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World Average Top-Quark Mass D. Glenzinski, Fermilab 20-May-2008

World Average Top-Quark Mass D. Glenzinski, Fermilab 20-May-2008. Outline. Introduction Details Discussion Outlook Closing Remarks. Introduction. CDF and D0 have been combining their top mass measurements for 10 years First:Fermilab-TM-2084 Latest: arxiv:0803.1683[hep-ex]

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World Average Top-Quark Mass D. Glenzinski, Fermilab 20-May-2008

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  1. World Average Top-Quark Mass D. Glenzinski, Fermilab 20-May-2008 D.Glenzinski, Fermilab

  2. Outline • Introduction • Details • Discussion • Outlook • Closing Remarks D.Glenzinski, Fermilab

  3. Introduction • CDF and D0 have been combining their top mass measurements for 10 years • First:Fermilab-TM-2084 • Latest: arxiv:0803.1683[hep-ex] • Updated about once a year when both experiments have major improvements • Method unchanged • BLUE (Best Linear Unbiased Estimator) • Concentrate today on • Some details of the latest combination • Challenges moving forward D.Glenzinski, Fermilab

  4. BLUE • Well established methodology widely used throughout HEP • Allows combination of correlated measurements of one or more parameters • Yields unbiased estimate of parameter with the smallest variance • Produces a fit 2 to evaluate consistency of inputs • Provides clean way to breakdown uncertainties L.Lyons, D.Gibaut, P.Clifford, NIM A270 (1988) A.Valassi, NIM A500 (2003) D.Glenzinski, Fermilab

  5. BLUE • Well established methodology widely used throughout HEP • Allows combination of correlated measurements of one or more parameters • Yields unbiased estimate of parameter with the smallest variance • Produces a fit 2 to evaluate consistency of inputs • Provides clean way to breakdown uncertainties • Measurement correlations required as input • Assumes all uncertainties Gaussian distributed L.Lyons, D.Gibaut, P.Clifford, NIM A270 (1988) A.Valassi, NIM A500 (2003) D.Glenzinski, Fermilab

  6. BLUE • Inputs • Output • where D.Glenzinski, Fermilab

  7. BLUE • In practice • Decompose total uncertainty into a set of contributions (e.g. Stat, Signal model, Bgd model, Method, etc.) • Stat correlations rigorously determined using MC pseudo-experiments; mostly all 0 now • Syst correlations harder… usually assign |ij|=0,1 D.Glenzinski, Fermilab

  8. Details • The latest combination uses 12 input measurements… • 5 Published Run-1 results • CDF: ljt, dil, had • D0: ljt, dil • 4 CDF Run-2 results • Latest/Greatest in ljt, dil, had • Published “lxy” (ljt channel, but uses b decay length) • 3 D0 Run-2 results • Latest/Greatest in ljt-run2a, ljt-run2b, dil • …and 12 separate uncertainty categories D.Glenzinski, Fermilab

  9. Uncertainty Categories • Statistical: limited data statistics • Signal modeling: ISR, FSR, PDF • Background modeling: normalization, shape, Q2 • Fit: fit method, b-tagging, finite MC statistics • MC: Pythia vs Herwig vs Alpgen vs MC@NLO • UN/MI: D0 Uranium noise and multiple interactions • Jet Energy Scale • aJES: Run-II e/h calibration • bJES: issues specific to b-jets • cJES: fragmentation and out-of-cone showering • dJES: relative (e.g. pseudo-rapidity dependent) JES corrections and in-situ Wjj (D0) • iJES: in-situ calibration from Wjj (CDF) • rJES: remaining JES dominated by uncertainty on absolute correction from single particle response and calorimeter non-linearities D.Glenzinski, Fermilab

