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

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

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.

Decay channel (1): All jets W+ 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

Decay channel (2): Dilepton q 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

Decay channel (3): Lepton+jets q 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

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

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

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:

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

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.

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

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

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)+2.1 -2.0(syst.) GeV/c2 0.4 fb-1

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

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

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

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% !

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

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.

End

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

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: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 . . . . . . . . . . . . . . . . . . . . . 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