Top Quark Mass Measurements at CDF Run II

CDF

Top Quark Mass Measurementsat CDF Run II

Top Quark Mass Measurementsat CDF Run II

Kohei YoritaUniversity of Chicago

For the CDF Collaboration

SLAC

June 7th 2005

bscdu

t

Brand New Results from CDF !Brand New Results from CDF !Run I World Average (hep-ex/0404010)

Mtop (world) = 178.0 GeV/c2+4.34.3

In the Lepton+Jets channel with 318 pb-1 data,　 (single meas.)

Current CDFOfficial Value !(Template Method)

Mtop (CDF) = 173.5 GeV/c2+4.14.0

Mtop (X-check) = 173.8 GeV/c2 (Very New !)+4.34.1

As a cross check, the same dataset and lepton+jets, but using Matrix Element MethodMatrix Element Method (DLM)

June 7th , 2005 Kohei Yorita , U of Chicago , SLAC Seminar 2/43

Run II

Better than Run I w

orld average

OutlineOutline

e bd

uμ

1. The Tevatron & CDF

2. Top Quark Physics3. Why Top Mass ?4. Top Quark Production and Decay

5. Key Points of the Measurements6. Top Quark Mass Measurements (L+jets) - Template Technique : (1D and 2D) - Dynamical Likelihood Method (DLM)

7. Summary

The World’s BestThe World’s BestMeasurementMeasurementThe World’s BestThe World’s BestMeasurementMeasurement

Dr. E. ParticleQ: How many particles in me?

The TeVatronThe TeVatron

The Tevatron is a proton-antiproton collider with 980 GeV/beam

RunI)(1.8TeV RunII in1.96TeV s

2 km

Record > 1.2 1032 !

The World’s only Top Factory !


Delivered luminosity : > 1fb-1 !!!(Run I : 110 pb-1)

Collider Detector at Fermilab (CDF)Collider Detector at Fermilab (CDF)

= 1.0= 1.0

= 2.8= 2.8

= 2.0= 2.0


> Tracking System

- New silicon tracker

b jet tagging !!!

- New central drift chamber

> New time of flight detector

> New Forward Calorimeter

- Jet (||<2.0) for top physics

> Extended muon coverage

> New Electronics, DAQ, Trigger ))2log(tan(

polar angle

Run II Upgrades

EEE /%14/ EEE /%80/

EM :

HAD :

Plug Calorimeter

Silicon Detector

COT

Some CDF PicturesSome CDF Pictures

Muon Chamber

Move In to Collision hall ! (Installation…)


Assembly hall at CDF

Sep. 2004shutdown

CDF Data TakingCDF Data Taking

90%

80%

CDF : Data taking efficiency is stably ~80-90% ! Now CDF has a total integratedluminosity of 800 pb-1 on tape!!!

Analyses for today’s talkbased on 318 pb-1

(Physics quality data until Sep. 2004)


Top Quark Production and DecayTop Quark Production and Decay

15% 85%

~100%

• Dilepton (e,μ) BR=5%

• Lepton (e, μ) +jets BR=30%

• All jets BR=44%

• + X BR=21%

• Dilepton (e,μ) BR=5%

• Lepton (e, μ) +jets BR=30%

• All jets BR=44%

• + X BR=21%

Final states : (depend on W decay)

* Higher statistics than dilepton * Lower background than All jets

Identify “leptonic W” by selecting (1) Isolated lepton (Et>20 GeV)(2) Missing Et > 20 GeV

Production Cross Section

qq , gg fractions reversed at LHC

Tree level Diagram

pb1.6)178( GeVmtpb7.6)175( GeVmt

pb7.5)180( GeVmt~30 % increase from Run I


Golden Channel

We have detected Top events!!! We have detected Top events!!!


Muon + Met + 4jets (2 bjets) candidate Counting Method (lepton+jets)

Control region Signal region

Top Quark PhysicsTop Quark Physics Interesting physics in the top sector

– Production Mechanism

– Direct contact with Vtb

– Decay into W+b before hadronization ( =410-25 s)

Unique opportunity to probe

bare quark properties.

