Top Quark Mass and Width using the Template Method

1. Top Quark Mass and Widthusing the Template Method

2. Why study tops? Loop diagrams from top quarks and Higgs bosons contribute to the W mass … when we think we have seen the Higgs, is it really the SM Higgs? Something else? Make precision Standard Model tests! Top quarks are the only quarks to decay before forming hadrons. Their spin information is not washed out by QCD top~ 10-25 seconds QCD~ 10-24 seconds Decay ~100% of time to a W boson and a b quark • So far, the top quark is the heaviest fundamental (point) particle observed in nature Heavy mass of the top quark -> new physics very likely to manifest itself in top quark sector. Mass = 170.9  1.8 GeV/c2 As heavy as ~170 protons As heavy as ~1 gold nucleus Almost twice as heavy as the next most massive Standard Model particle ~40 times as massive as its isospin partner, the b quark Until LHC turns on, the Tevatron is the only place that top quarks have EVER been observed! • Decays before hadronizing • Helps pin down the mass of the Higgs boson • Can constrain new physics • Because … we can ? ? • So far, the top quark is the heaviest fundamental (point) particle observed in nature • Decays before hadronizing • Helps pin down the mass of the Higgs boson • Can constrain new physics • Because … we can

3. The Tevatron CDF 36 bunches of ~1010 anti-protons Bunches cross 2.5 million times per second The Tevatron (center of mass energy = 1.96 TeV) DZero 36 bunches of ~1011 protons Berkeley (2000 miles)

4. CDF • SVX: Silicon important for good tracking, necessary for b-tagging • Leptons: Best-measured objects in events • COT: drift chamber w/ coverage: |h|<1, s(PT)/PT ~ 0.15%PT • 1.4 Tesla superconducting solenoid outside tracking system • EM cal: sE / E ~ 14% /ÖE • Hadronic calorimeter crucial for difficult jet measurements • Had cal:sE / E ~ 80% /ÖE • Muons – scintillator + chamber, coverage out to |h|=1.5 • Need entire detector to get a good measurement of momentum imbalance SVX EM cal Muon Had cal COT

5. Tevatron performance at CDF Top Mass analysis: 1.7 fb-1 of data

6. Top quark phenomenology • Tops always decay via t->Wb • Event topology then depends on W decays • Hadronic (quarks) • Leptonic (electron or muon + neutrino) • This analysis uses the Lepton+Jets channel • One W decays to hadrons, the other to leptons • Signature = 4 quarks, 1 charged lepton + undetected neutrino • OK, so just take the invariant mass and you’re done. Right? • Not so simple …

7. Why Mtop is difficult • With 4 (and only 4 jets!), there are 12 different ways of assigning jets to partons at hard scattering • No guarantee that you have the correct jets (ISR/FSR, splitting, merging) • Use b-tagging to reduce combinatorics • Work hard … • Use resonance of hadronic W decay • b-tagging helps • Test kinematics for ttbar hypothesis • Use independent estimates of background rates Balance energy in transverse plane (system overconstrained) • Neutrino from W decay • Non-negligible backgrounds • Jets are difficult • With 4 (and only 4 jets!), there are 12 different ways of assigning jets to partons at hard scattering • Neutrino from W decay • Non-negligible backgrounds • Jets are difficult

8. Jet Energy Scale c = unit of combined nominal CDF JES calibration uncertainty

9. Top Quark Mass: Some handles What we know What we don’t know 6 final-state particles *4 vectors = 24 needed 24 unknowns 4 jets and charged lepton 4-vectors = 4*5 = 20 4 unknowns We know the mass of the neutrino = 1 3 unknowns We know the W mass quite well (both of them) = 2 1 unknown Require mtop = manti-top = 1 0 unknowns Transverse components of p from momentum conservation = 2 2 constraints • Instead of taking the invariant mass of the system, we will have to make a measurement by comparing data to Monte Carlo simulation • Find the parent top mass distribution most consistent with our data • We want to measure a variable that’s correlated to the top mass • System is over-constrained (helps choose from 12 possible jet-parton assignments)

10. Event Selection • Use b-tagging in SVX to reduce combinatorics and increase S:B • Divide events into 2 exclusive subsamples with different S:B and different reconstructed mass shapes Top Event Tag Efficiency: 60% False Tag Rate (per jet): 0.5%

11. Reconstructed mass templates Reconstructed mass is correlated to (but not the same thing as) the true top quark mass 2-tag templates more sharply peaked than 1-tag templates

12. In-situ calibration using dijet mass templates • Kinematic fitter works well, but distributions are highly correlated not only to top quark mass, but also to calibration of jets in the detector • Introduce the dijet mass from the hadronically decaying W • Use as in situ calibration of jet energy scale (JES) • We use the dijet mass closest to the well-known W mass from any pair of untagged jets among leading 4 jets (studied other choices, this was best)

13. How do we use the templates? How do we get the probability to observe an event with mtreco and mjj? Previously, assume the two observables are uncorrelated, and parameterize as a function of mtop and shifts in JES Near-impossible to account for correlation between observables Parameterizations difficult, mathematically … bad New: Use a Kernel Density Estimate-based approach to form PDFs that are two-dimensional in observables

