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 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

Motivation 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

Theoretical Framework Predictions for Four-Jet Observables 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

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) 18-3-2002 Sílvia Bravo i Gallart

The Analysis Description 18-3-2002 Sílvia Bravo i Gallart

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 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

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. 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

Total Corrections 18-3-2002 Sílvia Bravo i Gallart

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. 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

Method I : x fixed to 1 Method II : x also fitted Method III : x fixed to xopt 18-3-2002 Sílvia Bravo i Gallart

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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 18-3-2002 Sílvia Bravo i Gallart

Method I : x fixed to 1 Method II : x also fitted Method III : S = 0.1170  0.0001(stat)  0.0014(sys) If systematic error added quadratically then 0.0022 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 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 = 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

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) Theoretical uncertainty dominates the total error 0.0022 quad. 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) 18-3-2002 Sílvia Bravo i Gallart

Simultaneous Measurement of the Strong Coupling Constant and the QCD Colour Factors 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

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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 18-3-2002 Sílvia Bravo i Gallart

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 18-3-2002 Sílvia Bravo i Gallart

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) 18-3-2002 Sílvia Bravo i Gallart

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Conclusions 18-3-2002 Sílvia Bravo i Gallart

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. 18-3-2002 Sílvia Bravo i Gallart