(top spin(/correlation)? charge?)

Top quark mass at EWSB scale what does this tell us?

– Is top the gateway to new physics?


Decay modes

Branching ratios

CKM matrix

Rare decaysFCNC e.t.c.

Non-SM decays

Production X section

Resonance production

Production kinematics

Top Spin polarization

Top Quark MassW helicity (V-A?)

Why is Top Mass Interesting?Why is Top Mass Interesting?

MW ( Mtop2, ln(MH) )

(2) Special Relation to Higgs mass, together with W boson mass.

(1) Fundamental Standard Model parameter.

RunII Goal : M~ 2 GeV at CDF !

(4) By using the top mass as a constraint, ttbar full event reconstruction can be possible. This is very powerful for a test of SM (spin correlation, W helicity 　 e.t.c), or search for non-SM physics ! (tt resonance e.t.c.)

12

v

my tt

(3) Top quark is heavy (~ 175 GeV = Mb-quark35) Yukawa coupling ~ 1. * Near the EWSB scale. * If we can measure strength of this coupling (i.e.ttH), a test of the Higgs sector in the SM can be possible.


Top Mass Run I ReviewTop Mass Run I Review

New World Average (2004) Mt = 178.0 4.3 GeV (2.73.3) hep-ex/0404010

Old World Average (1999)

New DØ l+j measurement, (Nature 429, 638-642 (2004))

Standard Model Higgs Mass:

Most probable: 96 GeV 126 GeV Upper limit(95% CL):219 GeV 280 GeV

73 48


Mt = 174.3 5.1 GeV (3.24.0) (Fermilab-TM-2084)

Key Points of The AnalysisKey Points of The Analysis

How ? : SECVTX b-tagging (excellent silicon detector !)B hadrons are long-lived.

Identify by Vertex of displaced tracksfrom primary.

Backgrounds and Combinations (jet-parton assignments)

- b jet taggingb jet tagging is very important.

Tight Tagger 40% / jet 60% / tt eventMistag : ~ 0.5% / jet

Background Reduction - Background processes are mostly non-heavy flavor (W+jets, QCD) Reduce Combinatorics (Ambiguity to form top and anti-top) 2 b tag : 2 jet-parton permutations 1 b tag : 6 jet-parton permutations 0 b tag : 12 ways to assign 4jets to 4 partons

2 due to -pz ambiguity4/12/24 for 2/1/0 tag


Key : Jet Energy ScaleKey : Jet Energy Scale

All Jets are formed by dR=0.4 cone-clustering algorithm.

Calibrate forward calorimeter to central calorimeter. - uniform response in eta correction

Correction for non-linearity and energy loss in un-instrumental region.

Correction for leakages outside the cone.

Non-uniform response

Diff. resp.of /i+-Non-linearity

Shower, frag.

~ Precision on the determination of jet energies is necessary for Mt measurements ~

(1) “Relative to Central”

(2) “Absolute Scale” (to Hadron)

(3) “Out of Cone” (to Parton)


(4) Other : Very Small Corrections - Multiple Interaction (minbias, func. of Nvertex) - Underlying Event (minbias, nVtx = 0)

OOCUEAbsMIelrCalorimete

jetParton CCCCCPP R

Jet Energy UncertaintyJet Energy Uncertainty

Run II 2005

Run II 2004 Run I

Central region

Total fractional uncertainty on jet PtJet Energy Systematic Run II 2005 : O(~3%)Run II 2004 : O(~6%)Now, better than Run I !

- Better understanding of Calorimeter tuning.

> In the top quark mass measurements, there are lots of constraints available to improve precision. e.g. ) W Mass Constraint


Top Quark Mass Measurements~ Lepton+jets ~

1D Template Method2D Template Method

Dynamical Likelihood Method(Matrix Element)

Top Quark Mass Measurements~ Lepton+jets ~


Dynamical Likelihood Method(Matrix Element)


(2) Additional selection cut on resulting2(<9)

Top mass isfree parameter

(1) For each event, top mass is extracted by minimizing2 defined as,

(3) Build templates of Mt with smallest 2 from MC - Signal with different top mass - Each background source

(5) Fit to the data using unbinned likelihood.

