2. Report from the LEP QCD Working Group Roger Jones Lancaster 6.3.2003 CERN Switzerland

3. Outline Short report of  Working Group Annihilations group  s from Event shapes Systematic errors Combination Open Questions and future

4. Introduction...  Group formed in 1996  primary focus on event shapes   group formed in 1997  early focus on model building & structure functions  Other QCD topics in other groups  e.g. Colour Reconnection in W group  Both groups have achieved success with limited and reducing manpower resources

5. The  Working Group Hoped to combine photon structure functions This presupposed very basic agreement on distributions – experiments apparently disagreed makedly –Input to model builders –Improved background estimates for other physics channels After much work, the differences were resolved and a paper was produced –Eur. Phys. J.C23(2002) 201-223.

6. Sadly, this is not enough for a structure function combination – the four analyses are so different and the manpower so short, the group has reached a natural end

7. The Annihilations Group The of  s Current active members: H Stenzel, M Ford, D Wicke, G Salam, S Banerjee, RWLJ + others in the past

8. Annihilations Working Group Combination of  s measurements and checks of consistency (paper in draft) Combination useful @ LEP II (stat. poor but theory uncertainties smaller)  Comparable exptl. systematic estimation  Common theory implementation, common understanding of matching schemes, modification schemes and kinematic limits  Exploration of theory uncertainties and common treatment (paper in draft)

9. Event Shapes : e+e+ e-e- Z/  * q q g Born x-section for Z qq “Bremsstrahlung”

10. “infrared and collinear safe“ Calculable for so-called “infrared and collinear safe“ variables, Cancellation of singularities in the radiative corrections Examples: Thrust, C-Parameter, broadenings…. General Structure of the cross- section In NLO:

11. In the 2 jet region it is necessary to re-sum all logarithms of the type  s n (ln 1/x) 2n,  s n (ln 1/x) n A better prediction combines the NLO with the re-summed predictions E.g. uncertainties: consistent codes, matching schemes, modifications (to restore physical limits in distributions) & renormalization scales  QCD Working Group Perturbative Predictions L = -ln x

12.  All levels of prediction mentioned violate the physical bounds  These can be restored by modification schemes  There are various possibilities  This lead to confusion in earlier LEP results, now resolved  Through the working group we have now standardised method and associated parameters

13. Experimental Procedure Calculate perturbative predictions Calculate the hadronization corrections using Monte Carlo (JETSET,HERWIG,ARIADNE)  Common level Correct to the hadron level accounting for acceptance, resolution, ISR etc. (`Detector corrections’) Measure the distributions from data Observables : T, M h 2, C par, B tot, B w, lny 3,... Data Theory

14. Thrust.. 3 jet region T << 1 2jet region T >> 0.5 perturbative = energetic gluons non-perturbative =soft gluons 1/21

15. Many measurements at LEPI & LEPII For example: OPAL at E CM = 189 GeV Many measurements at LEPI & LEPII For example: OPAL at E CM = 189 GeV

16. Many available measurements : Measurements using Data from 2000 Consider the various contributing uncertainties…  s (206) = 0.1054  0.0028(exp)  0.0038 (theo)  s (M Z ) = 0.1183  0.0023(exp)  0.0043 (theo) Combination of the 6 observables

17. Uncertainties (ALEPH 206 Example) : Experi. : 0.0028 Theory : 0.0038 0.0022 stat 0.0017 model dep. 0.0016 matching Use different MC To calculate acceptance etc 0.0034 scale 0.0007 hadronization 0.0001 quark masses

18. Theory Error Dominates at all energies, origin missing higher orders – NNLO and NNLLA predictions would give a better partial answer, if available Traditional approach – variation of renormalisation scale x  =  /Q in the fit –WG standardised to range 0.5-2. (conventional but arbitrary) –Size of resultant error is smaller for observables with worse  2 fit, contrary to expectations! –December 01 workshop with theorists to discuss the issue

