CDF実験におけるトップ・クォーク質量の測定
佐藤構二， 戸村友宣， 丸山和純， 金信弘（筑波大学数理物質研究科）
Luc Demortier（Rockefeller University）
他 CDF Collaboration

日本物理学会・秋季大会（2005年）
大阪市立大学, 2005年9月14日

Tevatron Run II
Run II sinceSummer 2001

p – p collisions at √s = 1.96 TeV (1.8 TeV in Run I).
32 cm-2.s-1.
z Peak luminosity record : 1.4x10-1 of collisions in Run II.
z Tevatron has already delivered ∼1.2 fb-1 of data.
z CDF has acquired ~1 fb-1 of data.
z Analysis in this presentation uses 318 pbzz

Direct study on top quark is only possible at Tevatron!

Collider Detector at Fermilab
Multi-purpose detector
Tracking in magnetic field.
¾ Tracking coverage |η|<~1.
¾ Magnetic field = 1.4 T.
z Precision tracking with silicon.
¾ 7 layers of silicon detectors.
z EM and Hadron Calorimeters.
¾ σ /E ~ 14%/√E (EM).
E¾ σ /E ~ 84%/√E (HAD).
Ez Muon chambers.
zTop Quark Mass - Introduction• Top is one of the least well studied elementary
particles (evidence by CDF in 1994 / discovery by
CDF/D0 in 1995).
• Top mass is a fundamental parameter of theStandard Model.
• Mass measurements of top andW constrain the Higgs mass.
WtWHbWzz

Tevatron Run I average :mtop = 178.0 ± 2.7 ±3.0 GeV/c2→ mhiggs <260 GeV/c2 (95%)

CDF Run II goal :-1∆mtop ~ 2 GeV/c2 ( ∫ L dt = 4 − 8 fb )z

mtop ∼ EWSB scale.
→Special role of top?

Top Quark Production and Decayzz

We use pair creation
events (σ~6pb-1) tomeasure mtop.

Top decays before
hadronization.

τtop=0.4x10-24 s < 1/ΛQCD∼10-23 s.

Br(t→Wb) ∼ 100%.

bg15%gq85%q∼100%l+t W+ νqt∼100% Wq’bFinal states : We measure top mass in l+jets channel.
ModeBr.(%)
dilepton 5% Clean but few signal. Two ν’s in final state.
lepton+jets 30% One ν in final state. Manageable bkgd.
all hadronic 44% Large background.
τ+X
21% τ-ID is challenging.

Flow of Mass Measurementz

SignalMCBkgd.
MCCollision
data

Event-by-event
top massParameterize distribution
as a function of true topmass.

Template Fit (Likelihood Fit)zχ2 Fitterz

1 isolated e or µw/ PT>20 GeV, |h|<~1Missing ET >20 GeV
4 jets (JetClu w/ ∆R=0.4)
B-tagging of jets.

Event Selectionz

Look for top massand backgroundfraction that
describes the data
distribution best.

B-Tagging Algorithms• SECVTX– Reconstructs secondary vertex of B-hadron
decay.
– Tags b-jets by displacement of secondry
vertex from primary vertex.

• Jet Probability (JP)– Looks at the impact parameters of tracks inthe jet and calculates probability of the jet tooriginate from the primary vertex.
– Tags b-jet according to the calculated
probability.
– We have optimized JP algorithm for thebest sensitivity to top mass.
εbεlight flavor

SECVTX

28%

0.34%

JP

33%

4.1%

JP has looser tagging condition
with larger b-tagging efficiency.

Subsample Categorization
4 jets in final state →12 parton-to-jet assignments.
B-tagging information helps in correctgreconstruction of signal events!
→ Uncertainty minimum in double tagged
gcandidates.
Use of JP doubles the double tagging efficiency!
Category

2-tag (S+S) 2-tag (S+J)

bl+qttqνW+qWb

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

0-tag

j1-j3

ET>15

ET>15

ET>15

ET>15

ET>21

j4

ET>8

ET>8

ET>15

15>ET>8

ET>21b-tag
condition

2 SECVTX# parton-jetAssignment

226

6

12S/N
(318 pb-1)

17/1

15/1

36/7

11/10

~20/20

1 SECVTX 1 SECVTX 1 SECVTX+ 1 JP

q’0 SECVTX

2-tag samples are much purer and easier to reconstruct!

