton+jets most recently published result (1 fb -1 )

20. APS 5-MAY-2009 G. Gutierrez, Fermilab Run II: Top mass at D0 lepton+jets most recently published result (1 fb -1 )

21. APS 5-MAY-2009 G. Gutierrez, Fermilab Run II: Top mass at D0 lepton+jets most recently published result (1 fb -1 )

22. APS 5-MAY-2009 G. Gutierrez, Fermilab Results presented at this conference

23. APS 5-MAY-2009 G. Gutierrez, Fermilab

24. APS 5-MAY-2009 G. Gutierrez, Fermilab

25. APS 5-MAY-2009 G. Gutierrez, Fermilab

26. APS 5-MAY-2009 G. Gutierrez, Fermilab Top, W and Higgs masses are related Accurate measurements of the top quark and W boson masses put constraints on the mass of the Higgs boson. Because of the log dependence to have meaningful constraints on the Higgs mass high precision measurement of the W and top quark masses are required.

27. APS 5-MAY-2009 G. Gutierrez, Fermilab LEP EWWG as of March 2009 These (almost) lines are EW the predictions.

28. APS 5-MAY-2009 G. Gutierrez, Fermilab Higgs limits as of March 2009 The SM Higgs mass limit from the EW fit is: m H <163 GeV/c 2 at 95% CL. Footnote: There is a 3 σ discrepancy between the hadronic and leptonic F-B asymmetries. If any of this two are removed there are big changes in the Higgs mass limits (see M. Chanowitz, PRD 66:073002, 2002 and Fermilab W&C 2/23/2007)

29. APS 5-MAY-2009 G. Gutierrez, Fermilab Other applications also presented at this conference

30. APS 5-MAY-2009 G. Gutierrez, Fermilab Top-antiquark mass difference measurement

31. APS 5-MAY-2009 G. Gutierrez, Fermilab

32. APS 5-MAY-2009 G. Gutierrez, Fermilab gg  H  W + W -  l + l - Basic selection: Two opposite sign isolated leptons missing transverse momentum Main backgrounds: WW, WZ, ZZ W+jets and Drell-Yang Geometry help Use full power of Matrix element

33. APS 5-MAY-2009 G. Gutierrez, Fermilab H  W + W - in CDF (1.9 fb -1 ) Calculate probabilitiesCalculate discriminantCheck for observation If no observation set limit

34. APS 5-MAY-2009 G. Gutierrez, Fermilab Conclusion To conclude I would like to thank my colleagues for the exiting times during the past decade (when all this work was done) and many thanks to the young people that are carrying this work forward.

35. APS 5-MAY-2009 G. Gutierrez, Fermilab Backup slides

36. APS 5-MAY-2009 G. Gutierrez, Fermilab The general method Most people would agree that if the probability of an event could be calculated accurately then the best estimate of a parameter will maximize a likelihood like: The detector and reconstruction effects are always multiplicative and independent of the parameter to be estimated: The probability P(x;α) can be calculated as: Where x is the set of variables measured in the detector, y is the set of parton level variables, dσ is the differential cross section and f(q) are the parton distribution functions. W(x,y) is the probability that a parton level set of variables y will show up in the detector as the set of variables x. The integration reflects the fact that we want to sum over all the possible parton variables y leading to the observed set of variables x.

37. APS 5-MAY-2009 G. Gutierrez, Fermilab Transfer function W(x,y) W(x,y) is the probability of measuring x when y was produced (x measured variables, y parton variables): where E y energy of the produced quarks E x measured (and corrected) jet energy p y e produced electron momenta p x e measured electron momenta  y j  x j produced and measured jet angles The energy of the electrons is considered well measured. And due to the excellent granularity of the D  calorimeter the angles are also considered as well measured. A sum of two gaussians is used for the jet transfer function (W jet ), the parameters were extracted from MC simulation.

38. APS 5-MAY-2009 G. Gutierrez, Fermilab Probability for tt events 2(in) + 18(final) = 20 degrees of freedom 3 (e) + 8 (  1..  4) + 3 (P in =P final ) + 1 (E in =E final ) = 15 constraints 20 – 15 = 5 integrals Sum over 12 combinations of jets All values of the neutrino momentum are considered  1 momentum of one of the jetsm 1,m 2 top mass in the event M 1,M 2 W mass in the eventf(q 1 ),f(q 2 ) parton distribution functions (CTEQ4) for qq incident chann. q 1,q 2 initial parton momenta  6 six particle phase space W(x,y) probability of measuring x when y was produced in the collision We chose these variables of integration because |M(α)| 2 is almost negligible everywhere except near the peaks of the four Breit-Wigners in |M(α)| 2.

39. APS 5-MAY-2009 G. Gutierrez, Fermilab Matrix Element no ttbar spin correlation included s qt sine of angle between q and t in the q q CM  top quark's velocity in the q q CM g s strong coupling constant Leptonic decay Hadronic decay M t, M W pole mass of top and W m t top mass in any event m e,m du invariant mass of the e and du (or cs) system  t,  W width of top and W g W weak coupling constant  (cos  eb,db ) angular distribution of the W decay

40. APS 5-MAY-2009 G. Gutierrez, Fermilab Acceptance Corrections Detector Acceptance Likelihood Production probability Detector acceptance Measured probability, and N gen (N) is the number of generated(accepted) events