# Presentation: 170605

## Measuring the Top Quark Mass

- Adam Gibson
- UC Berkeley Qualifying Exam
- November 21, 2003

- Why measure the top mass?
- What we’ve done so far – Run I style CDF measurement
- What I’m working on now – D0-style matrix element method
- Prospects for D0-style method at CDF, including work on transfer functions

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Standard Model

**Standard Model**

- SM so far very successful
- Predicted W, Z masses
- Compatible with a huge array of experimental data
- SM consistency checked to high precision
- A few loose ends tied up in last ten years
- Top quark, 
- Ongoing exploration
- Nature of ’s
- CKM matrix and CP violation
- H boson still not observed
- Tevatron unlikely to discover                  H with only 4 fb-1
- Top a fundamental particle
- Yukawa coupling a fundamental parameter of SM

- SM Graphic?
- Those boxes with fermions and gauge bosons?

-     H     |     ?     |    0

- EW (EWSB) spin = 0

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Radiative Corrections

- P. Renton hep-ph/0206231

- Fermions affect couplings

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## High-precision measurements of EW observables
LEP I, SLD
LEP II, SLD w/ polarized beams
Tevatron
N scattering (NuTeV)
Atomic Physics
Can “predict” top mass
’94 data at least consistent with first mt measurement
Today LEP plus LEP II                GeV
Today all Z pole            GeV
Today global fit                  GeV
Can predict H mass
          GeV, <219 GeV 95% CL

- LEP I, SLD
- LEP II, SLD w/ polarized beams
- Tevatron
- N scattering (NuTeV)
- Atomic Physics
- Can “predict” top mass
- ’94 data at least consistent with first mt measurement
- Today LEP plus LEP II                GeV
- Today all Z pole            GeV
- Today global fit                  GeV
- Can predict H mass
-           GeV, <219 GeV 95% CL

**Precision Electroweak**

- LEPEWWG/2003-01

- Bob Clare WIN ‘03

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## mt Consistency 

- LEPEWWG/2003-01

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## mW Also Key

**m****W ****Also Key**

- LEPEWWG/2003-01

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Top contribution

- P. Renton hep-ph/0206231

- Preliminary CDF Run II Results

- New (Preliminary) D0 Run I Result

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Future Prospects

**Future Prospects**

**Possible future Tevatron/LHC measurement**
**~2 GeV ********m****t**
**~15 MeV ********m****W**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## The Tevatron

**The Tevatron**

- ~330 pb-1  delivered to date

- ~260 pb-1 on tape

- ~180 pb-1 for l+jets mass w/ silicon now

- ~500 pb-1 for Spring 2005 thesis?

- Physics quality data

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Snapshot of CDF (Installing the SVX)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## t-t Overview

**t-t Overview**

- 85% q-qbar, 15% gluon fusion
- t  1.4 GeV,   10-24 s
- Leptons (e, ) well measured
- Quarks (jets) poorly measured
- And much QCD background
- B quarks (mesons) taggable
- Neutrinos don’t interact in detector
- Measured indirectly

| Dilepton
(e, ) | l+jets
(e, ) | All Hadronic | Other (’s) |
| --- | --- | --- | --- |
| 5%  | 30% | 45% | 20% |

- t-tbar Topologies

-     Production in p-pbar collisions at        = 1.96 TeV, NLO   6.7 pb

- Cacciari et al hep-ph/0303085

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Event Selection (CDF Run II measurement)

- High ET (20 GeV) e or 
- High ET (20 GeV)
- infer 
- 4 High ET jets
- At least one w/ displaced vertex B tag
- Combinatorics – which jets are from t?
- Combinatorics and jet energy measurements make mt a difficult measurement

**10.8 ******** **

**21.9 ******

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## CDF Detector

**e’s – EM calorimeter**
**     – ****tracking chamber**** **
******’****s – tracking chamber**
**     –  ****muon chambers**
**Jets – calorimeters**
**B Jets – calorimeters**
**           – ****silicon detectors**
******’****s – don’t interact in detector**

- Electron E resolution, few percent
- Muon p resolution, few percent
- Corrected jet resolution, ~12%
- B tag fraction, 60% of ttbar events have at least one?

