α s from inclusive EW observables in e + e - annihilation Hasko Stenzel

1. αs from inclusive EW observables in e+e- annihilation Hasko Stenzel

2. Outline • Experimental Input • measurement • pseudo-observables • Determination of αs • fit procedure • QCD/EW corrections • Systematic uncertainties • QCD uncertainties • experimental/parametric • Improvements/Outlook Inclusive observables H.Stenzel

3. Lineshape measurements at LEP • Measurement of cross sections and asymmetries around the Z resonance by the LEP experiments ADLO and SLD • interpretation in terms of pseudo-observables to minimize the correlation • combination of individual measurements and their correlation • inclusion of other relevant EW measurements (heavy flavour, mW,mt,...) • global EW fits to constrain the free parameters of the SM ... • in particular constraints on the mass of the Higgs... • but also determination of αs Results: Phys.Rep. 427 (2006) 257 LEPEWG 2006 PDG 2006 Inclusive observables H.Stenzel

4. Combined lineshape results • LEP combination of pseudo-observables • raw experimental input from ADLO converted into lineshape observables • unfolding of QED radiative corrections • minimize correlation between observables • determination of experimental correlation matrix • errors include stat. & exp. syst. • assume here lepton universality • not a unique choice of observables/assumptions • Most results dominated by experimental uncertainty, • important common errors are: • LEP energy calibration: mZ , ΓZ, σ0had • Small angle Bhabha scattering: σ0had • luminosity Inclusive observables H.Stenzel

5. From measured cross sections... Convolution of the EW cross section with QED radiator Inclusive observables H.Stenzel

6. ... to pseudo-observables Not independent observable but useful for αs Partial widths and asymmetries are conveniently parameterised in terms of effective EW couplings . Inclusive observables H.Stenzel

7. Partial width in the SM • g and ρeffectivecomplex couplings of fermions to Z • mass effects explicitly embodied for leptons • QCD corrections for quarks incorporated in the radiator Functions RA and Rv • factorizable EW x QCD corrections in the effective couplings • Non-factorizable EW x QCD corrections Inclusive observables H.Stenzel

8. Sensitivity of partial widths and POs to αs ratio to αs=0.1185 u,c d,s weak sensitivity for Γl only through O(ααs) corrections best sensitivity for σ0l • Overall rather weak sensitivity of inclusive EW observables to αs • for a 10% change of αs a ~0.3% change in the observables is obtained with respect to a nominal value O(αs = 0.1185) Inclusive observables H.Stenzel

9. General structure of QCD radiators NNLO massless NNLO mq2/s NLO mq4/s2 LO mq6/s3 In addition the effective EW couplings ρ and g incorporate mixed QCD x EW corrections i.e. O(ααs), O(ααs2), O(GF m t2αs)... Inclusive observables H.Stenzel

10. Radiator dependence on αs • αs – dependence of the widths dominated by the radiator dependence • Vector part of the radiators identical for all flavours, axial-vector part flavour-dependent Inclusive observables H.Stenzel

11. EW couplings dependence on αs Very weak dependence on αs through the mixed corrections, e.g. running of α H.Burkhardt, B.Pietrzyk, PRD 72(2005)057501 using here derived from lower energy annihilation data via the dispersion integral Inclusive observables H.Stenzel

12. Impact of higher order corrections • Three main ingredients of the QCD correction: • the NNLO part • the quark mass corrections • the mixed QCD x EW terms • What is their • relative impact? Inclusive observables H.Stenzel

13. Global EW fits Free parameters of the SM : fits with ZFITTER / TOPAZ0 • Δα2had(mZ2) • αs(mZ2) • mZ • mt • mH experimental input: • lineshape measurements • Δα2had(mZ2) • asymmetry parameters • heavy flavour measurements • top + W mass • 18 inputs, high Q2-set Fit results: χ2/Ndof : 18.3/13 w/o common systematic errors no QCD! Inclusive observables H.Stenzel

14. Fit results – SM consistency Inclusive observables H.Stenzel

15. Sensitivity to the Higgs Mass Inclusive observables H.Stenzel

16. EW fit result for the Higgs Mass • Claim: • Theory uncertainty for Higgs does not include QCD uncertainties • these are absorbed into the value of αs Purpose for the rest of this talk: • evaluate QCD uncertainties Inclusive observables H.Stenzel

17. QCD uncertainties for αs from EW observables • Implementation of the renormalisation scale dependence in ZFITTER • running of αs(µ) • running of the quark masses • explicit scale terms in the expansion H.S., JHEP07 (2005) 013 Inclusive observables H.Stenzel

18. Scale dependence for radiators and couplings QCD Radiators EW couplings Inclusive observables H.Stenzel

19. Scale dependence for the Pseudo-observables partial widths Evaluation of the PT uncertainty for the PO’s: scale variation Range of variation purely conventional, but widely used. pseudo-observables Uncertainty for observable O defined as: Typical uncertainty ≈ 0.5 ‰ Depends obviously on αs . Inclusive observables H.Stenzel

20. dependence of the PO uncertainty on αs Increase of the observables uncertainty by a factor of ~2 for 0.11 < αs<0.13 Inclusive observables H.Stenzel

21. Evaluation of uncertainty for αs as obtained from an EW observable • Technique based on the uncertainty-band Method: • Evaluate the observable O for a given value of αs • calculate the PT uncertainties for O using xµ scale variation at given αs • the change of O under xµ can also be obtained by a variation of αs • the corresponding variation range for αsis assigned as systematic uncertainty Uncertainty band method: R.W.L. Jones et al., JHEP12 (2003) 007 Inclusive observables H.Stenzel

22. Uncertainty for αs from EW observables For αs=0.119 the uncertainty is 0.0010-0.0012 Strategy adopted by LEPEWG: calculate QCD uncertainty of the observables in the covariance matrix included in the fit. Result: Δαs=±0.0010 Inclusive observables H.Stenzel

23. Best strategy for αs Inclusive observables H.Stenzel

24. Conclusion • Wealth of electroweak data from LEP and elsewhere allows • for precision measurements of Standard Model parameters • Constraints of the Higgs mass (upper limit) • Indirect determinations of mW and mt • precision measurement of αs • consistency tests of the SM For αs from EW observables the QCD uncertainty has been determined to ±0.0010, compared to αs=0.1188 ± 0.0027 (exp) ± 0.0010 (QCD) An outstanding verification is expected from event-shapes at LEP and NNLO calculations for differential distributions, where an experimental uncertainty of 1% is achieved. Inclusive observables H.Stenzel