Α s from inclusive ew observables in e + e - annihilation hasko stenzel
TRANSCRIPT
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
alpha_s and quark masses Inclusive observables H.Stenzel
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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
alpha_s and quark masses Inclusive observables H.Stenzel
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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)...
alpha_s and quark masses Inclusive observables H.Stenzel
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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
alpha_s and quark masses Inclusive observables H.Stenzel
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Sensitivity to the Higgs Mass
alpha_s and quark masses Inclusive observables H.Stenzel
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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
alpha_s and quark masses Inclusive observables H.Stenzel
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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.