Post on 06-Jan-2016
description
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
18-3-2002 Sílvia Bravo i Gallart 2
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
18-3-2002 Sílvia Bravo i Gallart 3
MotivationMotivation
18-3-2002 Sílvia Bravo i Gallart 4
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
18-3-2002 Sílvia Bravo i Gallart 5
Theoretical FrameworkTheoretical Framework
Predictions for Four-Jet ObservablesPredictions for Four-Jet Observables
18-3-2002 Sílvia Bravo i Gallart 6
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
18-3-2002 Sílvia Bravo i Gallart 7
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
18-3-2002 Sílvia Bravo i Gallart 8
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
18-3-2002 Sílvia Bravo i Gallart 9
The Analysis DescriptionThe Analysis Description
18-3-2002 Sílvia Bravo i Gallart 10
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).
18-3-2002 Sílvia Bravo i Gallart 11
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.
18-3-2002 Sílvia Bravo i Gallart 12
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
18-3-2002 Sílvia Bravo i Gallart 13
Total CorrectionsTotal Corrections
haddettot CCC
18-3-2002 Sílvia Bravo i Gallart 14
Measurements of the Measurements of the Strong Coupling Constant Strong Coupling Constant
from the Four-Jet Ratefrom the Four-Jet Rate
18-3-2002 Sílvia Bravo i Gallart 15
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
18-3-2002 Sílvia Bravo i Gallart 16
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
18-3-2002 Sílvia Bravo i Gallart 17
5627
Ndof
2.
484
Ndof
2.
18-3-2002 Sílvia Bravo i Gallart 18
Systematic StudiesFit RangeSelection CriteriaHadronization CorrectionsDetector CorrectionsTheoretical Predictions
Other Checks PerformedHadronization CorrectionsScale dependenceFits over different ranges
18-3-2002 Sílvia Bravo i Gallart 19
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)
If systematic error added quadratically then 0.0014 for S
Method III : Method III : xx fixed to x fixed to xoptopt
S = 0.1175 0.0001(stat) 0.0007(sys)
If systematic error added quadratically then 0.0033 for S
18-3-2002 Sílvia Bravo i Gallart 20
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
18-3-2002 Sílvia Bravo i Gallart 21
Simultaneous Simultaneous Measurement of the Measurement of the
Strong Coupling Constant Strong Coupling Constant and the QCD Colour and the QCD Colour
FactorsFactors
18-3-2002 Sílvia Bravo i Gallart 22
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
18-3-2002 Sílvia Bravo i Gallart 23
18-3-2002 Sílvia Bravo i Gallart 24
18-3-2002 Sílvia Bravo i Gallart 25
Systematic StudiesFit RangeSelection Criteria & Detector Corrections = ExperimentalHadronization CorrectionsTheoretical Predictions
Other Checks PerformedHadronization CorrectionsTwo- and Three-parton BackgroundsSensitivity to each observable
Dependence on the ycut
18-3-2002 Sílvia Bravo i Gallart 26
18-3-2002 Sílvia Bravo i Gallart 27
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)
18-3-2002 Sílvia Bravo i Gallart 28
18-3-2002 Sílvia Bravo i Gallart 29
ConclusionsConclusions
18-3-2002 Sílvia Bravo i Gallart 30
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.