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

1. Measurements of S and the QCD Colour Factors using Four-Jet Observables from Hadronic Z Decays 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 Sílvia Bravo i Gallart

3. Motivation Sílvia Bravo i Gallart

4. QCD=(?) theory for the description of the strong interaction of quarks and gluons LEP Experiments, as ALEPH, provided goodconditions for QCD studies High statistics High energy Clean environment New NLO calculations for 4-jet observables allowed us to perform Measurements of the strong coupling constant alone and together with the QCD colour factors from 4-jet observables 1st S measurementfrom a 4-jet observable Stringent test of QCD Sílvia Bravo i Gallart

5. Theoretical Framework Predictions for Four-Jet Observables Sílvia Bravo i Gallart

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 Sílvia Bravo i Gallart

7. The 4-jet Rate(resummation of large logarithms exists) with Where the Born and NLO functions depend linearly and quadratically on the Colour Factor Ratios Sílvia Bravo i Gallart

8. The 4-jet angular correlations Sílvia Bravo i Gallart

9. The Analysis Description Sílvia Bravo i Gallart

10. Two different analyses but same method Simultaneously S and the colour factors. S from R4 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). Sílvia Bravo i Gallart

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% –. Finally the sources of systematic uncertainty are studied: Corrections, fit range, selection cuts, etc. Sílvia Bravo i Gallart

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 For all observables Sílvia Bravo i Gallart

13. Total Corrections Sílvia Bravo i Gallart

14. Measurements of the Strong Coupling Constant from the Four-Jet Rate Sílvia Bravo i Gallart

15. 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 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 Sílvia Bravo i Gallart

16. Method I : x fixed to 1 Method II : x also fitted Method III : x fixed to xopt Sílvia Bravo i Gallart

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18. Systematic Studies • Fit Range • Selection Criteria • Hadronization Corrections • Detector Corrections • Theoretical Predictions • Other Checks Performed • Hadronization Corrections • Scale dependence • Fits over different ranges Sílvia Bravo i Gallart

19. Method I : x fixed to 1 S = 0.1170  0.0001(stat)  0.0014(sys) If systematic error added quadratically then0.0022 for S Method II : x also fitted S = 0.1175  0.0002(stat)  0.0013(sys) If systematic error added quadratically then 0.0014 for S Method III : x fixed to xopt S = 0.1175  0.0001(stat)  0.0007(sys) If systematic error added quadratically then 0.0033 for S Sílvia Bravo i Gallart

20. Results in good agreement with previous ALEPH results, as well as with a similar analysis by DELPHI S = 0.1170  0.0001(stat)  0.0014(sys) 0.0022 quad. Theoretical uncertainty dominates the total error ALEPH Preliminary Resummed 3-jet Event Shapes S = 0.1203  0.0001(stat)  0.0068(sys) 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) Sílvia Bravo i Gallart

21. Simultaneous Measurement of the Strong Coupling Constant and the QCD Colour Factors 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. QCD expected: CA=3 & CF=4/3 Sílvia Bravo i Gallart

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25. 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 Sílvia Bravo i Gallart

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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) Sílvia Bravo i Gallart

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29. Conclusions 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. Sílvia Bravo i Gallart