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Event by event reconstruction

- 4 jets, 1 central e or , large missing ET, at least one displaced vertex b tag
- 2x3(x2) ways to assign jets to partons with one tag, 2(x2) for double
- Enough measurements to overconstrain system
- 2-C fit to find the (one) best combination (lowest 2)
- 2 cut to help reject backgrounds

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Build Mass Templates for Various Masses

- Right combination ~50% of time.
- Gluon in four leading jets 30-40%?

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Backgrounds (For 22 Events in Data)

- b tagging involves a choice between efficiency and fake rate
- Choice determines background composition
- Overall S:B is 2.7:1
- 16:6

- Compare to ttbar cross section of ~7 pb

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Final Fit: Shape Comparison of Data to MC Gives mt

**Final Fit: Shape Comparison of Data to MC Gives m****t**

- Signal shape parameterized, and as function of top mass.
- Background shape parameterized
- Unbinned likelihood fit to parameterized templates, with a background constraint

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Systematics

- Jet energy measurement leads to dominant systematic
- Initial State and Final State Radiation (ISR/FSR) since gluons affect jet energy, top and W mass, etc.
- Run I numbers (turn on, off) for now.
- PDF’s use CTEQ6M eigenvector sets

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Understanding Jets

- (A. Korytov)

- 

- Jet

- Quarks and gluons appear in the calorimeter as jets: collection of hadrons
- Mostly ’s
- Reconstruct mt in terms of parton energies, want to correct jets back to parton level
- Difficult to calibrate at low particle energies typical in jets
- Cracks in detector, Non-linearities
- Understanding fragmentation
- Out of cone energy

- 90°

- 40°

- 15°

- 6°

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Traditional Analysis Continues

- ~180 pb-1

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## New D0 Run I Top Mass Analysis

- Use all of the information you measure well, integrate over things you don’t measure well.
- Compare to our best knowledge of the physics – compare to SM differential cross sections.
- Integrate cross sections over quark energies, using MC-extracted transfer functions to connect to measured jet energies.

- D0 l+jets (1998) mt = 173.3  5.6 (stat)  5.5 (syst) GeV/c2

- D0 l+jets (2003) mt = 180.1  3.6 (stat)  4.0 (syst) GeV/c2

- x measured quantities (e.g. jets)
- y matrix element quantities (e.g. partons)
- f(q) parton distribution functions
- q1, q2 incoming quark energies

- W(x,y) transfer functions

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Traditional CDF Template Method vs. New D0 Matrix Element Method

- Traditional CDF (Template)
- One mt per event, equal weight.
- Single best-fit (2) combination.
- Series of eight levels of jet corrections, get mean correct and assume Gaussian shape.
- Global mt fit from likelihood fit of data to signal and background templates

- New D0 (Matrix Element)
- P(x : mt) for each event, based upon comparison of fifteen kinematic variables (x) to SM matrix elements
- All combinations weighted according to signal probability, and events combined according to signal probability
- Transfer functions connecting parton energies to jet energies in detail
- Global mt fit from joint likelihood of signal (mass-dependent) and background (mass-independent) probabilities.

