1. Overview of the Systematic Uncertainties on Measured Top Mass by the CDF Collaboration Top Mass Conveners For the CDF Top Group Joint CDF and DO Workshop: Systematic Uncertainties on Top Physics Measurements September 8, 2008

2. Sep 08, 2008 2M. Datta, FNAL Outline Introduction: Current status of Top mass measurements Introduction: Current status of Top mass measurements General philosophy about the systematic uncertainties General philosophy about the systematic uncertainties Status of systematic uncertainties Status of systematic uncertainties Quick overview and prescriptions Quick overview and prescriptions Work in progress and to do list Work in progress and to do list Color reconnection Color reconnection NLO NLO Summary Summary Note: The same systematic prescriptions are also used by all the Top analyses

3. Sep 08, 2008 3M. Datta, FNAL Introduction Top mass measurement has entered a new era of precision Top mass measurement has entered a new era of precision Most of the measurement already systematics limited Most of the measurement already systematics limited Unprecedented level of precision even for each single analysis Unprecedented level of precision even for each single analysis Working hard for every 100 MeV improvement Working hard for every 100 MeV improvement Investigating systematic effects from sources, which might not taken into account Investigating systematic effects from sources, which might not taken into account

4. Sep 08, 2008 4M. Datta, FNAL  M top In channel/analysis not using in-situ JES  Systematics dominated by the uncertainty on parton energies (JES) In channel/analysis not using in-situ JES  Systematics dominated by the uncertainty on parton energies (JES) Other sources arise from the assumptions employed to infer M top Other sources arise from the assumptions employed to infer M top  M top per CDF Analysis Statistical (Including in-situ JES for LJ& All-Had) (GeV/c 2 ) JES (DIL) OR Residual JES (LJ and All-Had) (GeV/c 2 ) OtherSystematics Dilepton (1.9 fb -1 ) 2.72.51.5 Lep+Jets (2.7 fb -1 ) 1.30.50.9 All Jets (2.1 fb -1 ) 3.80.81.5 Statistical and systematical sensitivities by channel

5. Sep 08, 2008 5M. Datta, FNAL Systematic Uncertainties Syst. (GeV/c 2 ) Lep+JetsDilepton All Had Residual JES 0.5-0.8 JES-2.5- b-JES b-JES0.40.40.6 ISR and FSR 0.30.50.3 PDFs0.20.60.4 Generator0.50.90.5 In-time pileup 0.10.20.3 Lept energy scale 0.20.1- B-tag scale factor --0.4 Bkg fraction, Sample comp, Modeling, stat 0.4 0.5 (stat), 0.3 (Sample Comp), 0.2 (Modeling) 1.03 (Bkg Template), 0.26 (Sig Template) Calibration/Method0.10.40.4 Total1.02.91.7 other

6. Sep 08, 2008 6M. Datta, FNAL General philosophy ALL top mass analyses are calibrated to MC: pythia + CdfSim for signal. ALL top mass analyses are calibrated to MC: pythia + CdfSim for signal. Data used to model some backgrounds. Data used to model some backgrounds. Therefore we need systematic uncertainties for all and only those features of the data that may be incorrectly modeled by our MC. Therefore we need systematic uncertainties for all and only those features of the data that may be incorrectly modeled by our MC. In principle: In principle: list such effects list such effects determine variations that are consistent with data (ttbar or control samples) determine variations that are consistent with data (ttbar or control samples) propagate those variations to uncertainty on M top. propagate those variations to uncertainty on M top. But in practice… But in practice…

7. Sep 08, 2008 7M. Datta, FNAL General philosophy (Cont’) Explicit evaluation of systematics is an art. Explicit evaluation of systematics is an art. Beware of double counting Beware of double counting Beware of under counting Beware of under counting What to do when we don’t have all the information (~always)? Make further assumptions… What to do when we don’t have all the information (~always)? Make further assumptions… In all systematics so far: In all systematics so far: Assume “prior” for systematic variations is Gaussian Assume “prior” for systematic variations is Gaussian Assume a linear effect on M top Assume a linear effect on M top Results in symmetric Gaussian systematics Results in symmetric Gaussian systematics For each systematic variation determine the effect on measured top mass For each systematic variation determine the effect on measured top mass Perform data-size pseudo experiments, including the appropriate signal and background events Perform data-size pseudo experiments, including the appropriate signal and background events Most of the systematics are evaluated at top mass of 175 GeV Most of the systematics are evaluated at top mass of 175 GeV