  10. CDF Inputs Published Run-I Preliminary Run-II C1(HAD) C1(LJT) C1(DIL) C2(LJT) C2(DIL) C2(Lxy) C2(HAD) Mtop 186.0 176.1 167.4 172.7 171.2 180.7 177.0 Stat 10.0 5.1 10.3 1.2 2.7 14.5 3.3 iJES 0.0 0.0 0.0 1.3 0.0 0.0 1.8 aJES 0.0 0.0 0.0 0.0 0.0 0.0 0.0 bJES 0.6 0.6 0.5 0.4 0.2 0.0 0.1 cJES 3.0 2.7 2.6 0.5 1.7 0.0 0.6 dJES 0.3 0.7 0.6 0.1 0.1 0.0 0.1 rJES 4.0 3.4 2.8 0.2 1.8 0.3 0.5 Signal 1.8 2.6 2.8 0.6 0.7 1.4 0.6 MC 0.8 0.1 0.6 0.4 0.7 0.7 0.3 UN/MI 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Bgd 1.7 1.3 0.3 0.6 0.4 7.2 1.0 Fit 0.6 0.0 0.7 0.2 0.6 4.2 0.6 Syst 5.7 5.3 4.9 1.7 2.8 8.5 2.4 Total 11.5 7.3 11.4 2.1 3.9 16.8 4.1 (all quantities in GeV/c2) (original authors consulted in every case) (actual combination uses two significant digits) D.Glenzinski, Fermilab

  11. D0 Inputs Published Run-I Preliminary Run-2 D1(LJT) D1(DIL) D2(LJTa) D2(LJTb) D2(DIL) Mtop 180.1 168.4 170.5 173.0 173.7 Stat 3.6 12.3 1.9 1.3 5.4 iJES 0.0 0.0 0.0 0.0 0.0 aJES 0.0 0.0 0.7 0.8 1.9 bJES 0.7 0.7 0.2 0.1 0.9 cJES 2.0 2.0 0.0 0.0 2.1 dJES 0.0 0.0 1.7 1.4 0.9 rJES 2.5 1.1 0.0 0.0 0.0 Signal 1.1 1.8 1.0 0.5 0.8 MC 0.0 0.0 0.0 0.0 0.2 UN/MI 1.3 1.3 0.0 0.0 0.0 Bgd 1.0 1.1 0.5 0.4 0.6 Fit 0.6 1.1 0.1 0.2 0.9 Syst 3.9 3.6 2.2 1.7 3.4 Total 5.3 12.8 2.9 2.2 6.4 (all quantities in GeV/c2) (original authors consulted in every case) (actual combination uses two significant digits) D.Glenzinski, Fermilab

  12. Statistical Correlations M(ljt)-<Lxy> Stat correlation • All input measurements use statistically independent data samples except CDF Run-II ljt and lxy • Using S+B MC pseudo-exp found stat=0 (as expected) D.Glenzinski, Fermilab

  13. Systematic Correlations • Uncorrelated: Fit, iJES • Correlated across all inputs • in same run and same experiment: dJES, aJES • in same experiment: rJES, UM/MI • in same channel: Bgd • everywhere: Signal, bJES, cJES, MC • Correlation taken to be 0 or 100% • We don’t have negative correlations anywhere • Variations considered as part of cross-checks • Only pragmatic options (and also probably right) D.Glenzinski, Fermilab

  14. Total Correlation Coefficients C1L C1D C1H D1L D1D C2L C2D C2H C2Lxy D2La D2Lb D2D 1.0 0.29 1.0 0.32 0.19 1.0 0.26 0.15 0.14 1.0 0.11 0.08 0.07 0.16 1.0 0.30 0.17 0.16 0.22 0.09 1.0 0.45 0.27 0.33 0.21 0.11 0.24 1.0 0.17 0.11 0.15 0.09 0.05 0.11 0.17 1.0 0.11 0.03 0.02 0.10 0.01 0.16 0.03 0.02 1.0 0.16 0.09 0.06 0.11 0.05 0.16 0.07 0.06 0.10 1.0 0.11 0.06 0.04 0.09 0.03 0.12 0.04 0.04 0.09 0.20 1.0 0.18 0.12 0.11 0.17 0.08 0.14 0.19 0.07 0.01 0.21 0.14 1.0 C1ljt C1dil C1had D1ljt D1dil C2ljt C2dil C2had C2lxy D2ljta D2ljtb D2dil • Using the inputs and uncertainties from p10-11 and the correlations as specified on p12-13 D.Glenzinski, Fermilab

