# Presentation: 758622

## Top Quark Mass and Widthusing the Template Method

## Why study tops?

-  Decays before hadronizing
-  Helps pin down the mass of the Higgs boson
-  Can constrain new physics
-  Because ... we can

**Why study tops?**

## The Tevatron

**The Tevatron**

**36 bunches of ~10****11**** protons**

**36 bunches of ~10****10**** anti-protons**

**Bunches cross 2.5 million times per second**

**DZero**

**CDF**

**The Tevatron (center of mass energy = 1.96 TeV)**

**Berkeley**

**(2000 miles)**

## CDF

**CDF**

- Muon

- SVX

- COT

- EM cal

- Had cal

** ****SVX: Silicon important for good tracking, necessary for b-tagging**
** ****Leptons: Best-measured objects in events**
** ****COT: drift chamber w/ coverage:**** |********|<1, ********P****T****)/P****T**** ~ 0.15%P****T**
** ****1.4 Tesla superconducting solenoid outside tracking system**
** ****EM cal****: ********E**** / E**** ~ 14% /******
** ****Hadronic calorimeter crucial for difficult jet measurements**
** ****Had cal:**** ********E**** / E**** ~ 80% /******
** ****Muons – scintillator + chamber, coverage out to |********|=1.5**
** ****Need entire detector to get a good measurement of momentum imbalance**

## Tevatron performance at CDF

**Tevatron performance at CDF**

- Top Mass analysis:
- 1.7 fb-1 of data

## Top quark phenomenology

-  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 ...

**Top quark phenomenology**

## Why Mtop is difficult

**Why M****top**** is 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

## Jet Energy Scale

**Jet Energy Scale**

- c = unit of combined nominal CDF JES calibration uncertainty

## Top Quark Mass: Some handles

-  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)

**Top Quark Mass: Some handles**

## Event Selection

**Event Selection**

|  | 2-tag | 1-tag |
| --- | --- | --- |
| B-tags | >=2 | ==1 |
| Jet ET (GeV) (jets 1-3) | > 20 | > 20 |
| Jet ET (GeV) (jet 4) | > 12 | > 20 |
| Jet ET (GeV) (extra jets) | any | < 20 |
| 2 cut | < 9.0 | < 9.0 |
| MET (GeV) | > 20 | > 20 |
| e ET (GeV) or  PT (GeV/c) | > 20 | > 20 |

-  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%**

## Reconstructed mass templates

**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

## In-situ calibration using dijet mass templates

***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)

## How do we use the templates?

**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

## A 1d KDE pictorial tutorial

- Probability

- Mtreco

**A 1d KDE pictorial tutorial**

## Adaptive KDE

**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

## 2d KDE

**2d KDE**

## Backgrounds

**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

|  | 2-tag background fraction | 1-tag background fraction |
| --- | --- | --- |
| W+light flavor+QCD | 0.28 | 0.49 |
| W+heavy flavor | 0.52 | 0.41 |
| Single-top | 0.15 | 0.05 |
| Diboson | 0.05 | 0.05 |

|  | 2-tag | 1-tag |
| --- | --- | --- |
| Expected number of background events | 6.4 1.7 | 36.6  7.1 |
| Observed events (1.7 fb-1) | 89 | 218 |

## Backgrounds (1d)

**Backgrounds (1d)**

## Backgrounds (2d)

**Backgrounds (2d)**

- More correlation between observables for background events

## Likelihood Fit

**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

## Tests of machinery

**Tests of machinery**

- Machinery works and shows no significant bias

## Systematics

**Systematics**

| Systematic Source | Mtop (GeV/c2) |
| --- | --- |
| Residual JES | 0.6 |
| b-jet energy scale | 0.6 |
| Background JES | 0.4 |
| ISR | 0.4 |
| FSR | 0.2 |
| PDFs | 0.2 |
| Generators | 0.3 |
| Background shape | 0.2 |
| QCD modeling | 0.1 |
| MC statistics | 0.1 |
| TOTAL | 1.1 |

- Even with *in situ* calibration, JES systematic dominates

## Measurement!

**Measurement!**

**M****top**** = 171.6 ******** 2.0 GeV/c****2**

## Differential pulls ...

**Differential pulls ...**

- Scale all uncertainties by 4.7%

## Cross-checks

**Cross-checks**

| Measurement | Mtop (GeV/c2) |
| --- | --- |
| Nominal | 171.6  2.0 |
| No background prior constraint | 171.7  2.0 |
| No JES prior constraint | 171.6  2.1 |
| 1-tag only | 167.5  3.1 |
| 2-tag only | 175.0  2.6 |
| Electron-only (and no bkgd constraint) | 170.6  2.9 |
| Muon-only (and no bkgd constraint) | 172.3  3.0 |
| 1d-only fit (no projecting out JES) | 171.7  1.5 |

- All errors uncorrected

- would have 3 GeV JES systematic

## 1d projections

**1d projections**

## Plans for top mass measurement

**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)

## Switching gears ...

**Switching gears ...**

## 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

## 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

## 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

|  | 1-tag | 2-tag |
| --- | --- | --- |
| a priori background estimate | 31.4  7.6 | 5.7  2.2 |
| Observed # evt | 171 | 82 |

## Trusting the Monte Carlo?

- Mw+Mb

- General consensus from theorists: Can trust MC to ~30 GeV

- top = 1.5 GeV

- top = 30 GeV

- top = 50 GeV

## More on the Monte Carlo

- Parton level mean,
- before event selection

- Parton level RMS,
- before event selection

## Reconstructed mass templates

## Likelihood fit output for t 

- How might we use these to set limits? ...