8. Sep 08, 2008 8M. Datta, FNAL General philosophy (Cont’) When +/-1 sigma can be somehow defined: When +/-1 sigma can be somehow defined: Evaluate slope using shift method Evaluate slope using shift method If +/-1 sigma shift results in measured top masses M + and M - If +/-1 sigma shift results in measured top masses M + and M - Slope is |M + -M - |/2. Slope is |M + -M - |/2. When M + M nominal > M - When M + M nominal > M - Otherwise slope: Larger of |M + -M nominal |/2 and |M - -M nominal |/2 Otherwise slope: Larger of |M + -M nominal |/2 and |M - -M nominal |/2 Ignore uncertainty Ignore uncertainty When “1 sigma” is an elusive concept: When “1 sigma” is an elusive concept: Probe magnitude of our potential mis-modeling using whatever information we have at hand, then arbitrarily define 1 sigma and symmetrize. Probe magnitude of our potential mis-modeling using whatever information we have at hand, then arbitrarily define 1 sigma and symmetrize. Recognize that we have incomplete information, and the models we use to probe don’t necessarily cover our potential mistakes. Recognize that we have incomplete information, and the models we use to probe don’t necessarily cover our potential mistakes.

9. Sep 08, 2008 9M. Datta, FNAL General philosophy (Cont’) Analyses may be sensitive to modeling of some feature not in the standard list of systematics. Of course you have to include these! Analyses may be sensitive to modeling of some feature not in the standard list of systematics. Of course you have to include these! Examples: Top mass measurement using lepton P t and L xy method Examples: Top mass measurement using lepton P t and L xy method

10. Prescriptions for Systematic Uncertainties http://www-cdf.fnal.gov/physics/new/top/systematics/tevatron_systematics.html Jet Energy Scale (including residual) b-jet energy scale MC Generator ISR/FSRPDF Background fraction and shape Lepton p T Pileup Method/MC statistics

11. Sep 08, 2008 11M. Datta, FNAL Jet Energy Scale (JES) Details in Details in NIM A, 566, 375 (2006) Relative uncertainty (L1) L1 correction applied for making jet energy uniform along eta Multiple interaction uncertainty (L4) Absolute correction (L5) Correct jet back to the particle level Underlying event uncertainty (L6) Out-of-cone uncertainty (L7) Correct jet back to parton level Splash-out uncertainty (L8) Leakage beyone radius=1.3 In-situ calibration applied for most Lep+Jets and All-had analyses

12. Sep 08, 2008 12M. Datta, FNAL JES/ Residual JES Evaluate the separate uncertainties for ALL levels of the JES systematic (including higher levels in case analysis only correct up to parton level (L5)). Evaluate the separate uncertainties for ALL levels of the JES systematic (including higher levels in case analysis only correct up to parton level (L5)). Add those pieces in quadrature to get the systematic on the top mass. Add those pieces in quadrature to get the systematic on the top mass. The "total JES systematic" (all levels at once) can be used as a cross-check The "total JES systematic" (all levels at once) can be used as a cross-check Cross check recommended for analyses without in situ calibration. Cross check recommended for analyses without in situ calibration. If background is evaluated from MC, apply the same  1  JES variations to dominant background sources simultaneously with the signal variations If background is evaluated from MC, apply the same  1  JES variations to dominant background sources simultaneously with the signal variations Syst. (GeV/c 2 ):  M top Lep+JetsDilepton All Had Residual JES 0.5-0.7-0.8 JES-2.5-3.5-