  15. Combination Results Mt = 172.6 +/- 1.4 GeV/c2 c2/dof = 6.9/ 11 (81%) • Relative uncertainty: 0.8% D.Glenzinski, Fermilab

  16. Combination Weights C1(LJ) C1(DL) C1(HA) D1(LJ) D1(DL) C2(LJ) C2(DL) C2(HA) C2(Lx) D2(La) D2(Lb) D2(DL) Wght: -4% -0.7% -0.6% +2% +0.2% +36% +10% +8% -1% +15% +35% -0.6% D.Glenzinski, Fermilab

  17. Combination Pulls C1(LJ) C1(DL) C1(HA) D1(LJ) D1(DL) C2(LJ) C2(DL) C2(HA) C2(Lx) D2(La) D2(Lb) D2(DL) Pull: +0.5 -0.5 +1.2 +1.5 -0.3 +0.1 -0.4 +1.2 +0.5 -0.8 +0.2 +0.2 D.Glenzinski, Fermilab

  18. Combination Uncertainties Stat = 0.84 JES(Wjj) = 0.74 JES(rest) = 0.52 Sig = 0.54 Bgd = 0.36 Other = 0.24 (all quantities are in GeV/c2) D.Glenzinski, Fermilab

  19. Combination Uncertainties • Largest contributions scale with statistics Stat = 0.84 JES(Wjj) = 0.74 JES(rest) = 0.52 Sig = 0.54 Bgd = 0.36 Other = 0.24 (all quantities are in GeV/c2) D.Glenzinski, Fermilab

  20. Cross-Checks • Repeated combination with these variations • Used each extreme of asymmetric stat uncertainty • Varied (C2L-C2Lxy) by +/- 5% for their stat errors • Varied correlations among all inputs by 20% for bJES, cJES, rJES, Signal, MC, and Bgd simultaneously • Treated Signal and MC as stat uncertainties since dominated by precision of MC statistics • Set CDF=D0 for Signal,MC uncertainties • Varied treatment of Run I uncertainties • Central value and total uncertainty both affected by ~150 MeV/c2 or less in all cases • At present, we’re insensitive to the details of the systematic uncertainties and their correlations D.Glenzinski, Fermilab

  21. Consistency? • Is there a systematic trend here? 2j 4j 6j D.Glenzinski, Fermilab

  22. Fit to 3 Channels Total Correlation M(H) M(L) M(D) Fit Value (GeV/c2) M(HAD)177.3 +/- 3.91 M(LJT)172.4 +/- 1.50.12 1 M(DIL)169.8 +/- 3.10.18 0.26 1 • Same inputs, correlations, etc but fit to three observables: top mass in each channel • Use this to calculate 2 comparison M(L-D) = 2.73.1 M(H-L)=4.94.0 M(H-D)=7.54.5 (L-D) = 0.8/1 (39%) 2(H-L)=1.5/1 (23%) 2(H-D)=2.8/1 (10%) D.Glenzinski, Fermilab

  23. Other Fits • These are all for fun • not “official” in any way • Fit to two observables: CDF, D0 • Fit to two observables: Run-1, Run-2 D.Glenzinski, Fermilab

  24. Discussion • Some approximations are made • CDF and D0 do not quantify systematic uncertainties using the same prescription • Makes =1 assignments more suspect • A smaller uncertainty doesn’t necessarily mean a particular method is less sensitive… could bias the weights • The detailed breakdown of JES is a Run-II construction • Had to back propagate to Run-I inputs • From x-checks p20, we see these don’t really matter • Moving forward, they might • CDF/D0 would like to define common approaches to all the modeling related uncertainties (ISR, FSR, Q2, etc) D.Glenzinski, Fermilab

