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

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alpha_s and quark masses Inclusive observables H.Stenzel 2 Outline Experimental Input measurement pseudo-observables Determination of α s fit procedure QCD/EW corrections Systematic uncertainties QCD uncertainties experimental/parametric Improvements/Outlook

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alpha_s and quark masses 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, m W,m t,...) global EW fits to constrain the free parameters of the SM... in particular constraints on the mass of the Higgs... but also determination of α s Results: Phys.Rep. 427 (2006) 257 PDG 2006 LEPEWG 2006

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alpha_s and quark masses Inclusive observables H.Stenzel 4 Combined lineshape results mZmZ 91.1876 ± 0.0021 GeV ΓZΓZ 2.4952 ± 0.0023 GeV σ 0 had 41.540 ± 0.037 nb R0lR0l 20.767 ± 0.025 A 0,l FB 0.0171 ± 0.0010 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: m Z, Γ Z, σ 0 had –Small angle Bhabha scattering: σ 0 had –luminosity

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

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

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alpha_s and quark masses Inclusive observables H.Stenzel 7 Partial width in the SM g and ρ effective complex couplings of fermions to Z mass effects explicitly embodied for leptons QCD corrections for quarks incorporated in the radiator Functions R A and R v factorizable EW x QCD corrections in the effective couplings Non-factorizable EW x QCD corrections

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alpha_s and quark masses Inclusive observables H.Stenzel 8 Sensitivity of partial widths and POs to α s weak sensitivity for Γ l only through O(αα s ) corrections best sensitivity for σ 0 l u,c d,s Overall rather weak sensitivity of inclusive EW observables to α s for a 10% change of α s a ~0.3% change in the observables is obtained with respect to a nominal value O(α s = 0.1185) ratio to α s =0.1185

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alpha_s and quark masses Inclusive observables H.Stenzel 9 General structure of QCD radiators NNLO massless NNLO m q 2 /s NLO m q 4 /s 2 LO m q 6 /s 3 In addition the effective EW couplings ρ and g incorporate mixed QCD x EW corrections i.e. O(α α s ), O(α α s 2 ), O(G F m t 2 α s )...

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alpha_s and quark masses Inclusive observables H.Stenzel 10 Radiator dependence on α s α s – dependence of the widths dominated by the radiator dependence Vector part of the radiators identical for all flavours, axial-vector part flavour-dependent

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

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alpha_s and quark masses Inclusive observables H.Stenzel 12 Impact of higher order corrections Three main ingredients of the QCD correction: 1.the NNLO part 2.the quark mass corrections 3.the mixed QCD x EW terms What is their relative impact?

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alpha_s and quark masses Inclusive observables H.Stenzel 13 Global EW fits Free parameters of the SM : fits with ZFITTER / TOPAZ0 Δα 2 had (m Z 2 ) α s (m Z 2 ) m Z m t m H experimental input: lineshape measurements Δα 2 had (m Z 2 ) asymmetry parameters heavy flavour measurements top + W mass 18 inputs, high Q 2 -set Fit results: χ 2 /N dof : 18.3/13 w/o common systematic errors no QCD!

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alpha_s and quark masses Inclusive observables H.Stenzel 14 Fit results – SM consistency

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alpha_s and quark masses Inclusive observables H.Stenzel 15 Sensitivity to the Higgs Mass

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alpha_s and quark masses 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 α s Purpose for the rest of this talk: evaluate QCD uncertainties

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alpha_s and quark masses Inclusive observables H.Stenzel 17 QCD uncertainties for α s from EW observables Implementation of the renormalisation scale dependence in ZFITTER 1.running of α s (µ) 2.running of the quark masses 3.explicit scale terms in the expansion H.S., JHEP07 (2005) 013

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

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alpha_s and quark masses Inclusive observables H.Stenzel 19 Scale dependence for the Pseudo-observables Evaluation of the PT uncertainty for the POs: scale variation Range of variation purely conventional, but widely used. Uncertainty for observable O defined as: Typical uncertainty 0.5 Depends obviously on α s. partial widths pseudo-observables

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alpha_s and quark masses Inclusive observables H.Stenzel 20 dependence of the PO uncertainty on α s Increase of the observables uncertainty by a factor of ~2 for 0.11 < α s <0.13

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alpha_s and quark masses Inclusive observables H.Stenzel 21 Evaluation of uncertainty for α s as obtained from an EW observable Technique based on the uncertainty-band Method: 1.Evaluate the observable O for a given value of α s 2.calculate the PT uncertainties for O using x µ scale variation at given α s 3.the change of O under x µ can also be obtained by a variation of α s 4.the corresponding variation range for α s is assigned as systematic uncertainty Uncertainty band method: R.W.L. Jones et al., JHEP12 (2003) 007

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alpha_s and quark masses Inclusive observables H.Stenzel 22 Uncertainty for α s from EW observables For α s =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: Δα s =±0.0010

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alpha_s and quark masses Inclusive observables H.Stenzel 23 Best strategy for α s LEPEWG 5-parameter fit to 18 high Q 2 -data α s =0.1188 ±0.0027 (nominal) α s =0.1186 ±0.0029 (incl. QCD error) 1-parameter fit (α s ) with all other SM parameters fixed to experimental values, m H =150 GeV + 0.0010 m H 300 GeV

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alpha_s and quark masses 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 m W and m t precision measurement of α s consistency tests of the SM For α s from EW observables the QCD uncertainty has been determined to ±0.0010, compared to α s =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.

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