13. Sep 08, 2008 13M. Datta, FNAL Residual JES : LJ+DIL Template Analysis

14. Sep 08, 2008 14M. Datta, FNAL b-jet Energy Scale Recently revised Recently revised Old method : 0.6% shift of b-jet energies Old method : 0.6% shift of b-jet energies The old method was a) statistics limited in the original estimate, b) transfer to other analyses involved lots of averaging and rules of thumb. The old method was a) statistics limited in the original estimate, b) transfer to other analyses involved lots of averaging and rules of thumb. New Method: Three components New Method: Three components semi-leptonic decay BRs semi-leptonic decay BRs Reweight b and c BRs together +/- 1 sigma. Reweight b and c BRs together +/- 1 sigma. Fragmentation Fragmentation Reweight to LEP/SLD Bowler parameters Reweight to LEP/SLD Bowler parameters Full-sim sample using Bowler parameters from LEP (coming soon) Full-sim sample using Bowler parameters from LEP (coming soon) Cal response effect (0.2%) Cal response effect (0.2%) Shift b-jet energies by 1%, evaluate shift, multiply by 0.2. Shift b-jet energies by 1%, evaluate shift, multiply by 0.2. Syst. (GeV/c 2 ) Lep+JetsDilepton All Had b-JES b-JES0.2-0.40.2-0.40.3-0.6

15. Sep 08, 2008 15M. Datta, FNAL b-jet Energy Scale (Con’t) From Z-peak physics summary: From Z-peak physics summary: B(b  l) = 0.1071 ± 0.0022 B(b  l) = 0.1071 ± 0.0022 B(b  c  l) = 0.0801 ± 0.0018 B(b  c  l) = 0.0801 ± 0.0018 B(c  l) = 0.0969 ± 0.0031 B(c  l) = 0.0969 ± 0.0031 Our MC matches b→l exactly. Our MC matches b→l exactly. Use 23.9% +/- 0.7% Use 23.9% +/- 0.7% c→l not so clear, when we try to avg direct, cascade c decays. c→l not so clear, when we try to avg direct, cascade c decays. Use 18.82% +/- 2.0% Use 18.82% +/- 2.0% Fragmentation parametrization: (similar to D0 method) Fragmentation parametrization: (similar to D0 method) Using reweighting by the variable that includes just the non- perturbative part of the b fragmentation. Using reweighting by the variable that includes just the non- perturbative part of the b fragmentation. Exactly what the Bowler function is used for in Pythia. Exactly what the Bowler function is used for in Pythia. Take larger shift from reweighting to 1) LEP, 2) SLD fits. Take larger shift from reweighting to 1) LEP, 2) SLD fits. Still don’t understand why D0 sees large systematic (but only for tagged analysis). Still don’t understand why D0 sees large systematic (but only for tagged analysis).

16. Sep 08, 2008 16M. Datta, FNAL b-jet Energy Scale : Contribution from Different Sources Letpon+Jets Matrix Element Analysis

17. Sep 08, 2008 17M. Datta, FNAL MC Generator If different generators describes our data equally well.. take the difference between them as systematics If different generators describes our data equally well.. take the difference between them as systematics Why consider this systematic uncertainty, given some of these effects might already be included in other systematic categories (such as JES)? Why consider this systematic uncertainty, given some of these effects might already be included in other systematic categories (such as JES)? Cover effects of ttbar-like high multiplicity environment Cover effects of ttbar-like high multiplicity environment Many of the systematic corrections are derived from control samples which are not so busy as the ttbar events Many of the systematic corrections are derived from control samples which are not so busy as the ttbar events Currently taking the difference between Herwig and Pythia: Currently taking the difference between Herwig and Pythia: Difference in the showering models Difference in the showering models Difference in jet-resolution Difference in jet-resolution There might be overlap between generator and other systematics There might be overlap between generator and other systematics Hard to separate overlapping and non-overlapping contributions Hard to separate overlapping and non-overlapping contributions Syst. (GeV/c 2 ) Lep+JetsDilepton All Had Generator0.5-0.80.9-1.30.5-0.8

