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

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

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

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.

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

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

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 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:

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.

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: 173.0 ± 1.9(stat+JES)±1.0(syst) GeV/c2 Not shown is result for 1st 1fb-1 : 170.5 ± 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

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

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

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

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

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

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: 180.7 +15.5-13.4 (stat) ± 8.6 (syst) GeV/c2 0.7 fb-1

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

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.

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