  25. Discussion • We’re missing some sources of syst uncertainty • Most notably, Color-Reconnection • Potentially large (but at LEP2 initial theory estimates off by factor of 10 relative to final numbers) • Generator tuned to Tevatron min bias ~ready (LEP2 MC not useful since e+e- initial state is colorless, while p+p- is colorful!) • Others…? D.Glenzinski, Fermilab

  26. Discussion • We double count some uncertainties • ISR/FSR/Hadronization included in “JES” and again in “Signal” and “MC” • Experimentally UE/ISR/FSR/CR all tangled, but treated as separate orthogonal uncertainties • We overestimate others • Many of the modeling uncertainties are actually limited by the MC stats used to quantify the effect • It means we estimate the effect can’t be any bigger than the stat relevant for the comparison (e.g. MoreFSR vs LessFSR) • Standard practice since stat limits the sensitivity with which you can quantify a given systematic uncertainty • Typically at the 200-300 MeV/c2 level per effect D.Glenzinski, Fermilab

  27. Outlook • We’re going to get another x3-4 data • Possible to reach • Need to work harder to cleanly specify and determine modeling systematic uncertainties • Need common CDF and D0 approach • Eventually will want to add LHC to combo • Approach to modeling uncertainties and breakdown of JES ought to be synchronized D.Glenzinski, Fermilab

  28. What are we measuring? • All Mt measurements are calibrated to MC • MC calibration not unique to top mass • In the MC, the parameter we calibrate to is the top-quark pole mass • Numerous discussions with numerous authors • All say: “It’s pole mass w/i ~qcd~200 MeV/c2” D.Glenzinski, Fermilab

  29. What are we measuring? • There’s a theoretical issue since t-quark is not a color singlet • What we need is an experimental observable that’s • A color singlet • Sensitive to Mt • Well defined at a hadron collider • Can be modeled theoretically in a well defined manner • What we have are experimental observables that are affected by numerous non-perturbative (QCD) effects • Makes theoretical interpretation difficult, since mapping from the perturbative to observables requires non-perturbative model • This is what the modeling systematic uncertainties are meant to address… how sensitive are we to varying these effects in MC? A: moderately, ~500 MeV/c2 D.Glenzinski, Fermilab

  30. Closing Remarks • Tevatron combined top mass still improving • Have reached a relative uncertainty of 0.8% • Have surpassed Run-II goal by factor 2 • A total uncertainty of 1 GeV/c2 is possible • CDF/D0 need to adopt common methods for quantifying model related systematic uncertainties • LHC and Tevatron should dovetail their systematic methodologies in some areas D.Glenzinski, Fermilab

  31. Closing Remarks • We’re measuring the pole mass • Modeling related systematic uncertainties are meant to address the theoretical ambiguity associated with ExpObservables PoleMass (they’re presently ~500 MeV/c2) • I’m looking forward to discussing these issues with you over the coming days D.Glenzinski, Fermilab

  32. Backups D.Glenzinski, Fermilab

  33. Negative Weights • If >1/2, then w1<0 • An example M1 = 175 +/- 0.1 (sta) +/- 5 (jes) GeV/c2 M2 = 180 +/- 0.1 (sta) +/- 10 (jes) GeV/c2 jes=1 • What should <M> be? D.Glenzinski, Fermilab

  34. Negative Weights • If >1/2, then w1<0 • An example M1 = 175 +/- 0.1 (sta) +/- 5 (jes) GeV/c2 M2 = 180 +/- 0.1 (sta) +/- 10 (jes) GeV/c2 jes=1 • What should <M> be? • M1, M2 clearly statistically incompatible • <M>=170, and jes fluctuated by 1, since correlated that would yield M1=170+5, M2=170+10 D.Glenzinski, Fermilab

  35. Negative Weights • What does BLUE do? • Inputs: • Get the weights: • Combine: D.Glenzinski, Fermilab

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