18. Sep 08, 2008 18M. Datta, FNAL MC Generator (Cont’) Work in progress and plans Work in progress and plans Include ALPGEN ttbar sample (different diagrams): Compare ttbar+0p inclusive with ttbar+  1P Include ALPGEN ttbar sample (different diagrams): Compare ttbar+0p inclusive with ttbar+  1P Currently investigating the effect due to ALPGEN having zero-width for top and W masses Currently investigating the effect due to ALPGEN having zero-width for top and W masses Include NLO ttbar sample Include NLO ttbar sample MC@NLO samples have ~10% of events with negative weight! MC@NLO samples have ~10% of events with negative weight! Look at other NLO generators (such as POWHEG) Look at other NLO generators (such as POWHEG)

19. Sep 08, 2008 19M. Datta, FNAL Radiation (ISR/FSR) Constrain the ISR/FSR Pythia parameters from Drell-Yan events Constrain the ISR/FSR Pythia parameters from Drell-Yan events Works great for constraining ISR, but not directly FSR Works great for constraining ISR, but not directly FSR ISR and FSR are governed by the same physical processes and essentially the same empirical model as well. ISR and FSR are governed by the same physical processes and essentially the same empirical model as well. Constraints on ISR from D-Y events can thus be taken as constraints on FSR as well Constraints on ISR from D-Y events can thus be taken as constraints on FSR as well Since Since Pythia uses parallel sets of parameters to control both types of showers In the current "IFSR" samples are just simultaneous variations of the ISR and FSR parameters by 1 sigma. Treating these uncertainties as correlated should if anything result in a larger systematic

20. Sep 08, 2008 20M. Datta, FNAL Radiation (ISR/FSR) : Plans Update this study with more data including other distributions sensitive to the radiation, e.g. N jets,  for different mass (M ll ) regions. Update this study with more data including other distributions sensitive to the radiation, e.g. N jets,  for different mass (M ll ) regions. Needs more study on hard gluon radiation modeling. Needs more study on hard gluon radiation modeling. Overlaps with NLO effects. Overlaps with NLO effects. Plan: study MC samples with different component Plan: study MC samples with different component Hard ISR: ALPGEN – ttbar+jets Hard ISR: ALPGEN – ttbar+jets Hard FSR: Madgraph Hard FSR: Madgraph Loops: MC@NLO Loops: MC@NLO Based on the outcome of these studies may need to revise ISR/FSR systematic. Based on the outcome of these studies may need to revise ISR/FSR systematic. From Un-ki Yang 4<Et(L4)<15 GeV Syst. (GeV/c 2 ) Lep+JetsDilepton All Had ISR and FSR 0.2-0.30.2-0.50.3-0.6

21. Sep 08, 2008 21M. Datta, FNAL Parton Density Function (PDFs) Part I : Add in quadrature the difference between CTEQ6M 20 pairs of eigenvectors Part I : Add in quadrature the difference between CTEQ6M 20 pairs of eigenvectors Part II: Add in quadrature the difference between MRST with two different values of ΛQCD (e.g. MRST72 ΛQCD=228MeV vs. MRST75 ΛQCD=300MeV) Part II: Add in quadrature the difference between MRST with two different values of ΛQCD (e.g. MRST72 ΛQCD=228MeV vs. MRST75 ΛQCD=300MeV) Part III: Add in quadrature the effect of reweighting gg contribution from 5% (LO) to 20% (=15+5) (NLO) Part III: Add in quadrature the effect of reweighting gg contribution from 5% (LO) to 20% (=15+5) (NLO) Answer to D0’s question: The re-weighting is done on the our standard Pythia ttbar events, which uses LO PDF. Once we include systematic uncertainty from NLO, this might already be covered there Syst. (GeV/c 2 ) Lep+JetsDilepton All Had PDFs0.2-0.30.5-0.60.4