(4) Parameterization : Build signal p.d.f. as a function of generated mass.

- Jets resolution term- Unclustered Energy term- W mass constraint and Top mass term


1D Template : Subdivision1D Template : Subdivision Use 4 categories of events

with different background content and reconstructed mass shape.

2-tag 1-tag(T) 1-tag(L) 0-tag

j1-j3 ET>15 ET>15 ET>15 ET>21

j4 ET>8 ET>15 15>ET>8 ET>21

S:B 18:1 4:1 1:1 1:1 Subdivision improves statistical uncertainty. Subdivision does not improve systematic uncertainty.

Expected Fraction of Sensitivity

2-tag 1-tag(T) 1-tag(L)

0-tag

35%

27

45%

32

9%

31

11%

37

0tag1tag,3.5j1tag,4j2tag LLLLL


Template RMS (GeV)

1D Template : Data Fit1D Template : Data FitCurves: expected signal andbackground from global best fit

Mtop (1D)= 173.2 (stat.) 3.4 (syst.) GeV/c2 +2.92.8


16 ev 57 ev

25 ev 40 ev

1D Template : Systematics1D Template : Systematics

Jet Systematic Source Uncertainty(GeV/c2)

Relative to Central 0.6

Hadronic energy (Absolute Scale) 2.2

Parton energy (Out-of-Cone) 2.1

Total 3.1

Systematic Source Uncertainty(GeV/c2)

Jet Energy Scale 3.1

B-jet energy 0.6

Initial State Radiation 0.4

Final State Radiation 0.4

Parton distribution functions 0.4

Generators 0.3

Background Shape 1.0

MC statistics 0.4

B-tagging 0.2

Total 3.4

CDF Run II Preliminary (318 pb-1) This was ~ 6.2 GeV before (2004)


Our measurement is systematic dominant !> Statistical : <3.0 GeV> Jet Energy Scale : 3.1 GeV> Syst. Total : 3.4 GeV

Big Improvement since an year ago !

World’s Best Measurement !World’s Best Measurement !

Datasets and event selection are exactly the same as 1D template.

P1P1(mrecotop;mtop,JES) and P2P2(mreco

jj;mtop,JES)

2D Template Technique M top + JES Simultaneous Fit

using top mass and W mass templates

2D Template Technique M top + JES Simultaneous Fit

using top mass and W mass templates

Further Improvements of Jet Energy Scale(JES) Uncertainty

CDF’s improved Jet Energy Scale uncertainty almost half since an year ago.

1D Template : ~ 4.4 GeV total uncertainty1D Template : ~ 4.4 GeV total uncertainty

Run II 2005

Run II 2004 Run I

Central region

2D Template Why ? and What?

2D Template Why ? and What? Strong Motivation again.. :

- Current world average uncertainty (±4.3GeV/c2):

– 2.6 GeV/c2 from JES– 2.7 GeV/c2 from stat.

Jets are very hard to calibrate becausethere is no nice resonance.. Obviously, in the future, even now, this will give a limitation of precision!

Fractional error on jet Pt

Solution : Use W jj Mass !

1. Identify jets coming from W

2. Reconstruct their invariant mass mjj

3. mjj strongly dependent on JES

4. MW uncertainty is completely negligible (< 34 MeV)

5. mjj mostly independent of Mtop

JES from W jj is mostly statistical

mjj(W)

e

jetjet


Scale with Luminosity !!!!!

How to make Mjj template ?How to make Mjj template ? Which jets form W?• All Non-btagged jets pairs are take

n into account equally.• 1/3/6 mjj per event with 2/1/0 b-tag

Measuring JES• Make Mjj templates by varying JES 1 defined by CDF jet group • Fit data with Wjj to measure JES!


JES vs Mtop vs Mjj CorrelationsJES vs Mtop vs Mjj CorrelationsPDFs ( Mjj | Mtop, JES=0):2tag

Mjj

Mto

p

Mtop strongly depends on JESMjj independent of Mtop

So Mtop and JES are simultaneously determined in likelihood fit using shape comparisons of Mt and Mjj template to take into account these correlations.

