Report from the LEP QCD Working Group

Roger Jones

Lancaster

6.3.2003

CERNSwitzerland

Outline

• Short report of Working Group

• Annihilations groups from Event shapes

• Systematic errors

• Combination

• Open Questions and future

Introduction...

Group formed in 1996 primary focus on event shapes

group formed in 1997 early focus on model building & structure functions

Other QCD topics in other groups e.g. Colour Reconnection in W group

Both groups have achieved success with limited and reducing manpower resources

The Working Group

• Hoped to combine photon structure functions• This presupposed very basic agreement on

distributions – experiments apparently disagreed makedly– Input to model builders– Improved background estimates for other physics

channels

• After much work, the differences were resolved and a paper was produced– Eur. Phys. J.C23(2002) 201-223 .

Sadly, this is not enough for a structure function combination – the four analyses are so different and the manpower so short, the group has reached a natural end

The Annihilations Group

The of s

Current active members: H Stenzel, M Ford, D Wicke, G Salam, S Banerjee, RWLJ + others in the past

Annihilations Working Group

• Combination of s measurements and checks of consistency (paper in draft)

• Combination useful @ LEP II (stat. poor but theory uncertainties smaller)

Comparable exptl. systematic estimationCommon theory implementation, common

understanding of matching schemes, modification schemes and kinematic limits

Exploration of theory uncertainties and common treatment (paper in draft)

Event Shapes :

e+

e-

Z/*

q

q

gs

Born x-section for Z qq

gluon

s

gluon

qqg

EdE

d 1

20

“Bremsstrahlung”

)(ln)(2)()()()(1 3

2

2

0222

0s

CMss O

ExAxBxA

dx

d

Calculable for so-called “infrared and collinear safe““infrared and collinear safe“ variables,

Cancellation of singularities in the radiative corrections

Examples: Thrust, C-Parameter, broadenings….

General Structure of the cross-sectionIn NLO:

• In the 2 jet region it is necessary to re-sum all logarithms of the type s

n (ln 1/x)2n, sn(ln 1/x)n

• A better prediction combines the NLO with the re-summed predictions

• E.g.

• uncertainties: consistent codes, matching schemes, modifications (to restore physical limits in distributions) & renormalization scales QCD Working Group

Perturbative Predictions

2/)()()(

)()()(ln

2

323

222

221211

21

xAxBxA

LGLGLGLG

LgLgLx

ss

ss

ss

2/)()()(

)()()(ln

2

323

222

221211

21

xAxBxA

LGLGLGLG

LgLgLx

ss

ss

ss

L = -ln x

All levels of prediction mentioned violate the physical boundsThese can be restored by modification schemes

There are various possibilitiesThis lead to confusion in earlier LEP results, now resolved

Through the working group we have now standardised method and associated parameters

Experimental Procedure• Calculate perturbative predictions• Calculate the hadronization corrections using

Monte Carlo (JETSET,HERWIG,ARIADNE)Common level• Correct to the hadron level accounting for

acceptance, resolution, ISR etc. (`Detector corrections’)

• Measure the distributions from data

• Observables : T, Mh2, Cpar, Btot, Bw, lny3 , ...

Dat

aT

heo

ry

Many available measurements :Measurements usingMeasurements using

Data from 2000Data from 2000

Consider thevarious contributing

uncertainties…

s(206) = 0.1054 0.0028(exp) 0.0038 (theo)s(206) = 0.1054 0.0028(exp) 0.0038 (theo)

s(MZ) = 0.1183 0.0023(exp) 0.0043 (theo)s(MZ) = 0.1183 0.0023(exp) 0.0043 (theo)

Combination of the 6 observables

Uncertainties (ALEPH 206 Example) :

• Experi. : 0.0028

• Theory : 0.0038

0.0022 stat0.0022 stat

0.0017 model dep.0.0017 model dep.

