Measurements of S and the QCD Colour Factors using Four-Jet Observables from Hadronic Z Decays

18-3-2002 Sílvia Bravo i Gallart 1

Measurements of Measurements of SS and and

the QCD Colour Factors the QCD Colour Factors using Four-Jet using Four-Jet

Observables from Observables from Hadronic Z DecaysHadronic Z Decays

Sílvia Bravo i GallartIFAE, Barcelona

Moriond-QCD, 18 March 2002


OutlineOutline

Motivation for the Studies

Theoretical Framework

Analysis description

Results on measurements of S from R4

Results on the combined measurement of

S and the Colour Factors

Conclusions


MotivationMotivation


QCD =(?) theory for the description of the strong interaction of quarks and gluons

LEP Experiments, as ALEPH, provided good conditions for QCD studies

High statistics

Clean environment

High energy

Measurements of the strong coupling constant alone and together with the QCD colour factors from 4-jet observables

1st S measurement

from a 4-jet observable

Stringent test of QCD

New NLO calculations for 4-jet observables allowed us to perform


Theoretical FrameworkTheoretical Framework

Predictions for Four-Jet ObservablesPredictions for Four-Jet Observables


QCD shows its full gauge structure only in order S

2

R4 + 4-jet angular correlations a good set

of observables to perform a stringent

test of QCD


The 4-jet RateThe 4-jet Rate (resummation of large logarithms exists)

F

R

F

A

C

Ty

C

Cx

2yy4

xy4

2xx4

y4

x4

044

y4

x4

044

yCxyCxCyCxCCC

yBxBBB

cutcutcuttot

yByCxbyBR 443

0424

4 23 ln 21

2

Fs C

ZMx

depend linearly and quadratically on the Colour Factor Ratios

Where the Born and NLO functions

n,m

cutnm

S ylnwith


The 4-jet angular correlationsThe 4-jet angular correlations

,

:jets energylowest wo

,

:ReiterNachtmann Modified

, , 2

1

:WillrodtzSchierholtrneroK

,

:ZerwasBengtsson

4334

4321*

42313241

4321

ppCosαCos

T

ppppCosCos

ppppppppCosCos

ppppCosCos

NR

KSW

BZ

ACxbABdA

d4

304

2 ln 21 1

4321 EEEE


The Analysis DescriptionThe Analysis Description


Two different analyses but same method

S from R4Simultaneously S and the colour factors.

Hadronic Selection on 1994-95 ALEPH Data

Efficiency: 90.2% Non-hadronic bckg ~0.3%

Durham-E clustering algorithm, , ycut=0.008 for 4-jet events

Binned distributions are constructed from data (with correlations)• R4 is measured at 60 points -12.0 ln(ycut) -0.2• Each angular observable has 20 bins• NLO prediction from DEBRECEN (resummation for R4, normalized distributions for the angles).


The theoretical distributions are then corrected to HL

After correction for detector effects...

the following 2 is minimized

jiji 12 DLjjj ThDat

Where the Nentries in the DL vectors (i.e. the fit range) is determined by a cut in the total correction to each bin – 10% –.

Finally the sources of systematic uncertainty are studied:Corrections, fit range, selection cuts, etc.


Hadronization Hadronization CorrectionsCorrections

Four-jet rate

cut

PLcut

HL

cuthad

yR

yRyC

4

4

PL after showering and HL & PL dist. obtained from std PYTHIA

bin

PLbin

HL

binhad

iCosX

iCosXiC

Angular correlations

PL before the showering and HL & PL dist. obtained from 4-parton ME option in PYTHIA

Correction for hadronization effects & missing higher orders

Detector Detector CorrectionsCorrections

bincut

HLbincut

DL

bincut iyX

iyXiyC

4

4det For all observables


Total CorrectionsTotal Corrections

haddettot CCC


Measurements of the Measurements of the Strong Coupling Constant Strong Coupling Constant

from the Four-Jet Ratefrom the Four-Jet Rate


Method I : xMethod I : x fixed to fixed to 11

Method II : xMethod II : x also also fittedfitted

Method III : xMethod III : x fixed to x fixed to xoptopt

Standard in Aleph: •fit and all systematics with x=1• scale uncertainty 0.5 < x< 2.

