1. Sílvia Bravo i Gallart IFAE, Barcelona Moriond-QCD, 18 March 2002
Measurements of S and the QCD Colour Factors using Four-Jet Observables from Hadronic Z Decays
General remarks:
Theory: slowly, remark what are the parameters measured in this thesis.
CARE: do not pass the transparency till all the info has been given
Try not to say “I will not enter in the details of this”, but better “I will focus on that”. It is, give enphasis to what will be explained and not to what is skipped.
Remark DEBRECEN, what is it used for.
Try not to read too many numbers
Sílvia Bravo i Gallart
IFAE, Barcelona
Moriond-QCD, 18 March 2002
Sílvia Bravo i Gallart

2. Outline 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
Say that the measurement of the strong coupling constant from the four-jet rate was the first ever made
The combined measurement includes a check about the existence of the light gluino
Sílvia Bravo i Gallart

3. Motivation
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4. LEP Experiments, as ALEPH, provided good conditions for QCD studies
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
Reminder =(?) means believed to be
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5. Theoretical Framework
Predictions for Four-Jet Observables
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6. QCD shows its full gauge structure only in order S2
R4 + 4-jet angular correlations a good set of observables to perform a stringent test of QCD
The contributions are not really disentangled… I should say
Where the first term MAINLY comes from 2q2g common, etc.
The 4-jet rate is expected to be smaller for the Abelian Th.
Full gauge structure only in order alpha_s^2 because we need he gluon self-interaction to appear
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7. The 4-jet Rate (resummation of large logarithms exists)
with
Where the Born and NLO functions
Resummation. Only R matching available. The modified R matched could be calculated. There is no lnR matching because it does not satisfy a simple exponentiation.
The resummation is needed because at low ycut values terms as alpha_s^n lnx_mu^m are enhanced
The K coefficient in the resummation takes into account 2-loop contributions in the emission probabilites.
Be sure that I define eta, mu, xmu and the B and C functions.
Remark that we will measure only eta in one case (which is alpha_s by a factor), and eta + the colour factors in the other case.
Remark that R4 is mainly sensitive to eta, scale dependence reduced by resummation
depend linearly and quadratically on the Colour Factor Ratios
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8. The 4-jet angular correlations
Remark that the angular observables are mainly sensitive to the colour factor ratios and that were designed to exploit the difference between an abelian and a not-abelian theory (I.e. effects coming from the gluon-self interaction)
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9. The Analysis Description
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10. Simultaneously S and the colour factors. S from R4
Two different analyses but same method
Simultaneously S and the colour factors.
S from R4
Hadronic Selection on 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  ln(ycut)  -0.2
Each angular observable has 20 bins
NLO prediction from DEBRECEN (resummation for R4, normalized distributions for the angles).
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11. The theoretical distributions are then corrected to HL
After correction for detector effects...
the following 2 is minimized
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% –.
R4: it is not a distribution, but 60 different measurements
Correlations: explain the plot… for the angles x-axes bin number… each angle 20 bins. First cosbz, cosks,…
Finally the sources of systematic uncertainty are studied:
Corrections, fit range, selection cuts, etc.
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12. Hadronization Corrections
Angular correlations
Four-jet rate
PL before the showering and HL & PL dist. obtained from 4-parton ME option in PYTHIA
PL after showering and HL & PL dist. obtained from std PYTHIA
Correction for hadronization effects & missing higher orders
Detector Corrections
Should better describe our data provided that 2&3-jet bckg negligible and showering + hadronization ok
For all observables
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13. Total Corrections
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14. Measurements of the Strong Coupling Constant from the Four-Jet Rate
Remark that this has been the first measurement of the strong coupling constant from a four-jet observable.
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15. Method II : x also fitted
Method I : x fixed to 1
Standard in Aleph:
fit and all systematics with x=1
scale uncertainty 0.5 < x < 2.
Method II : x also fitted
The strong coupling constant and the scale are fitted together for all systematics
Method III : x fixed to xopt
Reminder: what is eta and what is x_mu
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
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16. Method I : x fixed to 1 Method II : x also fitted
Method III : x fixed to xopt
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17.
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18. Hadronization Corrections Detector Corrections Theoretical Predictions
Systematic Studies
Fit Range
Selection Criteria
Hadronization Corrections
Detector Corrections
Theoretical Predictions
Other Checks Performed
Hadronization Corrections
Scale dependence
Fits over different ranges
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19. Method I : x fixed to 1 Method II : x also fitted Method III :
S =  (stat)  (sys)
If systematic error added quadratically then for S
Method II :
x also fitted
S =  (stat)  (sys)
If systematic error added quadratically then for S
Method III :
x fixed to xopt
Added quadratically means also that individual contributions are not rescaled by the chi2.
Say that from now on alpha_s(mz) is shorten to alpha_s
S =  (stat)  (sys)
If systematic error added quadratically then for S
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20. Results in good agreement with previous ALEPH results, as well as with a similar analysis by DELPHI
S =  (stat)  (sys)
Theoretical uncertainty dominates the total error
quad.
ALEPH Preliminary Resummed 3-jet Event Shapes
S =  (stat)  (sys)
DELPHI Preliminary NLO 4-jet rate, EOS Method
Durham: S =  (stat)  (sys)
Cambridge: S =  (stat)  (sys)
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21. Simultaneous Measurement of the Strong Coupling Constant and the QCD Colour Factors
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22. Method as described previously. x was fixed to 1.
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.
Remind: eta, x_mu, x and y.
QCD expected: CA=3 & CF=4/3
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23.
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24.
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25. Selection Criteria & Detector Corrections = Experimental
Systematic Studies
Fit Range
Selection Criteria & Detector Corrections = Experimental
Hadronization Corrections
Theoretical Predictions
Other Checks Performed
Hadronization Corrections
Two- and Three-parton Backgrounds
Sensitivity to each observable
Dependence on the ycut
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26. 18-3-2002 Sílvia Bravo i Gallart The two elipses touch because
Stat error 0.02
Syst error 0.06
Then total error 0.063, I.e. 0.06
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27. Final results on the combined measurement
OPAL Published Results: aS=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)
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28.
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29. Conclusions
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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.
Sílvia Bravo i Gallart