19. Proposal - x L Variation Replace terms in ln(1/x) with ln(1/ x L.x) –Should test a different set of higher orders How to set the range? Many ideas tried –Vary x L to match the difference between O(  s 2 ) calculations with O(  s 2 ) expansion of NLLA expansion  Depends on range, cannot always match the change –For fixed  s, fit with standard x  variation and x L =1, then refit with x L free and symmeterize Stable under change of fit range Complementarity in regions where x  and x L important –Can choose x L to set various terms in expansion to zero –A priori range, 2/3 < x L < 3/2 roughly supported

20. Matching and Modification Scheme Uncertainties? Difference between mod. LogR and mod. R matching taken as standard Also, consistent modification scheme uncertainties Difference between modification limits derived from parton shower MC and 4- parton ME boundary Difference between linear and second quadratic modification

21. Treatment of Theory Uncertainties Theoretical errors scale with  s 3 (prediction & practice)   s value and its uncertainty are correlated, so potential bias towards downwards fluctuations  Uncertainties done centrally –Measured  s (M Z ) used @ M Z for uncertainties and  S run upwards for LEP II

22. All theory uncertainty sources define an envelope Any source can determine maximum uncertainty in bin Corresponding  s found that just `kisses’ the resulting envelope. Uncertainty band estimation of overall error

23. Hadronization uncertainties Much less important than `theory’ uncertainties Hadronization surprisingly inconsistent between models and between experiments Estimate uncertainty by observing result of changing between JETSET/HERWIG/ARIADNE –Surprisingly little correlation Different implementations of models and tunings Different fit ranges Ambiguities in definition of hadron level (neutrinos included? Before weak decays?) Resolved, small effect Difference mainly at parton level  tuning

24. Bin-by-bin hadronization correction from Pythia Monte Carlo

25. Combination We tried to do a detailed, fully-correlated combination a la LEP EW WG Bottom line – the method is unstable, giving negative weights in many cases  Need impossible accuracy to errors with 194x194 covariance matrix to be inverted, though improved with standardised theory errors  Small contributions (not well controlled) are important in the inversion (classic regularisation problem) Correlations are important regardless of the combination method Most important correlation is the theory correlation, which is large but hard to estimate

26. Correlations are important regardless of the combination method Most important correlation is the theory correlation

27. Theory Correlations Theory correlations are high but not 100% Fixed range  100% correlation (resummation matters at one end) Test: L3 theory errors fitted to faction of  s 3 and  s 4 terms ( pert + HO) – very consistent with 95% pert, estimate of correlation? Other experiments have more range variation, reduces correlation Better method, construct correlator for mesh of theory MCs, being done – x  : 0.4 0.6 1.0 1.5 2.0 – x L : 0.6 0.8 1.0 1.3 1.6 – mod : p=1,logR p=2,logR p=1,R

28. Safer Half-way Strategy Uncertainty band used for the theory error Use stat. and exp. covariance & theory and rms of experiments had. uncertainties on-diagonal  central value and weights, and the stat. and exp. uncertainties Repeat average with different hadronization models assumed and take rms for final hadronisation uncertainty  Takes most of correlations into account Is stable and shares weight between LEP 1&2 Better than previous estimates because of improved inputs and stat. correlation estimates

29. Construction of Covariance Matrix and Uncertainties

30. Combinations by Observable

31. By Energy Using only LEP Several measurements preliminary Mean value is stable LEP I:  s (M Z ) =0.1197  0.0002(stat)  0.0008(ex)  0.0010(had)  0.0048(th) LEP II:  s (M Z ) =0.1196  0.0005(stat)  0.0010(ex)  0.0007(had)  0.0044(th) All-energies does not beat LEP II because high correlation of theory uncertainty

32. Combine at each Q to investigate the running  2 /dof = 11.6/13

33. Conclusions Each LEP (I and II) has made important contributions in measuring  s and the current precision Big improvements in theory implementation and uncertainty estimation Improved combination of results Hopes for the future… –Power law corrections – NNLO calculations on the horizon? –We will continue with `best effort’, but will archive for future re-analysis