Top Mass Measurement
at the Tevatron
Koji Sato (Univ. of Tsukuba)
for CDF and D0 Collaborations

HEP2005 Europhysics Conference
Lisboa, Portugal, June 22, 2005

Top Quark Mass - Introduction• Top mass is a fundamental parameterof the Standard Model.
• Mass measurementsof top and W constrain
the Higgs mass.
Wt

HW

bW

z

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

zmtop ∼ EWSB scale.
→Special role of top?

Tevatron Run IIp – p collisions at√s = 1.96 TeV.
z Peak luminosity>∼ 1.2×1032 cm2 s-1.
-1 of data alreadyz ∼900 pb
acquired by CDF and D0.
z Current analyses use
300 – 400 pb-1.
zz

Direct study on top is
only possible at Tevatron!

CDF and D0 Detectors

Both multi-purpose detector

with: z Tracking in magnetic field.
z Precision tracking with silicon.
z Calorimeters.
CDFz Muon chambers.

Jet σET/ET ~ 84%/√ET (GeV/c2)

D0

Top Quark Production and Decayzz

We use pair creation
events to measure mtop. gTop decays before
hadronization.

τtop=0.4x10-24 s < 1/ΛQCD∼10-23 s.

Br(t→Wb) ∼ 100%.

∼100%q

15% 85%gqbl-t W+ νqtWqbFinal state :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.

L+jets

Event Selection¾ 1 lepton (e/µ)

Dilepton¾ 2lepton (e/µ)¾ ET¾ 2 jets (2 b-jets)¾ No b-tagging¾ ET¾ 4 jets (2 b-jets)¾ Special cut on for 0tag event(CDF:hard cut on ET4thjet)¾ Secondary vertex b-tagging.

Typical CDF event rate and S/B

Nevt (320pb-1)
S:B# Parton-jet assign.

0tag
40
<1:1
12L+jets
1tag
82
3:1
6

Dilepton2tag
16
10:1
2B-tagging helps reject wrong assignments
besides reduces background.

33
2:1
2

Measurement Methods
Template Methodzzzz

Reconstruct event-byevent Mtop.
Describe dependence ofMtop distribution on true
top mass mtop using MC— Templates.
Likelihood fit looks formtop that describes data
Mtop distribution best(template fit).
Less assumptions /robust measurement.

Matrix Element Methodzzzz

Calculate likelihood(probability) for mtop ineach event by Matrix
Element calculation.
Multiply the likelihood
over the candidate
events.
mtop determination by thejoint likelihood maximum.
Better statisticalprecision expected w/
using more info.

All methods in all channels are well validated by a blind sample.

CDF L+jets Template Method (1)Minimize χ2 to reconstruct event-by-event top mass.
Fluctuate particle momenta according to detector resolution.

χ2 = ∑( PTi , fit− PT

σii = l , jets+

( M jj − M W ) 2
ΓWi , meas . 22)+ ∑(UE jj= x, y− UE j

σ j2j , meas . 2)

Mtop asfree param.

2( M jjb − M top ) 2( M lν − M W ) 2 ( M lνb − M top )+++ΓtopΓtopΓW

Constrain masses of 2 W’s.

2 jets from W decay / 2 b-jets.
→12 jet-parton assignments.
 B-tagging helps reject wrong
assignments besides reduces
background.
zj , fitt and t have the same mass.

Subdivide candidate
events into 0, 1, 2 tag.
 Choose assignment
with smallest χ2.
¾

CDF L+jets Template Method (2)Largest uncertainty←Jet Energy Scale (JES)

Better understanding of JES¾Minimize JES uncertainty¾In situ JES calibration using W→jj in tt events.

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

Mtop and hadronic W invariant mass distributions are parametrized
as functions of true top mass and Jet Energy Scale (JES) using
Monte Carlo samples.
Mtop Template
Hadronic W mass TemplateCDF L+jets Template Method (3)Likelihood fit looks for top mass, JES and background fractionthat describes the data Mtop distribution best (template fit).
Mtop distributions :L = 318 pb-1

2tag

1tagT

1tagL0tag

mtop = 173.5 +2.7/-2.6 (stat) ± 3.0 (syst) GeV/c2
JES syst 2.5 compared to3.1 wo/ in situ calibration

CDF L+jets Template Method (4)- Future Projection zz

Total uncertainty of∆mtop ∼ 2 GeV/c2
in the end of CDF
Run II.
Conservative projection
assuming only stat. and JES
will improve.
→ We will do better!
(I will discuss later).