22. Sep 08, 2008 22M. Datta, FNAL Background Fraction and Shape No common prescription. Varies from analysis to analysis. No common prescription. Varies from analysis to analysis. Come up with something and convince the group that it makes sense. Come up with something and convince the group that it makes sense. Often includes pieces related to: Often includes pieces related to: Overall bg normalization (aka S:B) Overall bg normalization (aka S:B) bg composition (vary component normalizations within uncertainties) bg composition (vary component normalizations within uncertainties) bg shape bg shape W(+/-hf) +jets samples with varying Q 2 W(+/-hf) +jets samples with varying Q 2 Generate ALPGEN samples with Q=0.5 and Q=2.0 Generate ALPGEN samples with Q=0.5 and Q=2.0 fakes particularly poorly understood—deserve special treatment fakes particularly poorly understood—deserve special treatment Uncertainty on the background composition is from cross-section measurement Uncertainty on the background composition is from cross-section measurement Haven’t included in this talk. Topic for future workshops.. Haven’t included in this talk. Topic for future workshops.. Lep+Jets ME analysis (2.7 fb -1 )  M top (GeV/c2) Bkg fraction 0.36 Bkg composition 0.18 Bkg: Q 2 0.08  0.07 Bkg MC stat. 0.05

23. Sep 08, 2008 23M. Datta, FNAL Lepton P T For most analyses, shift e and  energies (separately) by +/-1% For most analyses, shift e and  energies (separately) by +/-1% This shift was originally assigned for e This shift was originally assigned for e NIM A, 566, 375 (2006), also checked by other di-electron analyses No strong evidence for  No strong evidence for  Take largest shift from nominal Take largest shift from nominal Work in progress Work in progress New analysis looking at Z  ee,  data New analysis looking at Z  ee,  data Syst. (GeV/c 2 ) Lep+JetsDilepton Lept energy scale 0.1-0.20.1-0.3

24. Sep 08, 2008 24M. Datta, FNAL In-time Pileup Luminosity profile increasing; this systematic becomes more important to understand precisely Luminosity profile increasing; this systematic becomes more important to understand precisely Two parts Two parts Part I : known discrepancy in lumi profile of data, MC. Part I : known discrepancy in lumi profile of data, MC. Part II : Even if lumi profile matched, there may be residual mismodeling of extra interactions. Part II : Even if lumi profile matched, there may be residual mismodeling of extra interactions. Taken into account by the JES uncertainty due to MI Taken into account by the JES uncertainty due to MI Possible uncounted effects due to high multiplicity environment Possible uncounted effects due to high multiplicity environment Part I: Part I: Evaluate the magnitude of the effect for each analysis. Evaluate the magnitude of the effect for each analysis. Suggest to run PEs reweighting to data Ninteractions profile Suggest to run PEs reweighting to data Ninteractions profile If significant effect, take case by case. Otherwise, uncertainty on the comparison can be added as a systematic. If significant effect, take case by case. Otherwise, uncertainty on the comparison can be added as a systematic. Part II: Part II: MC-based study in ttbar dilepton jets shows response changes by 250 MeV/vertex after MI corrections. MC-based study in ttbar dilepton jets shows response changes by 250 MeV/vertex after MI corrections. L4 jet systematic: 107 MeV/vertex L4 jet systematic: 107 MeV/vertex Probes magnitude of possible mis-modeling by scaling up the L4 (MI) systematic by a factor of 2.3. Probes magnitude of possible mis-modeling by scaling up the L4 (MI) systematic by a factor of 2.3.

25. Sep 08, 2008 25M. Datta, FNAL In-time Pileup (Cont’) Part I : Perform pseudo experiments by dividing the events into sub-samples with #Z vertex= 1, 2, 3,  4 Part I : Perform pseudo experiments by dividing the events into sub-samples with #Z vertex= 1, 2, 3,  4 Examine the resulting slope  m top /vertex and multiply by difference in average number of verticies for data-MC. Examine the resulting slope  m top /vertex and multiply by difference in average number of verticies for data-MC.  M top = (  m top /vertex) * ( - )  M top = (  m top /vertex) * ( - ) Part II: Part II: Check effect of x2.3 larger L4 systematic. Check effect of x2.3 larger L4 systematic. If important compared to first part above, use it instead. If important compared to first part above, use it instead. If existing L4 systematic evaluated with MC lumi profile, multiply also by: ( -1)/( -1). If existing L4 systematic evaluated with MC lumi profile, multiply also by: ( -1)/( -1). No direct data-MC comparisons we can use that aren’t statistically limited. No direct data-MC comparisons we can use that aren’t statistically limited. Syst. (GeV/c 2 ) Lep+JetsDilepton All Had In-time pileup 0.10.1-0.20.3-0.8