Extracting Top Mass foreach Candidate Event

Minimize χ2 to reconstruct event-by-event top mass (2-C fit).
Fluctuate particle momenta according to detector resolution.

χ = ∑( PT2i , fit− PTσii = l , jets+

( M jj − M W ) 2
ΓW

2i , meas . 22+ ∑j= x, yj , fit− UE jj , meas . 2)

σ j2

Mtop asfree param.

2( M jjb − M top ) 2( M lν − M W ) 2 ( M lνb − M top )+++222ΓW
Γtop
Γtop

Constrain masses of 2 W’s.
z)

(UE jt and t have the same mass.

2jets from W decay + 2b-jets. →12 jet-parton assignments.

Assignment inconsistent with b-tagging information is rejected.
2¾We choose the assignment with smallest χ as seemingly
correct event reconstruction.
¾z

We reject events with χ2>9, as seemingly background.

Top Mass Templates
Mtop distribution shape isparameterized as a function oftrue top mass using ttbar Monte
Carlo samples with different top
mass assumptions.
Signal Template (1tagT)

Background distribution is
also fit into a function, but
NOT dependent of topmass.
Background Template (1tagT)

Mtop (GeV/c2)

Result of Fit to Data

Likelihood fit looks for top mass that describes the data Mtop
distribution best (template fit).
zz

The background fraction is constrained by estimation for tagged samples.
The background fraction is free in 0 tag sample.

2tag (S+J)
Mtop (GeV/c2)

2tag (S+S)

1tagT

Mtop (GeV/c2)

Mtop (GeV/c2)

1tagL0tag

L = 318 pb-1

Mtop (GeV/c2)

Mtop (GeV/c2)

mtop = 173.0 +2.9/-2.8 (stat) ± 3.3 (syst) GeV/c2
Jet Energy Scale (JES) Uncertainty = ±3.0 GeV/c2

Improved Fitting•••••

In-situ JES calibration w/ W→jj invariant mass ingq
candidate events.
(Mtop, W invariant mass) are parametrized as functionsof (true top mass, JES).
qg
Likelihood fit is performed in(true top mass, JES) plane (2-D fit).
Currently only using SECVTXtagger.
Further improvement can beachieved by optimizing b-tagging
conditions.

bl+tt

ν

W+qWbq’

top mass (GeV/c2)

Even better than Run I World Ave!

L = 318 pb-1

mtop = 173.5 +2.7/-2.6 (stat) ± 3.0 (syst) GeV/c2
JES syst = ±2.5 compared to ±3.0 wo/ in situ calibration

Future Projection
Total uncertainty of 2-D fit
measurement will achieve∆mtop ∼ 2 GeV/c2
in the end of CDF Run II.
zConservative projection
assuming only stat. and JES
will improve.
z We can improve othersyst. uncertainties.
z We will optimize btagging condition for 2-D
fit in the next round.
Currently it only uses
SECVTX.
→ We will do better!
z

Aimed for luminosityof Tevatron Run II.

Summary of Run II Measurements
CDF Run II Top Mass Measurements

Preliminary World Average withCDF/D0, Run I/Run II Measurements
Only best analysis from eachdecay mode, each experiment.

Updated Electroweak Fit
w/ Preliminary CDF + D0, Run I + Run II Combined :mtop=172.7 ±2.9 GeV/c2

mhiggs=91 +45/-32 GeV/c2mhiggs<186 GeV/c2 (95% CL)
w/ Tevatron Run I average : 178.0 ± 4.3 GeV/c2 :mhiggs=114 +69/-45 GeV/c2, mhiggs<260 GeV/c2 (95% CL)

Summary• CDF L+Jets Template w/ JP :mtop=173.0 +4.4/-4.3 GeV/c2 (318 pb-1).
• Template fit with in-situ JES calibration is the best single
measurement and better than Run I World Average :mtop=173.5 +4.1/-4.0 GeV/c2 (318 pb-1).
This analysis will achieve ∆mtop ~ 2 GeV/c2 in the end of Run II.
• Preliminary combination of CDF and D0 (RunI + Run II):
mtop=172.7 ± 2.9 GeV/c2.

