Measurement of α s at NNLO in e+e- annihilation Hasko Stenzel, JLU Giessen, DIS2008.

Measurement of αs at NNLO in e+e- annihilation

Hasko Stenzel, JLU Giessen, DIS2008

alpha_s at NNLO H.Stenzel, JLU Giessen DIS2008 2

QCD processes in e+e- annihilation

leptonic initial state, EW interaction

hadronic final state

perturbative & non-perturbative effects

ideal testing ground for QCD

(almost) precision measurements of QCD parameters & properties


hard gluon radiation 3-jet events

Most prominent manifestation of QCD in e+e- : 3-jet events, hard gluon radiation

Cross section directly proportional to αs / gqqZee

TASSO 1979 OPAL 2000


Event-shape variables

Global observables sensitive to (multi)-gluon radiation, defined infrared-and collinear-safe, experimentally robust, receiving small hadronisationcorrections (1/Q).

jet 3jet 2parameter resolutionjet

broadeningjet total

,max||2

||broadeningjet wide

seigenvalue 3||||

1Parameter

,max1

massjet Heavy

||

||maxThrust

3

21

21

212121

2

2

2

1

2

2

2

y

BBB

BBBp

npB

Cp

pp

pC

MMMpE

M

p

npT

T

W

jj

HkTk

i

ii i

ii

ii

HHk

k

vis

i

ii

iTi

n

i

i

T

30-50% correlation between variables


Theoretical predictions : Pre-NNLO state of art

Standard analysis at LEP using NLO + NLLA predictions

)(2

)(2

12

XBXAdX

d ss

1

, )/1log(

exp,

0

21

dzdz

dσ

σX,αRXL

LgLLgFXRx

xs

ssss

matchingNLLAorder fixed RRRR

pure NLO

resummation of leading and next-to-leading logs to all ordersNLLA

matched predictions combining fixed order and resummed

calculations with subtraction of double-counting terms


LEP combination of αs from event shapes at NLO+NLLA

radiative events

th

hadexp

statZs M

0047.0

0013.00009.0

0003.01202.0

LEPQCDWG combination

Preliminary!


NNLO calculation

extremely challenging

calculation careful subtraction of real and

virtual divergencies subtraction obtained by antenna

method implemented in the EERAD3

integration program numerical integration requires

heavy CPU non-negligible statistical

uncertainties

A.Gehrmann-De Ridder, T.Gehrmann, E.W.N Glover, G.Heinrich JHEP 0711:058, JHEP 0712:094, 2007

nsubtractio virtualloop-2:

nsubtractio virtualloop-1 :

nsubtractio real :

2,

1,

2,1,

1,1,

345

4

5

V

VS

S

d

V

d

VS

d

S

d

VSV

d

SR

NNLO

d

d

d

ddd

dd

ddd


Theoretical predictions for event-shape distributions at NNLO

)(2

)(2

)(2

132

XCXBXAdX

d sss

For a generic event-shape variable X=T,MH,BT,BW,C, Y3

Normalisation for σ

2

0 246.049.7

221

s

fs

had N

Renormalisation scale dependence

21

2220

20

20

122

2

22

loglog)(log)(2)()(

, log)()()(

2 NNLO ,2

xxXAxXBXCXC

sxxXAXBXB

id

d

i

i

sis

s

NNLO term


Analysis outline for αs at NNLO

Use the public ALEPH data A. Heister et al., EPJC 35 (2004) 457 on event shapes (T, MH, BW, BT, C, y3 )

follow closely experimental procedure applied by ALEPH

data are corrected to hadron level using MC corrections accounting for ISR/FSR QED radiation and background

data are fit by NNLO perturbative prediction, including NLO quark mass corrections, folded to hadron level by MC generators

combine 6 variables and 8 data sets (LEPI + LEPII)

prediction theory :1

ondistributi data :

,

/

,

hadNLO

massiveb

NNLO

masslessb

correctedth

detFSRISRbackgroundrawcorrectedexp

Cdy

dR

dy

dR

dy

d

CCdy

d

dy

d

dy

d


LEP data

At LEPI: selected high quality Z0 peak data validated standard correction scheme

At LEPII: special cuts for ISR suppression 4-fermion background subtraction limited statistics (10k events)

ALEPH data set at LEPII


Hadronisation corrections

Perturbative predictions are fold to hadron level by means of a transition matrix partons->hadrons computed with Monte Carlo Generators

– PYTHIA6.1– HERWIG6.1– ARIADNE4.1– parton shower / color dipole– string/cluster fragmentation– all generators tuned to LEP1 data