The strong coupling constant and the scale are fitted together for all systematics

Experimentally optimized scale Method. The strong coupling constant and the scale are fitted. The fitted scale is called the exp.opt.scale and is fixed to this value for all systematics. The scale uncertainty 0.5xopt < x <2 xopt


Method I : xMethod I : x fixed to 1 fixed to 1

Method II : xMethod II : x also fitted also fitted

Method III : xMethod III : x fixed to x fixed to xoptopt

0001.01170.0 ZS M

05.073.0

0002.01175.0

x

M ZS

73.0

0001.01175.0

x

M ZS


5627

Ndof

2.

484

Ndof

2.


Systematic StudiesFit RangeSelection CriteriaHadronization CorrectionsDetector CorrectionsTheoretical Predictions

Other Checks PerformedHadronization CorrectionsScale dependenceFits over different ranges


Method I : Method I : xx fixed to 1 fixed to 1

S = 0.1170 0.0001(stat) 0.0014(sys)

If systematic error added quadratically then 0.0022 for S

Method II : Method II : xx also fitted also fittedS = 0.1175 0.0002(stat) 0.0013(sys)


Method III : Method III : xx fixed to x fixed to xoptopt

S = 0.1175 0.0001(stat) 0.0007(sys)



S = 0.1170 0.0001(stat) 0.0014(sys)

S = 0.1203 0.0001(stat) 0.0068(sys)

0.0022 quad.

ALEPH Preliminary Resummed 3-jet Event Shapes

DELPHI Preliminary NLO 4-jet rate, EOS Method

Durham: S = 0.1178 0.0005(stat) 0.0029(sys)Cambridge: S = 0.1203 0.0005(stat)

0.0021(sys)

Results in good agreement with previous ALEPH results, as well as with a similar analysis by

DELPHI

Theoretical uncertainty dominates the total error


Simultaneous Simultaneous Measurement of the Measurement of the

Strong Coupling Constant Strong Coupling Constant and the QCD Colour and the QCD Colour

FactorsFactors


The simultaneous measurement of the Strong Coupling Constant and the QCD Colour Factors has been performed using resummed predictions for R4 and normalized NLO for the 4-jet angular observables.Method as described previously. x was fixed to 1.

020370

060172

0003002550

..y

..x

..M Z

070351

140932

00601190

..C

..C

..M

F

A

ZS

8450

4500

.

.

xy

y

QCD expected: CA=3 & CF=4/3


Systematic StudiesFit RangeSelection Criteria & Detector Corrections = ExperimentalHadronization CorrectionsTheoretical Predictions

Other Checks PerformedHadronization CorrectionsTwo- and Three-parton BackgroundsSensitivity to each observable

Dependence on the ycut


Final results on the combined measurement

)(07.0)(02.037.0

)(09.0)(06.017.2

)(0014.0)(0003.00255.0

sysstaty

sysstatx

sysstatM Z

)(26.0)(07.035.1

)(58.0)(14.093.2

)(026.0)(006.0119.0

sysstatC

sysstatC

sysstatM

F

A

ZS

OPAL Published Results: S=0.120±0.011(stat)±0.020(sys)

CA=3.02±0.25(stat)±0.49(sys)

CF=1.34±0.13(stat)±0.22(sys)


ConclusionsConclusions


Three different measurements of the strong coupling constant from the four-jet rate have been presented, all of them in agreement with previous results and representing one of the most precise measurements at present. This is the first measurement of the strong coupling constant from a four-jet observable.

A simultaneous measurement of the strong coupling constant and the colour factors has been presented, showing a good agreement with previous results.

Measurements of S and the QCD Colour Factors using Four-Jet Observables from Hadronic Z Decays

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