## 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)

- true

- L-fit

- L-fit

- Prob

- 95% of curve

- Data

## 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)

- true

- L-fit

- L-fit

- Prob

- 95% of curve

- Data

## Does setting limits always work?

-  Sometimes with this technique, you don’t set a limit!
-  And what about two-sided limits?

- true

- L-fit

- Data

## 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:

- Width with max prob at x

- x: output of likelihood fit

- i: “true” width being examined

## 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

## Likelihood ratio functions

-  We parameterize the likelihood output so that we have a likelihood ratio and confidence band for arbitrary t

## Does it work?

## 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 ...

## 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

## 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)

## 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

## Smeared likelihood output

- Make new parameterizations, new L ratios all over again after convoluting with systematics

- Systematics included
- Original PDF

## Likelihood fit!

## Likelihood fit!

## Confidence bands with data

- top < 12.7 GeV
- at 95% CL

## What about assuming Mtop = 175?

-  All our MC was generated with Mtop = 175 GeV/c2, but world average is Mtop = 170.9  1.8 GeV/c2
-  (How) does this affect our measurement?

- mtreco

- Prob

- Mass = 175

- Mass = 171

- Mass = 168

- To accommodate a different mass, likelihood fit prefers a larger width - we conservatively do NOT take a systematic

## Plans for top width measurement

-  World’s first direct limit on the top quark width
-  Set an upper limit with 95% confidence only 1 order of magnitude from the SM prediction
-  Still statistics limited
-  Result to be published -  PRL going through internal review process

- top < 12.7 GeV at 95% CL

## Conclusion

- top < 12.7 GeV at 95% CL

- Mtop (GeV/c2) =
- 171.6  2.1 (stat+JES)
-  1.1 (syst)

## Backup

**Backup**

## The top quark

**The top quark**

**The top quark**
-  Discovered only ~13 years ago at the Tevatron
-  Weak isospin partner of the bottom quark
-  Charge = +2/3 (-2/3 for anti-top)

## Boundary cuts

**Boundary cuts**

|  | Mtreco | Wjj | Sig Eff (175/0.0) | Sig Eff 
(150/-2.0) | Sig Eff (190/2.0) |
| --- | --- | --- | --- | --- | --- |
| 1-tag | 110<mtr<350
 | 50<wjj<115 | 99.0% | 98.4% | 99.2% |
| 2-tag | 110<mtr<350 | 30<wjj<120 | 98.6% | 98.6% | 97.9% |

-  KDE doesn’t know about hard/soft cutoffs in the observables
-  Probability “leaks” into unpopulated regions
-  Easiest fix is to explicitly set boundaries and force kernels to stay inside via renormalization inside the boundary
-  Amounts to extra selection cut on mtreco, mjj
-  Efficiency high for signal events passing 2 cut, somewhat worse for background events

## Fit for JES (just a cross-check)

**Fit for JES (just a cross-check)**

## Did we get lucky?

**Did we get lucky?**

- p-value = 23.4%

## Likelihood fit output mean vs t

## On adaptive density estimates

-  The adaptive density estimates have smoothing that varies from MC point to MC point
-  Tails have larger smoothing, core of distribution has less smoothing
-  Intuitively makes some sense, but can lead to trouble - if function changes faster than sqrt(x), can have bizarre nonlocal behavior

- Evaluating estimate for f(x)
- MC point at x1 farther away than MC point at x0
- Point at x1 contributes weight but point at x0 does not! Counterintuitive ...

- x

- x0

- x1

## Clipped adaptive density estimates

-  Try to remove some of the non-locality of the adaptive estimates by not allowing the smoothing to get too large
-  Previously, h could be larger than the entire width of the template!
-  Clip the pilot density estimates: fpilot(xi) -> max[0.1*fpilot(x0), fpilot(xi)]
-  fpilot(x0) is pilot density estimate with maximum value
-  Equivalent to setting hmax= sqrt(10)*hmin
-  Don’t let h get too large!
-  Recommended in one of the very early adaptive density estimate papers

## Other “weird” systematics

## Are we statistics or systematics limited?

- Limited by statistics

## An outline of the steps ahead

-  Run Monte Carlo through an extended maximum likelihood fit just as before in mass analysis
-  Measured top quark width: one number per event

-  Parameterize discrete Monte Carlo to form density functions of reconstructed mass at any arbitrary top quark width

-  Run MC through kinematic fitter to get an estimator of top quark mass
-  Same reconstructed top quark mass as before

**An outline of the steps ahead**

-  Start out with signal and background Monte Carlo

-  Parameterize likelihood output to get expected distribution of measured top quark width for at any arbitrary top quark width
-  Defines the limit-setting machinery

-  Run data through kinematic fitter and likelihood fit
-  Set limit!

## ISR/FSR

- qq -> tt vs 

- In Run I, switch  ISR on/off
-      using PYTHIA, Mtop = 1.3GeV
- In Run II: systematic approach
- ISR/FSR effects are governed
- by DGALP evolution eq.:
- <Pt> of the DY(ll) as a function of Q2

- (2Mt)2

- log(M2)

- +

- -

**Pt(tt) at generator**

## Ensuring continuity

-  Sometimes (due to fluctuations in tails), can have discontinuities in confidence bands. Be conservative and ensure that things stay continuous