Offline Software Commissioning

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as from inclusive EW observables in ee-
annihilation Hasko Stenzel
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Outline

• Experimental Input
• measurement
• pseudo-observables
• Determination of as
• fit procedure
• QCD/EW corrections
• Systematic uncertainties
• QCD uncertainties
• experimental/parametric
• Improvements/Outlook

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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 as
• Results Phys.Rep. 427 (2006) 257

LEPEWG 2006
PDG 2006
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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 , GZ, s0had
• Small angle Bhabha scattering s0had
• luminosity

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From measured cross sections...
Convolution of the EW cross section with QED
radiator
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... to pseudo-observables
Not independent observable but useful for as
Partial widths and asymmetries are conveniently
parameterised in terms of effective EW couplings
.
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Partial width in the SM

• g and ? effective complex 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

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Sensitivity of partial widths and POs to as
ratio to as0.1185
u,c
d,s
weak sensitivity for Gl only through O(aas)
corrections
best sensitivity for s0l

• Overall rather weak sensitivity of inclusive EW
  observables to as
• for a 10 change of as a 0.3 change in the
  observables is obtained with respect to a nominal
  value O(as 0.1185)

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General structure of QCD radiators
NNLO massless
NNLO mq2/s
NLO mq4/s2
LO mq6/s3
In addition the effective EW couplings ? and g
incorporate mixed QCD x EW corrections i.e. O(a
as), O(a as2), O(G F m t2 as)...
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Radiator dependence on as

• as 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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EW couplings dependence on as
Very weak dependence on as through the mixed
corrections, e.g. running of a
H.Burkhardt, B.Pietrzyk, PRD 72(2005)057501
using here
derived from lower energy annihilation data via
the dispersion integral
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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?

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Global EW fits
Free parameters of the SM fits with ZFITTER /
TOPAZ0

• ?a2had(mZ2)
• as(mZ2)
• mZ
• mt
• mH

• experimental input
• lineshape measurements
• ?a2had(mZ2)
• asymmetry parameters
• heavy flavour measurements
• top W mass
• 18 inputs, high Q2-set

Fit results ?2/Ndof 18.3/13 w/o
common systematic errors no QCD!
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Fit results SM consistency
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Sensitivity to the Higgs Mass
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EW fit result for the Higgs Mass

• Claim
• Theory uncertainty for Higgs does not include QCD
  uncertainties
• these are absorbed into the value of as
• Purpose for the rest of this talk
• evaluate QCD uncertainties

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QCD uncertainties for as from EW observables

• Implementation of the renormalisation scale
  dependence in ZFITTER
• running of as(µ)
• running of the quark masses
• explicit scale terms in the expansion

H.S., JHEP07 (2005) 013
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Scale dependence for radiators and couplings
QCD Radiators
EW couplings
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Scale dependence for the Pseudo-observables
partial widths
Evaluation of the PT uncertainty for the POs
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
as .
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dependence of the PO uncertainty on as
Increase of the observables uncertainty by a
factor of 2 for 0.11 lt aslt0.13
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Evaluation of uncertainty for as as obtained from
an EW observable

• Technique based on the uncertainty-band Method
• Evaluate the observable O for a given value of as
• calculate the PT uncertainties for O using xµ
  scale variation at given as
• the change of O under xµ can also be obtained by
  a variation of as
• the corresponding variation range for asis
  assigned as systematic uncertainty

Uncertainty band method R.W.L. Jones et al.,
JHEP12 (2003) 007
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Uncertainty for as from EW observables
For as0.119 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
?as0.0010
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Best strategy for as
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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 as
• consistency tests of the SM
• For as from EW observables the QCD uncertainty
  has been
• determined to 0.0010, compared to
• as0.1188 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.