JEStagtagLtagTtagtotal

JES

STD

LLLLLL

JESJESJES

0112

2

2

2

2

JES12

)0(

2

)(lnL-

A Gaussian constraint on JES

from the standard calibration is

included in likelihood as a priori

(01)


How about b jets?How about b jets?

b Jet Systematic Source Uncertainty(GeV/c2)

HQ Fragmentation

(Peterson b=25-6010-4)

0.4

Semileptonic decay 0.4

B-jets colour flow 0.3

Total 0.6

Most b-jets energy scale

can be set using W→jj

Mtop measurement is sensitive to energy scale of b jets.

(W mass is constrained.)

- But studies show most uncertainty is shared by light quark and b jets.

- Only 0.6 GeV/c2 additional

uncertainty on Mtop due to

b-jet-specific systematics.


Top Mass Result with 318 pb-1Top Mass Result with 318 pb-1

Mtop (2D)= 173.5 (stat) 2.5(JES) 1.7(syst.) GeV/c2

+2.72.6

c.f. 1D JES : 3.1 GeV

Black curvefrom globalbest fit.


16 ev 57 ev

25 ev 40 ev

JES Results with 318 pb-1JES Results with 318 pb-1

Agreement data-MC JES is

quite good. Combined W jj and prior

JES yield 20% improvement

78.080.010.0

JES

Reconstructed dijet (W) mass:

Black curvefrom globalbest fit.


Statistical uncertaintyStatistical uncertainty

We are a bit on the lucky side, but reasonable. (~9.2%) June 7th , 2005 Kohei Yorita , U of Chicago , SLAC Seminar 28/43

Higgs Mass (SM global fit)using only 2D Template Results

Higgs Mass (SM global fit)using only 2D Template Results

Only based on this measurement, SM global fit returned,

25435 /94 cGeVM Higgs

(upper limit (95%CL) 208 GeV/c2)

C.f) Run I world average constraint:273

48 /126 cGeVM Higgs

Mtop (CDF) = 173.5 GeV/c2+4.1

4.0

150


Very preliminary Projection and Fit result.

The Future ProjectionsThe Future Projections Traditional calibrations of JE

S based on dijet and/or gamma-jet balance are expected to be limited in the future.

Using W jj : JES uncertainty scales with statistics.

So we can reach JES uncert. below 1 GeV/c2 in Run II

Reaching a total top mass uncertainty of 2 GeV/c2 can be possible in Run II

Now !


Other Technique?Other Technique?

Mtop = 173.0 (stat.) 3.3 (syst.)GeV/c22.92.8

> Another category : - 1D template (Secvtx + Jet Probability Algorithm for b tagging)

= 173.0 + 4.4 – 4.3 GeV All lepton+jets results are obtained from template technique. and consistent each other. (173.5(2D), 173.2(1D), 173.0(1D+JP))

What else ? Matrix Element Technique should be a good cross check and even can aim to have the best result. Dynamical Likelihood Method (DLM) !

Brief summary so far…… > Results from 1D and 2D template are presented.


Dynamical Likelihood Method Introduction

Dynamical Likelihood Method Introduction


- Originally proposed in 1988 by K. Kondo.(J.Phys. Soc. 57, 4126)

The Method :- Basic idea is to use matrix elements convoluted likelihood.

The year Leon M. Lederman won the Nobel Prize !

For the neutrino beam methodand the demonstration of the

doublet structure of the leptonsthough the discovery of the

muon neutrino.

(1) Exactly 4 tight jets : Et > 15 GeV, |eta| < 2.0 do not use 4 more jets and loose 4th jet (Et > 8)(2) At least one SVX b-tagged jet do not use 0 b tag events. (to increase S/B.)

Event Selection : (Not the same as template !!!)

> DLM : 63 events> Template : 138 events

Likelihood Definition in DLMLikelihood Definition in DLM

xyx dwMPtfzzFFlux

MLt sI I

batopi ),(||)(),(

2)( 2

4

For i-th event, likelihood is defined as,

M : Matrix element of tt process,

F : Parton distribution function for (za,zb) and f : Pt of tt system

w : Transfer function, x ; partons y ; observables

)(2)( top

event

itop MLlnM

It : Jet-parton, Is : neutrino Pz (Sw=(l+)2)

222 ||)(|||| decrprod MsMM


All possible combinatory is taken into account.