(Run I World Average : 178.0 ± 4.3 GeV/c2)→ mhiggs=91 +45/-32 GeV/c2, mhiggs<186 GeV/c2 (95% CL).

(mhiggs<260 GeV/c2 using Run I World Average)z

Next Winter with ∼1fb-1 dataset (×3 statistics).

- Improvement of dominant uncertainties by ∼1/√L.
- D0 Run II Dilepton and All Hadronic channel from CDF/D0 Run II will
be newly included in combined measurement.
- We expect a good improvement in precision of measurement again!

BackupResults of Template
Measurements
Template

Template+ JP

Template+ JES

Summer2004

176.7+6.0-5.4±7.1

177.2+4.9-4.7±6.6−

Summer2005

173.2+2.9-2.8±3.4

173.0+2.9-2.8±3.3

173.5+2.7-2.6±3.0

CDF L+jets Template Group
Intstitutes :Tronto 3
UC Berkeley 2
Chicago 4
JINR 2Fermilab 1
Pisa 1
Tsukuba 4
Rockefeller 1•Template Method measurement was reported by– Fermilab Today "CDF Tops the Top World Average“ (April 21, 2005)– KEK News "質量起源の解明をめざして" (May 19, 2005)

Event Selection• One isolated high PT lepton (e/µ).
– e : ET > 20 GeV, |η|<1.1, shower shape, matching between
calorimeter cluster and track.
µ : PT > 20 GeV, |η|<1.0, matching between muon chamber hits
and track, energy deposit in calorimeter.

•Missing ET > 20 GeV, to ensure there was a ν in the final state.

• 4 Jets reconstructed using JETCLU algorithm with cone size 0.4.
Sample subdivision by b-tagging conditions.
– 1 and 2 tag channels :• More than 3 jets with ET >15 GeV, |η|<2.0.

• The 4th jet with ET >8 GeV, |η|<2.0.

– 0 tag channel :• 4 jets with ET >21 GeV, |η|<2.0.

• We only consider the leading 4 jets as products of ttbar decay, when
≥5 jets are found in a event.
• Two b-tagging algorithms – SECVTX and Jet Probability.

Jet Probability Algorithm (1)Jet Probability Algorithm (2)Uncertainty on Jet Energy
Measurement

Jet Energy Uncertainty
Compared with Run I

Optimization of Jet Probability• Jet Probability algorithm
calculates probability ofthe jet to originate fromthe primary vertex.
• We apply a cut on thecalculated probability forb-tagging.
• We optimized the cut
value for the best
statistical sensitivity to top
quark mass in a Monte
Carlo study.

Statistical error minimum for
top mass measurement!

Expected Number of Events
Comparison of number of events between data andexpectation :mtop =175mtop =178GeV/c2GeV/c2

Fraction of CorrectlyReconstructed Events
In ttbar MC events with mtop=178 GeV/c2.

47%

40%

25%

15%

20%

Fraction of CorrectlyReconstructed Events
In ttbar MC events with mtop=178 GeV/c2. Categorization with SECVTX only.

47%

28%

18%

20%

Definition of Likelihood

Result of Fit to Data

Likelihood fit looks for top mass that describes the data Mtop
distribution best (template fit).
zz

The background fraction is constrained by estimation for tagged samples.
The background fraction is free in 0 tag sample.

2tag (S+J)

2tag (S+S)

Mtop (GeV/c2)

Mtop (GeV/c2)

1tagT
Mtop (GeV/c2)

L = 318 pb-1
1tagL

Mtop (GeV/c2)

0tag
Mtop (GeV/c2)

Measured Top Mass
Breakdown of Systematic Errors-ln(L/Lmax)

Likelihood vs mtop

Top mass (GeV/c2)

Jet Energy Scale (JES) is dominant!