0.0016 matching0.0016 matching

Use different MC To calculate acceptance etc

0.0034 scale0.0034 scale

0.0007 hadronization0.0007 hadronization

0.0001 quark masses0.0001 quark masses

Theory ErrorTheory Error

• Dominates at all energies, origin missing higher orders – NNLO and NNLLA predictions would give a better partial answer, if available

• Traditional approach – variation of renormalisation scale x=/Q in the fit

– WG standardised to range 0.5-2. (conventional but arbitrary)

– Size of resultant error is smaller for observables with worse 2 fit, contrary to expectations!

– December 01 workshop with theorists to discuss the issue

Proposal - xProposal - xLL Variation Variation

• Replace terms in ln(1/x) with ln(1/ xL.x)– Should test a different set of higher orders

• How to set the range? Many ideas tried– Vary xL to match the difference between O(s

2) calculations with O(s

2) expansion of NLLA expansion Depends on range, cannot always match the change – For fixed s, fit with standard x variation and xL=1, then

refit with xL free and symmeterizeStable under change of fit rangeComplementarity in regions where x and xL important– Can choose xL to set various terms in expansion to zero– A priori range, 2/3 < xL< 3/2 roughly supported

Matching and Modification Scheme Matching and Modification Scheme Uncertainties?Uncertainties?

• Difference between mod. LogR and mod. R matching taken as standard

Also, consistent modification scheme uncertainties

• Difference between modification limits derived from parton shower MC and 4-parton ME boundary

• Difference between linear and second quadratic modification

Treatment of Theory UncertaintiesTreatment of Theory Uncertainties

• Theoretical errors scale with s3 (prediction & practice)

s value and its uncertainty are correlated, so potential bias towards downwards fluctuations

Uncertainties done centrally– Measured s(MZ) used @ MZ for uncertainties and S run upwards for LEP II

•All theory uncertainty sources define an envelope•Any source can determine maximum uncertainty in bin•Corresponding s

found that just `kisses’ the resulting envelope.

Uncertainty band estimation of overall errorUncertainty band estimation of overall error

Hadronization uncertainties• Much less important than `theory’ uncertainties• Hadronization surprisingly inconsistent between

models and between experiments• Estimate uncertainty by observing result of

changing between JETSET/HERWIG/ARIADNE– Surprisingly little correlation

• Different implementations of models and tunings• Different fit ranges

• Ambiguities in definition of hadron level (neutrinos included? Before weak decays?) Resolved, small effect

• Difference mainly at parton level tuning

CombinationCombination

• We tried to do a detailed, fully-correlated combination a la LEP EW WG

• Bottom line – the method is unstable, giving negative weights in many cases Need impossible accuracy to errors with 194x194 covariance matrix

to be inverted, though improved with standardised theory errors Small contributions (not well controlled) are important in the

inversion (classic regularisation problem)

• Correlations are important regardless of the combination method

• Most important correlation is the theory correlation, which is large but hard to estimate

Safer Half-way StrategySafer Half-way Strategy

• Uncertainty band used for the theory error• Use stat. and exp. covariance & theory and rms of

experiments had. uncertainties on-diagonal central value and weights, and the stat. and exp. uncertainties

• Repeat average with different hadronization models assumed and take rms for final hadronisation uncertainty

Takes most of correlations into account Is stable and shares weight between LEP 1&2Better than previous estimates because of

improved inputs and stat. correlation estimates

Construction of Covariance Matrix and Construction of Covariance Matrix and UncertaintiesUncertainties

Combinations by ObservableCombinations by Observable

By Energy• Using only LEP• Several measurements

preliminary• Mean value is stable• LEP I:

s(MZ) =0.1197

0.0002(stat) 0.0008(ex) 0.0010(had)0.0048(th)• LEP II:

s(MZ) =0.1196

0.0005(stat) 0.0010(ex) 0.0007(had)0.0044(th)

All-energies does notbeat LEP II becausehigh correlation oftheory uncertainty

Combine at each Q to investigate the running

2/dof = 11.6/13

Conclusions• Each LEP (I and II) has made important contributions in

measuring s and the current precision

Big improvements in theory implementation and uncertainty estimation

Improved combination of results

• Hopes for the future…– Power law corrections– NNLO calculations on the horizon?– We will continue with `best effort’, but will archive for future re-analysis