26. Sep 08, 2008 26M. Datta, FNAL MC Statistics Most analyses take something like a calibration systematic or an MC statistics systematic to account for the uncertainties in the calibration process due to limited MC stats. Most analyses take something like a calibration systematic or an MC statistics systematic to account for the uncertainties in the calibration process due to limited MC stats. The bootstrap is the approved way to understand calibration uncertainties due to MC sample stats. The bootstrap is the approved way to understand calibration uncertainties due to MC sample stats. Think a bit about how to do this; don’t over- or under-count background effects, etc. Think a bit about how to do this; don’t over- or under-count background effects, etc.

27. Additional Sources : Not Included Yet

28. Sep 08, 2008 28M. Datta, FNAL Non-perturbative Effects What about a color reconnection systematic? What about a color reconnection systematic? Based on the paper by Skands & Wicke. Working to evaluate the models they used for their rough generator- level results in the context of a full analysis. Based on the paper by Skands & Wicke. Working to evaluate the models they used for their rough generator- level results in the context of a full analysis. Already generated some ttbar samples with different models from Skands & Wicke’s paper Already generated some ttbar samples with different models from Skands & Wicke’s paper To drive a real systematic, the models need to be validated for consistency with Tevatron data, e.g. minbias. To drive a real systematic, the models need to be validated for consistency with Tevatron data, e.g. minbias. In the long run, if these effects turn out to be important, constrain them using e.g. high-Q 2 Drell-Yan and bbbar events. In the long run, if these effects turn out to be important, constrain them using e.g. high-Q 2 Drell-Yan and bbbar events.

29. Sep 08, 2008 29M. Datta, FNAL NLO Pythia includes corrections for hard radiation in t→Wb and W→jj vertices. Missing pieces are: Pythia includes corrections for hard radiation in t→Wb and W→jj vertices. Missing pieces are: loops - small effect on kinematics expected; loops - small effect on kinematics expected; higher-order radiation effects - should be “small”. higher-order radiation effects - should be “small”. Ongoing work for understanding of NLO, including loops, hard radiation, soft radiation and PDFs. Ongoing work for understanding of NLO, including loops, hard radiation, soft radiation and PDFs. Mentioned in the plans for ISR/FSR Mentioned in the plans for ISR/FSR Issues Issues Hard to separate to different pieces Hard to separate to different pieces

30. Sep 08, 2008 30M. Datta, FNAL Jet Resolution : Cross Check D0 quotes an uncertainty due to jet resolution. CDF does not. D0 quotes an uncertainty due to jet resolution. CDF does not. The generator systematic “Pythia VS Herwig” should cover a large part of this systematics The generator systematic “Pythia VS Herwig” should cover a large part of this systematics From photon+jets studies, find the resolution in Herwig is much closer to that in data, and different from that in Pythia From photon+jets studies, find the resolution in Herwig is much closer to that in data, and different from that in Pythia Currently all-hadronic analyses are checking the effect by smearing the jets with P T dependent resolution functions Currently all-hadronic analyses are checking the effect by smearing the jets with P T dependent resolution functions If the effects are small, use just as a cross check If the effects are small, use just as a cross check

31. Sep 08, 2008 31M. Datta, FNAL Summary Working towards the final systematic uncertainty on measured top mass Working towards the final systematic uncertainty on measured top mass Many of the sources are already incorporated Many of the sources are already incorporated Continue studies for better understanding Continue studies for better understanding ISR/FSR, …. ISR/FSR, …. Take into account possible missing sources Take into account possible missing sources Color reconnection Color reconnection NLO effects NLO effects Work with D0 Top group to come up with a final revisited systematic uncertainties by the end of the year. Work with D0 Top group to come up with a final revisited systematic uncertainties by the end of the year. Include systematics for other Top analysis (cross-section etc.) in the discussion Include systematics for other Top analysis (cross-section etc.) in the discussion