Generator tuning is essential, in ALEPHup to 16 model parameters were tuned to 12 observables (event-shapes and inclusive charged particle distributions)

– Next generation generators combining NLO+PS have not been tuned and are not used here


Theoretical predictions: quark mass corrections

masslessonly )(

)(

)()( , )(for idem

),()(),()(1),(

XC

qqZ

bbZQRXB

QXAQRQXAQRQXA

b

massivebmasslessb

Corrections for heavy quarks at NLO, relevant at LEPI

For heavy quarks gluon radiation is suppressed by mass effects

– was used to measure the running b-quark mass

– applied as correction for αsfits

3-jet rate b/d-quarks


NNLO fits to the data

data are fit in the central part of event shape distributions only statistical uncertainties are included in the χ2

LEP II

LEP I

fit range

G.Dissertori,A.Gehrmann-De Ridder,T.Gehrmann, E.W.N Glover, G.Heinrich,HSJHEP 0802:040, 2008


NNLO fits to the data

clear improvement of NNLO over NLO

good fit quality (but includes still large statistical uncertainties for C-coefficient)

extended range of good description (3-jet region)

matched NLO+NNLA (resummation) still yields a better prediction in the 2-jet region

value of αs is rather high...

... but decreases from NLO to NNLO


Perturbative uncertainty: scale dependence

0.25.0 x

range of variation

scale uncertainty reduced by a factor of 2 from NLO to NNLO NNLO about 30% better than NLO+NLLA fits with free scale don’t improve description of data at NNLO

Thrust -log(y3)


NNLO results at LEPI

consistent results at NNLO

scattering between variables much reduced

independent check of theoretical uncertainties

αs(MZ)

0033.0RMS 0083.0RMS 0045.0RMS


Evaluation of perturbative uncertainty

Technique based on the uncertainty-band Method to estimate the impact of missing higher orders:

1. Evaluate distribution of event shape O for a given value of αs with a reference theory (here NNLO, xµ=1)

2. calculate the PT uncertainties for O (xµ variation) ->uncertainty band

3. fill the uncertainty band with the nominal prediction by varying αs

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

In addition, an uncorrelated uncertainty is evaluated for the b-quark mass correction, available only at NNLO. This uncertainty amounts to ≈1%.

Uncertainty band method:

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


Fit results & systematic uncertainties

experimental systematics evaluated according to the ALEPH procedure

hadronization: difference between PYTHIA, HERWIG and ARIADNE experimental: dominant sources

LEPI: modeling energy flow , <1% LEPII: ISR corrections


Fit results at LEPII and the running of αs


Combination of αs(MZ)

This analysis NNLO ALEPH NLO+NNLA

Data set LEP1+LEP2 LEP2 LEP1+LEP2 LEP2

αs(MZ) 0.1240 0.1238 0.1214 0.1217

Stat.error 0.0008 0.0009 0.0009 0.0010

Exp.error 0.0010 0.0011 0.0011 0.0012

Pert.error 0.0029 0.0028 0.0045 0.0044

Hadr.error 0.0011 0.0010 0.0011 0.0010

Total error 0.0033 0.0033 0.0048 0.0048

Calculate a weighted average for αs(Q) from 6 variables at each energy

Repeat systematics for the weighted average Evolve measurements at LEPII to Q= MZ

Calculate the combination of 6 variables and measurements at 8 energies

2

6

1

1 ,

i

ii

i

sis ww


Conclusion

A new analysis of αs from event shapes at NNLO is presented:

αs(MZ)=0.1240 ± 0.0033

• major achievement in NNLO calculations

• substantial improvement over NLO and NLO+NNLA

• competitive results compared to other processes

• our result for αs is ‘somewhat high’ compared to other measurements ....

Further improvements in near future can be expected

• matching of NLLA (or higher) large logs resummation to all orders to NNLO (see talk of G.Luisoni)

• inclusion of electroweak corrections to event shapes, not factorizable on σhad

• hadronisation corrections from modern NLO+PS Monte Carlo generators


BACK UP


Global QCD observables

ijsJij

EEy ji cos122

,min2

Jet rates defined accordingto a given algorithm e.g.Durham

Event-shape distributions used to extract αs

A.Gehrmann-De Ridder et al., hep-ph 0802.0813 A.Gehrmann-De Ridder et al.,

JHEP 0712:094,2007

Measurement of α s at NNLO in e+e- annihilation Hasko Stenzel, JLU Giessen, DIS2008.

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Transcript of Measurement of α s at NNLO in e+e- annihilation Hasko Stenzel, JLU Giessen, DIS2008.