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

αs from inclusive EW observables in e+e- annihilation

Hasko Stenzel

alpha_s and quark masses Inclusive observables H.Stenzel

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Outline

Experimental Input measurement pseudo-observables

Determination of αs 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 αs

Results: Phys.Rep. 427 (2006) 257

ffZee /

PDG 2006

LEPEWG 2006


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Combined lineshape results

mZ 91.1876 ± 0.0021 GeV

ΓZ 2.4952 ± 0.0023 GeV

σ0had 41.540 ± 0.037 nb

R0l 20.767 ± 0.025

A0,lFB 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 universalitynot a unique choice of observables/assumptions

Most results dominated by experimental uncertainty,important common errors are:– LEP energy calibration: mZ , ΓZ, σ0

had

– Small angle Bhabha scattering: σ0had

– luminosity


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From measured cross sections...

1

/4 2

)(),()(sm

EWQED

f

sxsxdxHs Convolution of the EW cross section with QED radiator


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... to pseudo-observables

22,0

0

220

2 ,

4

3

12

AlVl

AlVlfle

lFB

ll

hadl

Z

hadee

Zhad

gg

ggAAAA

R

m

Partial widths and asymmetries are conveniently parameterised in terms of effective EW couplings .

Not independent observable but useful for αs

220 12

Z

lee

Zl m


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Partial width in the SM

QCDEWZqAZ

qV

lZ

qZCq

Z

llZ

Z

ll

Z

Z

llZl

mRmRgN

m

mg

m

mQ

m

m

m

/222

0

2

22

2

22

2

2

2

0

)()(||||

6)||1(

21

)(

4

31

41||

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

RA and Rv

factorizable EW x QCD corrections in the effective couplings Non-factorizable EW x QCD corrections

quarks-b MeV, 040.0

quarks-s d-, MeV, 160.0

quarks-c u-, MeV, 113.0/

QCDEW

MeV 945.82224

3

0

ZmG


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Sensitivity of partial widths and POs to αs

weak sensitivity for Γl

only through O(ααs) correctionsbest sensitivity for σ0

l

u,c

d,s

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)

ratio to αs=0.1185


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General structure of QCD radiators

)(

)()(

)()()(

)()()(

)()(

4

1)(

4

31

31

303

6

222

21

202

4

313

212

11

10

2

303

202

22

sCC

s

m

sC

sCC

s

m

sC

sC

sCC

s

m

sC

sC

s

ssQ

sQR

sq

ssq

sssq

sss

sqq

NNLO massless

NNLO mq

2/s

NLO mq

4/s2

LO mq

6/s3

In addition the effective EW couplings ρ and g incorporate mixed QCD x EW corrections i.e. O(α αs), O(α αs

2), O(G F m t2 αs)...


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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


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EW couplings dependence on αs

Very weak dependence on αs through the mixed corrections, e.g. running of α

)()()()(1

)0()(

)5( sssss

stlephad

00035.002758.0)( 2)5( Zhad musing here H.Burkhardt, B.Pietrzyk, PRD 72(2005)057501

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:

1. the NNLO part2. the quark mass corrections3. the mixed QCD x EW terms

What is their relative impact?

5.1GeV

7.4GeV

150GeV

175GeV

1875.91GeV

1185.0

0276.0

:here using

2

2)5(

c

b

H

t

Z

Zs

Zhad

M

M

m

m

m

m

m


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Global EW fits

Free parameters of the SM :

fits with ZFITTER / TOPAZ0

• Δα2had(mZ

2)• αs(mZ

2)• mZ

• mt

• mH

experimental input:• lineshape measurements• Δα2

had(mZ2)

• asymmetry parameters • heavy flavour measurements• top + W mass• 18 inputs, high Q2-set

74

49

2

2)5(

129GeV

9.35.178GeV

0021.01874.91GeV

0027.01188.0

00034.00276.0

H

t

Z

Zs

Zhad

m

m

m

m

m

Fit results:

χ2/Ndof : 18.3/13

w/o commonsystematic errorsno 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

C.L. % 95 @ GeV 285 GeV 114 Hm

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


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QCD uncertainties for αs from EW observables

Implementation of the renormalisation scale dependence in ZFITTER 1. running of αs(µ)2. running of the quark masses 3. explicit scale terms in the expansion

scccccR

n

i

n

sn

2

102221

ln e.g. ,

s

sxxL s

2 , ,ln

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

Evaluation of the PT uncertaintyfor the PO’s: scale variation

7.0ln7.0

2 2

1

x

x

Range of variation purelyconventional, but widely used.

Uncertainty for observable Odefined as:

)1(

)1()(

xO

xOxOO

Typical uncertainty ≈ 0.5 ‰ Depends obviously on αs .

partial widths

pseudo-observables


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dependence of the PO uncertainty on αs

Increase of the observablesuncertainty by a factor of ~2 for 0.11 < αs<0.13


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Evaluation of uncertainty for αs as obtained from an EW observable

Technique based on the uncertainty-band Method:

1. Evaluate the observable O for a given value of αs

2. calculate the PT uncertainties for O using xµ scale variation at given αs

3. the change of O under xµ can also be obtained by a variation of αs

4. the corresponding variation range for αsis assigned as systematic uncertainty

Uncertainty band method:

R.W.L. Jones et al., JHEP12 (2003) 007


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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


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Best strategy for αs

LEPEWG

5-parameter fit to 18 high Q2-data

αs=0.1188 ±0.0027 (nominal)

αs=0.1186 ±0.0029 (incl. QCD error)

1-parameter fit (αs) with all other SM parameters fixed to experimental values, mH=150 GeV

+ 0.0010 mH300 GeV

0011.00021.01202.0,,

0011.00027.01191.0,,

0010.00030.01187.0

0013.00037.01231.0

0006.00065.01076.0

0012.00041.01174.0

valuecentralPO

00

00

0

0

0

exp

llepZ

lhadZ

lep

l

had

Z

QCD

R

R

R


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Conclusion

Wealth of electroweak data from LEP and elsewhere allowsfor 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 beendetermined 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.

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

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Transcript of Α s from inclusive EW observables in e + e - annihilation Hasko Stenzel.