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Global mt Fit Schematically: Combining Events

**P****signal**

**P****background**

**M****t**

- Signal Events

- Background Event

- P

- Mt

- Mt

- Mt

- Mt

- x

- x

- x

- =

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## D0 Results From Data (l+jets With No B Tag Requirement)

**D0 Results From Data (l+jets With No B Tag Requirement)**

**M****t****= 180.1 ******** 3.6 GeV (stat)**
- Compared with 5.6 GeV statistical error from previous D0 mass analysis.           The statistical error you’d expect from the old D0 analysis with a                      factor of 2.4 more data.                                                                                              22 events in data: 12  3 signal (from fit), 10  3 background

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Systematics at D0

- D0’s new analysis has a significantly smaller systematic due to jet energies.
- More detailed connection between jets and partons (transfer functions)
- Other systematics smaller as well
- Using more event information, and combining events and combinations more effectively

- Phys. Rev. D {58} 052001 (1998)

- D0 (1998)

- D0 (2003)

- Total systematic error 	    4.0 GeV/c2

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Applying D0’s Methods at CDF

- Very similar methods have been proposed by CDF members (Kondo) and others (Dalitz and Goldstein)
- Studied in Run I at CDF, but no mass measurement published.
- Dynamical Likelihood Method work well underway in Run II
- No magnetic field at D0 Run I
- Muons poorly measured, integrated over.
- Poor or no silicon coverage at D0 Run I
- 2003 mass analysis didn’t use displaced vertex tags.
- Easy to use binary SVX tags at CDF, more in keeping with the method to use a tag probability.  Either way should help dramatically reduce backgrounds.  But, there may be more backgrounds to consider (more matrix elements).
- Straightforward to add extra signal and background matrix elements.
- More difficult to incorporate extra matrix element with gluon radiation, either just extra diagrams or full NLO calculation

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## D0-Style Transfer Functions at CDF

- We have eight levels of jet corrections at CDF to get from jets back to parton-level quantities.

- 			Eparton – Ejet (GeV)
- 		for B jets from ttbar MC

- In general, their goal is to get the mean right, while assuming a gaussian shape
- Our transfer functions use jets that have been corrected back to particle-jet level (detector effects removed) (level 5 of 8)
- The goal is to start with partons, and accurately model the distribution of jet energies (shape as well as mean)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Transfer Function W(Eparton,Ejet)

- D0 plot from F. Canelli

- where
-      n(Eparton)*** ***is the (process dependent)
-         distribution of parton energies
**     **W(Eparton,Ejet) is the probability                       	distribution to have
-           	Ejet given a Eparton
- So, we hope to separate the
- process-dependent n(Eparton) from
- the largely process-independent W(Eparton, Ejet)

***E** = E**parton** - E**jet*

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Testing the transfer functions

- Parton information along with the transfer functions (previous page) allow us to make predictions (**blue curves**) of jet level quantities, and compare with simulation (histograms)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## E = Eparton-Ejet (GeV) for b quarks

- 10 < Eparton< 60 GeV

- 60 < Eparton< 80 GeV

- 150 < Eparton< 800 GeV

- 120 < Eparton< 150 GeV

- 80 < Eparton< 100 GeV

- 100 < Eparton< 120 GeV

- prediction

- simulation, reconstruction

**Remake these plots to make the axis labels visible.**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Hadronic W and top mass from transfer functions – correct combination

- Hadronic W mass (GeV)

- Hadronic top mass (GeV)

- Chi2 / ndf

- Shift (GeV)

- Chi2 / ndf

- Shift (GeV)

- Histogram from simulated, reconstructed Herwig jets.
**Blue curve** is prediction from transfer function, using parton level Herwig.
- Inset is chi2 as we shift the histogram against the prediction.
- Prediction is systematically high.

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## D0 transfer function tests

- Examples of the transfer functions D0 used for their analysis
- D0 saw a small bias also and was able to show that it didn’t significantly affect the final top mass measurement (took a 0.5 GeV shift)
- Showed that ttbar transfer functions worked with background samples