Aimed for luminosityof Tevatron Run II.

CDF L+jets Dynamical Likelihood
Method (1)Calculate likelihood as a function of mtop according toMatrix Element for each event.
Sum over jet-parton combination.
Probability for PT(tt)

2πL(mtop) = ∑ ∫PDFa/ p (za )⋅ PDFb/ p (zb )⋅ f (PT )Flux
4×| Mtt (a,b →x; mtop) | ⋅w(x, y) dx
2Matrix Elementfor signalx(Parton), y(Observable)

Transfer func.
(parton ET→jet ET)

CDF L+jets Dynamical Likelihood
-1
L=318
pb
Method (2)zz

63 candidates with exact 4 jets (≥1 jet b-tagged).
to reduce impact of gluon radiation events
Signal fraction ~ 85.5%.

Mtop = 173.8 +2.6/-2.4(stat) ± 3.2(syst) GeV/c2

D0 L+jets Matrix Element
Method (1)Calculate probability density for mtop.
z Matrix Element for background included.
z In situ calibration of JES.
Hadronic W
Probability density for mtop
mass in ME
zSignal probability for mtop
In situ JES calib.
calculated w/ Matrix Element

Pevt (mtop , JES) = f top ⋅ Psig (y; mtop , JES)
+ (1 − f top ) ⋅ Pbkgd (y; JES)
Signal fraction inmeasurement sample

Background probability
Calculated w/ ME

D0 L+jets Matrix Element
Method (2)z150 candidates w/ exactly 4 jets (w/o b-tagging).

z

Signal fraction ~ 36.4%.

L = 320 pb-1

Mtop = 169.5 ±4.4(stat+JES) +1.7/-1.6(syst) GeV/c2

D0 Dilepton Matrix Weighting
Dilepton→2ν’sMethod (template method) →under-constrained system→need kinematic assumptionzzAssume (x1,x2).
Calculate weight for each event.

W(Mtop) = ∑ PDFa/ p (x1)⋅ PDFb/ p (x2 )CDF assumes(ην1, ην2 ), (φν1, φν2 ), Pz(tt)L = 230 pb-1

solution**× p(El | Mtop)⋅ p(El | Mtop)
Probability to observe El* in top decay• Scan (x1,x2).
• Pick Mtop at maximum weight.
• Template fit (w/ 13 candidates).

mtop = 155 +14/-13 (stat) ± 7 (syst) GeV/c2

CDF Dilepton
Matrix Element Method• Calculate per-event
differential cross section
due to LO Matrix Element.
z
Background ME is also
considered to reduce theimpact of backgroundcontamination.
zCalculates probability vsmtop for each event.

L = 340 pb-1

Mtop = 165.3 ± 6.3 (stat) ± 3.6 (syst) GeV/c2

New

CDF L+jets LXY Method

Boost of b in top rest frame : γb ~ 0.4 mtop/mb

Transverse decay length LXY of B depends on mtop

Use 216 secondary vertex b-tagged jets found in 178 events w/ ≥3 jets.
LXY distribution for signal

to increase efficiency

LXY distribution

L = 318 pb-1

Mtop = 207.8 +27.8/-22.3 (stat) ± 6.5 (syst) GeV/c2
Syst. highly uncorrelated Data/MC <L > scale factor : ±5.1 GeV/c2
XYfrom other measurements. JES : ±0.3 GeV/c2¾¾

Summary of Measurements

Combination of Measurements
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

Future Improvement
Combined Result:zGeV/c2
Result

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

2.9

Basic improvement by ∼1/√L- L∼1fb-1 in next Winter.
- Further improvement on JES
by direct b-jet JES calibration by
Z → bb events. Current b-jet
JES taken same as generic jet +additional uncertainty according toLEP/SLD measurements.

zzz

Sig./Bkgd. Modeling (ISR/FSR/Q2dependence etc.) can be improved byusing our own data.
Measurement in All Hadronicmode is coming soon.
Syst. of LXY method is highly
uncorrelated w/ other analyses.

