Overview of the Systematic Uncertainties on Measured Top Mass by the CDF Collaboration

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

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

4. Mtop • 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 Mtop Statistical and systematical sensitivities by channel M. Datta, FNAL

5. Systematic Uncertainties other M. Datta, FNAL

6. General philosophy • ALL top mass analyses are calibrated to MC: pythia + CdfSim for signal. • 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. • In principle: • list such effects • determine variations that are consistent with data (ttbar or control samples) • propagate those variations to uncertainty on Mtop. • But in practice… M. Datta, FNAL

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

8. General philosophy (Cont’) • When +/-1 sigma can be somehow defined: • Evaluate slope using shift method • If +/-1 sigma shift results in measured top masses M+ and M- • Slope is |M+-M-|/2. • When M+ < Mnominal < M- or M+ > Mnominal > M- • Otherwise slope: Larger of |M+-Mnominal|/2 and |M--Mnominal|/2 • Ignore uncertainty • 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. • Recognize that we have incomplete information, and the models we use to probe don’t necessarily cover our potential mistakes. M. Datta, FNAL

9. 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! • Examples: Top mass measurement using lepton Pt and Lxy method M. Datta, FNAL

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/FSR PDF Background fraction and shape Lepton pT Pileup Method/MC statistics

11. Jet Energy Scale (JES) • 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 M. Datta, FNAL

12. 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)). • 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 • 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 M. Datta, FNAL

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

14. b-jet Energy Scale • Recently revised • 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. • New Method: Three components • semi-leptonic decay BRs • Reweight b and c BRs together +/- 1 sigma. • Fragmentation • Reweight to LEP/SLD Bowler parameters • Full-sim sample using Bowler parameters from LEP (coming soon) • Cal response effect (0.2%) • Shift b-jet energies by 1%, evaluate shift, multiply by 0.2. M. Datta, FNAL

15. b-jet Energy Scale (Con’t) • From Z-peak physics summary: • B(bl) = 0.1071 ± 0.0022 • B(bcl) = 0.0801 ± 0.0018 • B(cl) = 0.0969 ± 0.0031 • Our MC matches b→l exactly. • Use 23.9% +/- 0.7% • c→l not so clear, when we try to avg direct, cascade c decays. • Use 18.82% +/- 2.0% • Fragmentation parametrization: (similar to D0 method) • 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. • 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). M. Datta, FNAL

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

17. MC Generator • 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)? • 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 • Currently taking the difference between Herwig and Pythia: • Difference in the showering models • Difference in jet-resolution • There might be overlap between generator and other systematics • Hard to separate overlapping and non-overlapping contributions M. Datta, FNAL

18. MC Generator (Cont’) • Work in progress and plans • 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 • Include NLO ttbar sample • MC@NLO samples have ~10% of events with negative weight! • Look at other NLO generators (such as POWHEG) M. Datta, FNAL

19. Radiation (ISR/FSR) • Constrain the ISR/FSR Pythia parameters from Drell-Yan events • 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. • Constraints on ISR from D-Y events can thus be taken as constraints on FSR as well • 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 M. Datta, FNAL

20. Radiation (ISR/FSR) : Plans From Un-ki Yang • Update this study with more data including other distributions sensitive to the radiation, e.g. Njets, for different mass (Mll) regions. • Needs more study on hard gluon radiation modeling. • Overlaps with NLO effects. • Plan: study MC samples with different component • Hard ISR: ALPGEN – ttbar+jets • Hard FSR: Madgraph • Loops: MC@NLO • Based on the outcome of these studies may need to revise ISR/FSR systematic. 4<Et(L4)<15 GeV M. Datta, FNAL

21. Parton Density Function (PDFs) • 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 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 M. Datta, FNAL

22. Background Fraction and Shape • No common prescription. Varies from analysis to analysis. • Come up with something and convince the group that it makes sense. • Often includes pieces related to: • Overall bg normalization (aka S:B) • bg composition (vary component normalizations within uncertainties) • bg shape • W(+/-hf) +jets samples with varying Q2 • Generate ALPGEN samples with Q=0.5 and Q=2.0 • fakes particularly poorly understood—deserve special treatment • Uncertainty on the background composition is from cross-section measurement • Haven’t included in this talk. Topic for future workshops.. M. Datta, FNAL

23. Lepton PT • For most analyses, shift e and  energies (separately) by +/-1% • This shift was originally assigned for e • NIM A, 566, 375 (2006), also checked by other di-electron analyses • No strong evidence for  • Take largest shift from nominal • Work in progress • New analysis looking at Zee,  data M. Datta, FNAL

24. In-time Pileup • Luminosity profile increasing; this systematic becomes more important to understand precisely • Two parts • 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. • Taken into account by the JES uncertainty due to MI • Possible uncounted effects due to high multiplicity environment • Part I: • Evaluate the magnitude of the effect for each analysis. • 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. • Part II: • MC-based study in ttbar dilepton jets shows response changes by 250 MeV/vertex after MI corrections. • 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. M. Datta, FNAL

25. In-time Pileup (Cont’) • Part I : Perform pseudo experiments by dividing the events into sub-samples with #Z vertex= 1, 2, 3, 4 • Examine the resulting slope mtop/vertex and multiply by difference in average number of verticies for data-MC. • Mtop = (mtop/vertex) * (<Nvtxdata> -<NvtxMC>) • Part II: • Check effect of x2.3 larger L4 systematic. • If important compared to first part above, use it instead. • If existing L4 systematic evaluated with MC lumi profile, multiply also by: (<Nvtxdata>-1)/(<NvtxMC>-1). • No direct data-MC comparisons we can use that aren’t statistically limited. M. Datta, FNAL

26. 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. • 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. M. Datta, FNAL

27. Additional Sources : Not Included Yet

28. Non-perturbative Effects • 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. • 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. • In the long run, if these effects turn out to be important, constrain them using e.g. high-Q2 Drell-Yan and bbbar events. M. Datta, FNAL

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

30. Jet Resolution : Cross Check • 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 • 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 PT dependent resolution functions • If the effects are small, use just as a cross check M. Datta, FNAL

31. Summary • Working towards the final systematic uncertainty on measured top mass • Many of the sources are already incorporated • Continue studies for better understanding • ISR/FSR, …. • Take into account possible missing sources • Color reconnection • NLO effects • 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 M. Datta, FNAL