Analysis procedure(1) At first, all events are considered as signal ttbar.(2) “Signal Likelihood” is calculated for each event.(3) Take joint likelihood of all events.(4) Bias correction by using “mapping function”. Mapping function : function of bkg fraction.

- 12/4 sum for 1/2 b tag in total.

DLM : Demonstration!DLM : Demonstration!

L

Mtop (GeV)165 185 10 events likelihood distributions: L(M)

For ppt user!


Using SM-Matrix Element is too much assumption ?

Using SM-Matrix Element is too much assumption ?

(1) CDF has probed the properties of top quark but - NO significant discrepancy has been observed. (Discovery mode Detailed study)(2) In the Standard Model, no fundamental/direct prediction of Mt.(3) Too much rely on SM ? - All Monte Carlo Events are generated based on SM.

(4) Only considering Leading-Order ME. How about NLO? - At first order, selecting events with exactly 4 jets minimizes it. Need careful study (related to ISR/FSR, PDF uncertainty)

(5) BIG ADVANTAGE : Using maximal event information. The most effective term is “propagator” (not too much assumption here!!!)

< Apparently, it is worth pursuing !!!>


How likelihood dist. looks like?How likelihood dist. looks like?

Signal example: - log(likelihood)

Blue : all added upRed : right comb.Black : wrong comb.

Blue : all added upBlack : each comb.

Peak around 175 GeVLikelihood tends to be higher inlower mass region.

Range[155-195]GeV

Bkg example: - log(likelihood)

25 events example for sig and bkg using generator level input


Background Effect/CorrectionBackground Effect/Correction

Source W+4jets (318pb-1)

Mistag 5.97 ± 0.80

Wbb 1.87 ± 0.83

Wcc 0.99 ± 0.46

Wc 0.60 ± 0.25

Single top 0.41 ± 0.09

Diboson 0.39 ± 0.08

QCD 2.85 ± 1.33

Bkg Total 13.07 ± 2.19

Data 63 (e:39, mu:24)

Each Background Effect ~ 2 GeV shift at 21 %.


Mapping Function Slope changes stably.

slope

Bkg : 21%

* From 1000 pseudo expt. for each point

Linearly / Pull checkLinearly / Pull check

1.05 biasSlope of 1

No bias for central value. 5% correction for the statistical uncertainty. - Assumption is only held for tt events. (4p-4j matched.)

- Not held if ISR/FSR gluon enters leading 4jets. - Not held for dilepton or backgrounds…..


DLM Results (318 pb-1)DLM Results (318 pb-1)Correction at background fraction of 21%.

Mtop (DLM)= 173.8 (stat.) 3.3 (syst.) GeV/c2 +2.72.5


DLM Stat. and SystematicsDLM Stat. and Systematics

Sources Mtop(GeV/c2)

Jet Energy 3.0

Transfer Function 0.2

ISR 0.4

FSR 0.5

PDF 0.5

Generator 0.3

bkg fraction (6.7%) 0.6

bkg Modeling 0.6

b tagging 0.2

b jet energy 0.6

TotalTotal 3.3 3.3

Data/MC comparison ofData/MC comparison ofStatistical uncertaintyStatistical uncertainty

Systematic uncertaintySystematic uncertainty


10% prob.MC < Data

Data/MC ComparisonsData/MC Comparisons

195

155)( dMMLL ii

ev

For i-th event,

Event likelihood Event-by-event Maximum Likelihood Mass

Note : Last bin includes over flow.


Improvement for JES uncertainty ?~ Hadronic W(jj) Mass ~

Improvement for JES uncertainty ?~ Hadronic W(jj) Mass ~

Remove W Mass constraintfrom likelihood. Instead, topMass is constrained.Then pick up 2 jets W massAt maximum likelihood point.

(1) We have a confidence to use W Mass as a constraint !