New ElectroWeak Fit
ElectroWeak fit is under update w/ new combined mtop.
w/ previous Preliminary CDF Run II + D0 Run I Combined :mtop=174.3 ±2.0 (stat) ±2.8 (syst) GeV/c2

mhiggs=98 +52/-36 GeV/c2, mhiggs<206 GeV/c2 (95%)
w/ Tevatron Run I average : 178.0 ± 2.7 ±3.3 GeV/c2 :mhiggs=114 +69/-45 GeV/c2, mhiggs<260 GeV/c2 (95%)

Summary• CDF L+Jets Template Method is the best
single measurement :mtop=173.5 +4.1/-4.0 GeV/c2and will achieve ∆mtop<∼2 GeV/c2 in Run II.
• Preliminary combination of CDF and D0 :mtop=172.7 ± 2.9 GeV/c2 .

(Run I average : 178.0 ± 4.3 GeV/c2)
From previous preliminary world ave. mtop=174.3 ± 3.4 GeV/c222higgs=98 +52/-36 GeV/c , mhiggs<206 GeV/c (95%).

→ m→ This will be updated shortly!
zNext Winter with ∼1fb-1.
- Improvement of dominant uncertainties better than by ∼1/√L.
- D0 Run II dilepton and All Hadronic channel from CDF/D0 will
be included in combined measurement.

Backup

D0 L+jets Template Method
Event-by-event Mtop by χ2 fit.
z Use 69 candidate events with ≥1 b-tagged jet.
z

L = 229 pb-1

mtop = 170.6 ± 4.2 (stat) ± 6.0 (syst) GeV/c2

CDF L+jets Matrix ElementMethod (1)Similar to D0 L+jets ME, but does not include JES inprobability definition.

x ≡ measured quantities, y ≡ parton level
LO qqbar matrix element from Mahlon & Parke
Structure functions, (qi ≡ momentum fraction)
Transfer functions (Map measured quantities
into parton level quantities).

CDF L+jets Matrix ElementMethod (2) L = 318 pb-1

63 candidates with exact 4 jets (≥1 jet b-tagged).

to reduce impact of gluon radiation events

mtop = 172.0 ± 2.6 (stat) ± 3.3 (syst) GeV/c2

Dilepton Template Methods
With 2 ν’s, dilepton decay of tt is anunder-constraint system evensupposing pole mass of W.

How do we measure top mass?

D0 matrix weighting
z CDF ν weighting
z CDF φ of νz CDF P (tt)zzMake an assumption.
z(x1,x2), (ην1, ην2 ), (φν1, φν2 ), Pz(tt), etc., ….
Calculate probability for Mtop.
Scan the assumed variable due to Monte Carlo distributions.
Calculate the most probable Mtop for each event.
Template fit.

CDF Dilepton
Neutrino Weighting Method
Assume pseudo-rapidityof 2 ν’s and Mtop.
z Solve the 4-vector of ν’s
due to (E,p) conservation.
z Calculate the probability ofmeasuring observed ET.
z Scan over assumedvariables.
→ probability of Mtop.
z Pick the most probablevalue of Mtop for the event.
→ Template fit.
z

L = 359 pb-1

mtop = 170.6 +7.1/-6.6 (stat) ± 4.4 (syst) GeV/c2

CDF Dilepton Pz(tt) Method
By assuming Pz of tt system,
momenta of the 6 final
particles can be calculated
from the observables.
z Calculate the invariant massof top.
z Scan over assumedvariables.
→ probability of Mtop.
z Pick the most probablevalue of Mtop for the event.
→ Template fit.
z

L = 340 pb-1

mtop = 170.2 +7.8/-7.2 (stat) ± 3.8 (syst) GeV/c2

CDF Dilepton φ of ν Methodχ =2∑( PTi , fit− PT+ΓW)

σ i2i = l , jets

( M l1ν 1 − M W ) 2i , meas . 2++ ∑(UE jj , fit

ΓW+j , meas . 2)

σ j2

j= x, y( M l 2ν 2 − M W ) 2− UE j

( M l1ν 1b1 − M top ) 2
Γtop+( M l 2ν 2 b2 − M top ) 2
ΓtopAssume (φν1,φν2).
2z Calculate M
top by χ fit.
z Scan over assumedvariables.
→ probability of Mtop.
z Pick the most probablevalue of Mtop for the event.
z→ Template fit.

L = 340 pb-1

mtop = 169.8 +9.2/-9.3 (stat) ± 3.8 (syst) GeV/c2

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

ZbbTrigger :• 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.