- ttbar MC events, hadronic top mass

- W+jets MC events, 3 jet invariant mass

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## 1-D Template Method, Run I CDF Method
Stat error 4.1 – 5.0 GeV (scale mean expected Run II error, scale current Run II error) 
Syst error: with no brand new methods (W->qq, Z->bb calib) perhaps 5.0 GeV, with new methods, and reinterpretation of ISR/FSR, perhaps 3.0 GeV
Total error 5.1 – 7.1 GeV
Matrix element method
Stat error 2.6 – 3.2 GeV (scale CDF error by factor of           more stat power)
Syst error – scale template method systematics by 0.73? 			2.2 – 3.7 GeV (or perhaps as large as template method, 5.0 GeV)
Total error 3.4 – 4.9 GeV (or 5.9 GeV) 
The lower statistical error is of short term interest (while statistics are still very limited) 
Always nice to make your statistical error as small as possible
Possibility for smaller systematics intriguing for the medium and long-term. 

- Stat error 4.1 – 5.0 GeV (scale mean expected Run II error, scale current Run II error)
- Syst error: with no brand new methods (W->qq, Z->bb calib) perhaps 5.0 GeV, with new methods, and reinterpretation of ISR/FSR, perhaps 3.0 GeV
- Total error 5.1 – 7.1 GeV
- Matrix element method
- Stat error 2.6 – 3.2 GeV (scale CDF error by factor of           more stat power)
- Syst error – scale template method systematics by 0.73? 			2.2 – 3.7 GeV (or perhaps as large as template method, 5.0 GeV)
- Total error 3.4 – 4.9 GeV (or 5.9 GeV)
- The lower statistical error is of short term interest (while statistics are still very limited)
- Always nice to make your statistical error as small as possible
- Possibility for smaller systematics intriguing for the medium and long-term.

**Expected reach with ~500 pb****-1**

**Why is our run 2 expected error, 6.9 with 180 pb, higher than run 1 – 6.6 with 106 pb? And 108-180 not scaling?**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Summary

- The top mass is interesting in and of itself
- Especially interesting as a precision EW observable
- Constrain SM, predict SM Higgs mass
- Constrain physics beyond the SM
- I’ve participated in a template based mass analysis
- mt =                    (stat)  7.1 (syst) GeV/c2  (108 pb-1)
- Will continue to contribute to important tools like -jet balancing.
- Will pursue a matrix-element based analysis with the prospect of substantially improving the statistical power of the data we collect while also lowering the systematic uncertainty.
- mt = 1xx.x  2.6 (stat)  3.7 (syst) GeV/c2 ?? (500 pb-1)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Backup Slides

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Constrain mH

- mH best fit          GeV, <219 GeV 95% CL

- LEPEWWG/2003-01

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Looking to the Future

- Bob Clare Win 03

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Statistical Error – Run I vs Run II

**Statistical Error – Run I vs Run II**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Initial Luminosity

- Record init lumi 5.2 E 31

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Detailed Event Selection

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Pseudo-experiments

- Take a large number (e.g. 10,000) of samples of x events, drawn from signal and background MC.
- Run through the full machinery.
- Consistency checks, and evaluation of systematics

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Pull distributions

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Chi^2 cut

- 60-70% of background pass
- What percent for data?

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Detailed Jet Systematics

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## -Dependent Corrections, Di-Jet Balancing

- To account for cracks (gaps, or less sensitive regions) in the calorimeter
- Trigger Jet, Probe Jet
- 	B = (Ptprobe- Ptprobe) / 0.5 (Ptprobe+Ptprobe)
- Corrected low energy pion response in calorimeter MC

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Raw Scale, -Jet Balancing

- -Jet Balancing primary check of jet scale
- Run I – Run II Differences partially understood
- Data-MC differences still extant

| cone | Run 1 fb | Run 2 fb | Run2-Run1 KJ |
| --- | --- | --- | --- |
| 0.4 | -32.1±0.3 | -36.2±0.1 | 1.065±0.005 |
| 0.7 | -24.8±0.2 | -28.7±0.1 | 1.055±0.004 |
| 1.0 | -18.9±0.2 | -23.3±0.1 | 1.058±0.003 |