L = 318 pb-1

mtop = 173.0 +2.9/-2.8 (stat) ± 3.3 (syst) GeV/c2

Cross Check• The obtained statistical uncertainty is consistent withexpectation from Monte Carlo study.

Improved Fitting Method• Syst. Uncertainty = ±3.3 GeV/c2 is dominated by JES
uncertainty (±3.0 GeV/c2 ).
• Most JES uncertainties are shared between light flavor
and b-jets. Only 0.6 GeV/c2 additional uncertainty on
mtop due to b-jet specific systematics.
→Likelihood fit with constraint on the dijet mass incandidate events.

bgg

qql+t W+ νqt
Wq’bUse dijet invariant
mass for in-situ
JES calibration.

Templates with JES(Mtop, hadronic W invariant mass) are parametrized asfunctions of (true top mass, JES).
mjj varies significantly
as a function of JES.
z

JES shifted by –3σ,-1σ,…
of generic jet calibration

Event-by-event Mtop is
also largely dependent
on JES.
→ Mtop distribution is
now parameterized
as a function of true
top mass mtop andJES.
z

Hadronic W mass TemplateResult of 2-D Fit (with only SECVTX)

Likelihood fit looks for top mass, JES and background fractionthat describes the data Mtop and mjj distributions best.
Mtop distributions :L = 318 pb-12tag
Mtop (GeV/c2)

1tagT
Mtop (GeV/c2)

1tagL
2

Mtop (GeV/c )0tag
2

Mtop (GeV/c )Top mass (GeV/c2)

mtop = 173.5 +3.7/-3.6 (stat+JES) ± 1.7 (syst) GeV/c2

mtop = 173.5 +2.7/-2.6 (stat) ± 3.0 (syst) GeV/c2
Even better than Run I World Ave!

JES syst 2.5 compared to
3.1 wo/ in situ calibration

Future Projectionz

Total uncertainty of 2-D
fit measurement will be∆mtop ∼ 2 GeV/c2
in the end of CDF Run II.

Conservative projection assuming
only stat. and JES will improve.
z
We can improve other syst.
uncertainties.
z
We will optimize b-tagging
condition for 2-D fit. Currently it
only uses SECVTX.
→ We will do better!

z

Aimed for luminosityof Tevatron Run II.

Summary of Run II
Measurements

Run II Combined Top Mass
Only best analysis from eachdecay mode, each experiment.

Correlation :z

uncorrelatedstat.
¾ fit method¾ in situ JES¾z

100% w/i exp (same period)¾z

100% w/i channel¾z

JES due to calorimeterbkgd. model

100% w/i all
JES due to fragmentation,¾ signal model¾ MC generator¾

New Preliminary World Average
Combination of the best analysis from each decay mode, each experiment.

Correlation :Split into 2 toisolate “in situ”
JES systematics
from other JES

mtop=172.7 ±1.7 (stat) ±2.4 (syst) GeV/c2

Future ImprovementszCombined Result:
GeV/c2Result

172.7

Stat.

1.7

JES

2.0

Sig. Model

0.9

Bkgd. Model

0.9

Multi-Interaction

0.3

Fit Method

0.3

MC Generator

0.2

Total Syst.

2.4

Total Error

2.9zzzz

Syst. already dominates theuncertainty!
Basic improvement by ∼1/√L- L∼1fb-1 in next Winter.
- In-situ JES calibration is a
powerful tool. It can be
introduced to other L+jetsanalyses.
Sig./Bkgd. Modeling (ISR/FSR/Q2
dependence etc.) can be improved byusing our own data.
D0 Run II Dilepton
measurement is coming soon.
Measurements in All Hadronicmode (CDF/D0) are underdevelopment.

Zbb
Trigger :• 2 SVT track + 2
10GeV clusters.
Offline Cuts :• N==2 jets w/
ET>20GeV, |η|<1.5(JetClu cone 0.7).
• Both jets are
required to havesecondary vertex tag.
z
∆φ(j1,j2)>3.0.
• ET3rd-jet<10GeV.