14. A 1d KDE pictorial tutorial Add up all the blobs (ie Kernels) and you have an estimate for the true, underlying PDF Let’s move from the delta function to something else (a blob). If the shape is a rectangular box & we force the box to straddle the bin boundaries, we get a histogram Start with the reconstructed top quark masses in Monte Carlo, with no binning. Right now, each event is represented by a delta function on the x-axis Let’s remove the forcing to bin edges and instead center our blob (Kernel function) around each MC point. Also, let’s try something more smooth Probability Mtreco

15. Adaptive KDE • Want smoothing to depend on statistics within sample • First pass: fixed kernel width • Second pass: Varying width kernels • Narrower kernel in high-stats region  sharper peak • Wider kernel in low-stats region  smoother tail

16. 2d KDE

17. Backgrounds • Must deal with non-negligible backgrounds arising mostly from W+jets (real heavy flavor and mistags) • Estimate W+jets, QCD normalizations from data • Wbb/Wcc/Wc fractions from MC • MC estimates for single-top and dibosons

18. Backgrounds (1d)

19. Backgrounds (2d) More correlation between observables for background events

20. Likelihood Fit • Maximize likelihood for expected number of 1-tag and 2-tag signal and background events in a grid of over 2000 Mtop-JES points • Fit a 2d parabola (including correlation cross-term) to the minimized negative log(likelihood) values Example pseudoexperiment

21. Tests of machinery Machinery works and shows no significant bias

22. Systematics Even with in situ calibration, JES systematic dominates

23. Measurement! Mtop = 171.6  2.0 GeV/c2

24. Differential pulls … Scale all uncertainties by 4.7%

25. Cross-checks All errors uncorrected would have 3 GeV JES systematic

26. 1d projections

27. Plans for top mass measurement • Add more data (2 fb-1 measurement) for publication • Our group also has a template-based measurement in the dilepton channel using KDE • Will be extended to two observables and 2d KDE for better statistical power • We plan on combining the measurements in the same likelihood • Will move away from fitting a 2d quadratic and instead smooth out the likelihood using more non-parametric statistical tricks (local polynomial smoothing)

28. Switching gears …

29. Top quark decays • In SM, tops decay with a lifetime of ~4x10-25 seconds • |Vtb| ~ 1, and Mtop >> MW+Mb • Total width ~1.5 GeV  (Mtop)3 and calculated to ~1% • Only measurement so far is unpublished CDF result: c < 52.5 m at 95% CL • Lower limit on top quark width, t> 0.002 eV

30. The idea … • Use the kinematic fitter with templates that vary not as a function of top quark mass, but as a function of top quark width • Use a likelihood fit: gives the measured top quark width • Use the likelihood output to set a 95% CL on the top quark width

31. In practice • Selection is the same EXCEPT: • No 2 cut (was found to reduce sensitvity) • Allow extra jets in 1-tag events • Use only 1 fb-1 of data

32. Trusting the Monte Carlo? top = 50 GeV top = 1.5 GeV top = 30 GeV Mw+Mb General consensus from theorists: Can trust MC to ~30 GeV

33. More on the Monte Carlo Parton level mean, before event selection Parton level RMS, before event selection

34. Reconstructed mass templates

35. Likelihood fit output for t How might we use these to set limits? …

36. How to set upper limits • Let’s say we want to set a 95% upper limit on the top quark width. We have likelihood output from MC samples with varying t = 1.5, 5.0, 10.0, …. (GeV) 95% of curve Prob true Data L-fit L-fit

37. How to set lower limits • Let’s say we want to set a 95% lower limit on the top quark width. We have likelihood output from MC samples with varying t = 1.5, 5.0, 10.0, …. (GeV) 95% of curve Prob Data true L-fit L-fit

38. Does setting limits always work? • Sometimes with this technique, you don’t set a limit! • And what about two-sided limits? Data true L-fit

39. Feldman-Cousins machinery • Frequentist approach to setting limits that guarantees that we can always make a measurement • Tells us how to choose our confidence bands (aka an “ordering principle”) • Choose bands based on likelihood ratios. For every MC point, define a likelihood ratio: x: output of likelihood fit i: “true” width being examined Width with max prob at x

40. Use of likelihood ratio functions • Use the likelihood ratio to select the 95% confidence region for a particular true width • Order (select) by the most likelihood ratio

41. Likelihood ratio functions • We parameterize the likelihood output so that we have a likelihood ratio and confidence band for arbitrary t

42. Does it work?

43. Systematics • Move to Bayesian approach, as is typical • Easy to incorporate into Feldman-Cousins • Systematics change our confidence bands • Unfortunately, systematics in limit-setting procedures are a bit more tricky than in simple measurements (such as the top quark mass)… • Systematics = study of the unknown …

44. Reiterating Systematics • Typically, we have a PDF of the systematic parameter (such as scale of jets, background fraction, etc.), which we assume is Gaussian • Typically, we assume that linear shifts in the systematic parameter cause linear shifts in the parameter we are measuring Jet Energy Scale

45. But … • What if linear shifts in JES do not cause linear shifts in the top quark width out of the likelihood? This is the function we use to smear out the likelihood output (it’s Gaussian for normal systematics)

46. Systematics summary Jet resolution = smear jets to worsen resolution by extra 5% Systematics studied at different top widths when possible, systematic taken to be conservative * = non-Gaussian systematics

47. Smeared likelihood output Systematics included Original PDF Make new parameterizations, new L ratios all over again after convoluting with systematics

48. Likelihood fit!

49. Likelihood fit!

50. Confidence bands with data top < 12.7 GeV at 95% CL