- fb=Pt(jet)/Pt(γ)-1

- fb(run1)+1

- fb(run2)+1

- KJ=

** **Z -> bbar

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## From Fermilab W&C, 4/21/03, 	J. Estrada

**From Fermilab W&C, 4/21/03, ****	****J. Estrada**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## From Fermilab W&C, 4/21/03, 	J. Estrada

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Transfer Function (Estrada)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Probability (Estrada)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## D0 results from data

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Bias due to background fraction

- D0 saw, in MC, a bias as a function of background fraction
- Applied a cut on background probability
- Eliminated 70% of W+jets and 77% of QCD background
- Eliminated 30% of ttbar events.
- 22 events in data, 12  4 background

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## D0 check for bias of method

- 1.014 0.05?
- How big of a correction would this make?

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Signal model systematic

- Vary u, the fraction of events in MC where you cannot (can?) match all 4 jets to partons.
- 1.5 GeV systematic error.

- D0 (2003)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## We have separate transfer functions for light quark and b quark jets.
We use two gaussians, hoping that one gaussian will take the peak and the other (stretched out) gaussian the asymmetric tails.  May be able to find a better parameterization.

- We use two gaussians, hoping that one gaussian will take the peak and the other (stretched out) gaussian the asymmetric tails.  May be able to find a better parameterization.

**Extracting the transfer functions**

- W(Eparton,Ejet) = F(***E** *)
- Parameters depend linearly on parton energy: pi = ai + biEparton
- Normalized so that, for a given Eparton, W is the probability density function for getting a given Ejet.

- 10 total parameters, extracted from an unbinned likelihood fit of ordered (Eparton, Ejet) pairs.

***E** = E**parton** - E**jet*

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Possible that the fits of the transfer function parameterization to the reconstructed MC are just bad.
Difficult to consider goodness of fit globally.
Could take slices in Eparton and compare fit to MC.
The two jets from W decay are correlated
Transfer functions treat them as independent.
Given Eparton, when r is small transfer functions will overestimate Ejet.
			When ris large transfer functions will underestimate. 
We have a hard cutoff at Ejet = 15 GeV, parameterization doesn’t take this into account.
May be able to change normalization to account for this.

- Difficult to consider goodness of fit globally.
- Could take slices in Eparton and compare fit to MC.
- The two jets from W decay are correlated
- Transfer functions treat them as independent.
- Given Eparton, when r is small transfer functions will overestimate Ejet.
- 			When ris large transfer functions will underestimate.
- We have a hard cutoff at Ejet = 15 GeV, parameterization doesn’t take this into account.
- May be able to change normalization to account for this.

**Possible sources of systematic bias**

- When taking integrals for mass, we’re under weighting events with low parton energies – they already passed event selection at jet level.
- May be able to reweight them.
- Or, can start with a more inclusive sample, where the deweighting would be appropriate.

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Hadronic W and top mass from transfer functions – 12 combinations

- Hadronic W mass (GeV)

- Hadronic top mass (GeV)

- Chi2 / ndf

- Shift (GeV)

- Chi2 / ndf

- Shift (GeV)

- Histogram from simulated, reconstructed Herwig jets.
- Blue curve is prediction from transfer function, using parton level Herwig.
- Inset is chi2 as we shift the histogram against the prediction.
**Note that the prediction is systematically high!**

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Test of mass dependence of transfer functions

- Predicted hadronic top mass        vs. simulated, reconstructed top mass (GeV)

- Predicted hadronic W mass         vs. simulated, reconstructed W  mass (GeV)

- Extract transfer functions from 175 GeV Herwig ttbar MC
- Apply them to 165,170,175,180,185 GeV Herwig, compare prediction to simulation

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003

## Systematics

- Run I CDF syst

- Phys. Rev. D {58} 052001 (1998)

- D0 (1998)

- D0 (2003)

- A. Gibson, UC Berkeley Qualifying Exam

- November 21, 2003