(2) In principle, DLM can use this to reduce jet energy uncertainty like 2D Template!!! - Future improvement here!!!


SummarySummary> Tevatron is performing very well. Delivered luminosity more than1 fb-1

CDF recorded >800 pb-1 data

> 2D template (Mt+JES) provided the best measurements in the world.

-- Lots of work to reduce systematics, - especially JES!!!

> New techniques are developed. DLM and template results are consistent.> Other technique/channel (dilepton/all jets) are coming very soon!

> Plan to publish these two results by the endof this summer.(PRDs)

> Combination on going..

Will reach goal of measuring mt to ~ 2 GeV in Run II ! Getting Close !!!


BackupBackup

JES : Relative CorrectionJES : Relative CorrectionThe Central Calorimeters( = 0.2-0.6) are better calibrated/understood.Correction factor is a function of Pt and extracted from dijet balance. (check -jet balance)

Uncertainty : ~ 1% level(depends on region and Pt)- estimated by varying the selection requiremens and fitting procedure.

JES : Absolute Scale Correction(to hadron level)

JES : Absolute Scale Correction(to hadron level)

Uncertainty : 2 ~ 3% level (strong dependency on Pt)- Single particle E/P, fragmentation. - Smaller error : MC/data in tower boundaries, cal. calibration with time.

Correction for non-linearly and un-instrumental region, based on MC by using single particles (pion,protons,neutrons ). We tuned MC much better and map to hadron level from cal. level.

JES : Out of Cone Correction(to parton level)

JES : Out of Cone Correction(to parton level)

Correction for energy leakage outside the cone.(0.4 for top physics)0.4 is small compared to typical QCD events since tt events are crowded butLose >10% energy for jets with Et<20 GeV.

Uncertainty : 2 ~ 8% level (strongly depends on Pt)- Difference between data and MC is taken into account. (We can compare energy sum outside the cone of jets.)

Results on Blind SampleResults on Blind Sample

* Some are Pythia, Others are Herwig. (P - H Syst. = - 0.3 GeV)

We observed “NO BIAS”.

5 blinds samples generatedby CDF Top Mass group

0.3 GeV is stat. only.

All is w/I 1 standard deviation.

DLM measurements of nonSM model (tt resonance X(700))

DLM measurements of nonSM model (tt resonance X(700))

Sample : X(700) to tt (M=175 GeV), top decay follows SM

Reconstructed mass from 30 events P.E. is 176.8 0.4GeV. If X(700) is 100% in the sample, we see 2 GeV bias.

Additional Checks on DLMAdditional Checks on DLM

-4.1 GeV

16 events overlap between this round and before (162 pb-1)

Transfer function w(x,y)Transfer function w(x,y)

definition Sample Other

T.F. All Mass

130-230, 5 GeV step averaged

1/Nx weight

Comment Slicing “Et” of jets into 10bins and eta into 3 bins

To minimize top mass dependence of TF.. 130-230 is wide enough for search range.

Avoid double counting

)(

)()(

PartonE

JetEPartonE

T

TT

Parton Energy is inferred by random generation along the T.F.

Et dep.Eta dep.

Details on Systematic UncertaintyDetails on Systematic Uncertainty

Systematic TMT 2-D TMT 1-D

Mtop (GeV)Mtop (GeV) JES()

JES (2.5 ) - 3.1

b-jet modeling 0.6 0.25 0.6

ISR 0.4 0.08 0.4

FSR 0.6 0.06 0.4

PDFs 0.3 0.04 0.4

Generators 0.2 0.15 0.3

Bkgd shape 1.1 0.17 1.0

b-tagging 0.1 0.01 0.2

MC statistics 0.3 0.04 0.4

Method 0.5 0.02 -

TOTAL 1.7 0.36 3.4 = 3.1 1.4

Details on Systematics : ISR/FSRDetails on Systematics : ISR/FSR In Run I, switch ISR on/off

using PYTHIA, dM top = 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)

ISR syst: 0.4 GeV

Pt(tt) at generator

μ+

μ-

Details on Systematics : b jetDetails on Systematics : b jet

Documents

Top Quark Mass Measurements at CDF Run II