1. Measurement of α s at NNLO in e+e- annihilation Hasko Stenzel, JLU Giessen, DIS2008

2. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 2 QCD processes in e+e- annihilation  leptonic initial state, EW interaction  hadronic final state  perturbative & non-perturbative effects  ideal testing ground for QCD  (almost) precision measurements of QCD parameters & properties

3. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 3 hard gluon radiation  3-jet events Most prominent manifestation of QCD in e+e- : 3-jet events, hard gluon radiation Cross section directly proportional to α s TASSO 1979 OPAL 2000

4. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 4 Event-shape variables Global observables sensitive to (multi)-gluon radiation, defined infrared- and collinear-safe, experimentally robust, receiving small hadronisation corrections (1/Q). 30-50% correlation between variables

5. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 5 Theoretical predictions : Pre-NNLO state of art Standard analysis at LEP using NLO + NLLA predictions pure NLO resummation of leading and next-to-leading logs to all orders NLLA matched predictions combining fixed order and resummed calculations with subtraction of double-counting terms

6. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 6 LEP combination of α s from event shapes at NLO+NLLA radiative events LEPQCDWG combination Preliminary!

7. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 7 NNLO calculation  extremely challenging calculation  careful subtraction of real and virtual divergencies  subtraction obtained by antenna method  implemented in the EERAD3 integration program  numerical integration requires heavy CPU  non-negligible statistical uncertainties A.Gehrmann-De Ridder, T.Gehrmann, E.W.N Glover, G.Heinrich JHEP 0711:058, JHEP 0712:094, 2007

8. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 8 Theoretical predictions for event-shape distributions at NNLO For a generic event-shape variable X=T,MH,BT,BW,C, Y3 Normalisation for σ Renormalisation scale dependence NNLO term

9. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 9 Analysis outline for α s at NNLO  Use the public ALEPH data A. Heister et al., EPJC 35 (2004) 457 on event shapes (T, M H, B W, B T, C, y 3 )  follow closely experimental procedure applied by ALEPH  data are corrected to hadron level using MC corrections accounting for ISR/FSR QED radiation and background  data are fit by NNLO perturbative prediction, including NLO quark mass corrections, folded to hadron level by MC generators  combine 6 variables and 8 data sets (LEPI + LEPII)

10. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 10 LEP data At LEPI:  selected high quality Z 0 peak data  validated standard correction scheme At LEPII:  special cuts for ISR suppression  4-fermion background subtraction  limited statistics (10k events) ALEPH data set at LEPII

11. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 11 Hadronisation corrections Perturbative predictions are fold to hadron level by means of a transition matrix partons->hadrons computed with Monte Carlo Generators –PYTHIA6.1 –HERWIG6.1 –ARIADNE4.1 –parton shower / color dipole –string/cluster fragmentation –all generators tuned to LEP1 data Generator tuning is essential, in ALEPH up to 16 model parameters were tuned to 12 observables (event-shapes and inclusive charged particle distributions) –Next generation generators combining NLO+PS have not been tuned and are not used here

12. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 12 Theoretical predictions: quark mass corrections Corrections for heavy quarks at NLO, relevant at LEPI For heavy quarks gluon radiation is suppressed by mass effects –was used to measure the running b-quark mass –applied as correction for α s fits 3-jet rate b/d-quarks

13. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 13 NNLO fits to the data  data are fit in the central part of event shape distributions  only statistical uncertainties are included in the χ 2 LEP II LEP I fit range G.Dissertori, A.Gehrmann-De Ridder, T.Gehrmann, E.W.N Glover, G.Heinrich, HS JHEP 0802:040, 2008

14. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 14 NNLO fits to the data  clear improvement of NNLO over NLO  good fit quality (but includes still large statistical uncertainties for C- coefficient)  extended range of good description (3-jet region)  matched NLO+NNLA (resummation) still yields a better prediction in the 2-jet region  value of α s is rather high... ... but decreases from NLO to NNLO

15. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 15 Perturbative uncertainty: scale dependence range of variation  scale uncertainty reduced by a factor of 2 from NLO to NNLO  NNLO about 30% better than NLO+NLLA  fits with free scale don’t improve description of data at NNLO Thrust -log(y3)

16. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 16 NNLO results at LEPI  consistent results at NNLO  scattering between variables much reduced  independent check of theoretical uncertainties α s (M Z )

17. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 17 Evaluation of perturbative uncertainty Technique based on the uncertainty-band Method to estimate the impact of missing higher orders: 1.Evaluate distribution of event shape O for a given value of α s with a reference theory (here NNLO, x µ =1) 2.calculate the PT uncertainties for O (x µ variation) ->uncertainty band 3.fill the uncertainty band with the nominal prediction by varying α s 4.the corresponding variation range for α s is assigned as systematic uncertainty In addition, an uncorrelated uncertainty is evaluated for the b-quark mass correction, available only at NNLO. This uncertainty amounts to ≈1%. Uncertainty band method: R.W.L. Jones et al., JHEP12 (2003) 007

18. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 18 Fit results & systematic uncertainties  experimental systematics evaluated according to the ALEPH procedure  hadronization: difference between PYTHIA, HERWIG and ARIADNE  experimental: dominant sources  LEPI: modeling energy flow, <1%  LEPII: ISR corrections

19. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 19 Fit results at LEPII and the running of α s

20. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 20 Combination of α s (M Z ) This analysis NNLOALEPH NLO+NNLA Data setLEP1+LEP2LEP2LEP1+LEP2LEP2 α s (M Z )0.12400.12380.12140.1217 Stat.error0.00080.0009 0.0010 Exp.error0.00100.0011 0.0012 Pert.error0.00290.00280.00450.0044 Hadr.error0.00110.00100.00110.0010 Total error0.0033 0.0048  Calculate a weighted average for α s (Q) from 6 variables at each energy  Repeat systematics for the weighted average  Evolve measurements at LEPII to Q= M Z  Calculate the combination of 6 variables and measurements at 8 energies

21. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 21 Conclusion A new analysis of α s from event shapes at NNLO is presented: α s (M Z )=0.1240 ± 0.0033 major achievement in NNLO calculations substantial improvement over NLO and NLO+NNLA competitive results compared to other processes our result for α s is ‘somewhat high’ compared to other measurements.... Further improvements in near future can be expected matching of NLLA (or higher) large logs resummation to all orders to NNLO (see talk of G.Luisoni) inclusion of electroweak corrections to event shapes, not factorizable on σ had hadronisation corrections from modern NLO+PS Monte Carlo generators

22. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 22 BACK UP

23. alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 23 Global QCD observables Jet rates defined according to a given algorithm e.g.Durham Event-shape distributions used to extract α s A.Gehrmann-De Ridder et al., hep-ph 0802.0813 A.Gehrmann-De Ridder et al., JHEP 0712:094,2007