Event shape distributions Event shape distributions at LEPat LEP

Marek Taševský (Physics Institute Marek Taševský (Physics Institute Prague)Prague)

for all LEP collaborationsfor all LEP collaborations

21 April 2006 KEK-Tsukuba, Japan21 April 2006 KEK-Tsukuba, Japan

OutlineOutline- Data samples and Event selection

- Definitions & Properties of Event shape observables

- Event shape observables at LEP1 and LEP2 energies

The LEP alphaS measurement itself covered by T.Wengler

ALEPH: EPJC35 (2004) 457 DELPHI: EPJC37 (2004) 1L3: Phys.Rep.399 (2004) 71OPAL: EPJC40 (2005) 287, PN519 (Preliminary)

Data samples and Event selectionData samples and Event selection

Typical numbers (ALEPH, 1994-2000)

Main background: ISR for √s > 91 GeV- reduced by requiring

- √s - √s, < 10 GeV

WW,ZZ->4 fermionsfor √s > 2mW (2mZ)

Ecm Lumi Nev BG

[GeV] [pb-1] [%]

91 41 > 106 < 1

133 12 806 < 1

161 11 319 5

172 10 257 10

183 57 1319 12

189 174 3578 13

200

206

208

216

3528

3590

15

15

Correction procedureCorrection procedure

1.Select hadronic event candidates

2.Construct distributions from tracks and clusters (avoid

double counting)

3.Subtract bin-by-bin residual 4f-bg using grc4f and KORALW

4.Correct data bin-by-bin for effects of detector acceptance, resolutions and residual ISR

using MC models. Justified by a good description of data and correlation between hadron and det.levels

Properties of event shape observablesProperties of event shape observables

To make exper.tests of pert.QCD and to measure alphaS, we define

physical observables that are sensitive to the HE pert.process but

little sensitive to subsequent non-pert. hadronisation and decays.

INCLUSIVE: - characterize geometry of event (2-jet or pencil-like, 3-jet or planar, 4+ -jet or spherical) - non-identified particles - only p and E needed to know

pQCD ME diverge for process involving soft or collinear gluon emission

Hence pQCD applicable only for quantities that are INFRA-RED SAFE: – not affected by soft gluon emissionCOLLINEAR SAFE: - not affected by replacing a parton by collinear

partons with the same total 4-momentum

Properties of event shape observablesProperties of event shape observables3-jet observables: sensitive to non-collinear emission of single

hard gluon4-jet observables: vanish in 3-jet limitAll quantities approach 0 in the 2-jet limit. In experiment, pure 0 isnever reached due to hadronisation.

Measurement of alphaS:Based on fits of pQCD predictions to the corrected distributions of eventshape observables.

Standard set of observables is {1-T, MH, C, BT, BW, y23}. But let’s

look at more of them. As theory predictions exist at parton level, they need to be corrected to

hadron level by applying hadronisation corrections.

For details about the alphaS measurement, see talk by T.Wengler

Thrust Thrust

Thrust axis nT chosen to

maximise the expression

1-T=0: 2-jet event

1-T=1/2: spherical event

Thrust major Thrust major

Thrust major axis nchosen to maximise theexpression and to be orthogonal to nT

Tmaj = 0: 2-jet event

Tmaj =1/2: spherical event

Thrust minor Thrust minor

Tmin =0: 2-jet event

Tmin =0: 3-jet event

Tmin =1/2: spherical event

- 4-jet observable

Oblateness Oblateness

O=0: 2-jet and spherical event

O=Tmaj for 3-jet events

Sphericity Sphericity

Quadratic momentumtensor:

has three eigenvalues orderedsuch that λ1 < λ2 < λ3. Being

quadratic in pα,β, Sαβ is not IRsafe.

Sphericity

cannot be predicted reliably inpQCD

S=0: 2-jet event S=1: spherical event

Aplanarity Aplanarity

Sphericity tensor

has three eigenvalues orderedsuch that λ1 < λ2 < λ3. Being

quadratic in pα,β, Sαβ is not IRsafe.

Aplanarity

cannot be predicted reliably inpQCD

A=0: 2-jet and 3-jet event- 4-jet observable

C- parameter C- parameter Linearised momentum

tensor

-linear in pα,β => it is IR safe.-has three eigenvalues orderedsuch that λ1 < λ2 < λ3. M has unit

trace => λ1 + λ2 + λ3 = 1. We can

thus form two indep. combinat.:

2nd Fox-Wolfram moment

C low: planar event (one of λ=0) C=1: isotropic event

(λ1=λ2=λ3=1/3)

D- parameter D- parameter Linearised momentum

tensor

-linear in pα,β => it is IR safe.-has three eigenvalues orderedsuch that λ1 < λ2 < λ3. M has unit

trace => λ1 + λ2 + λ3 = 1. We can

thus form two indep. combinat.:

D=0: 2-jet and 3-jet event D=1: isotropic event

(λ1=λ2=λ3=1/3)

- 4-jet observable

Hemisphere observablesHemisphere observables

So far, the variables have been constructed as global sums over all particles in the event. From now, let’s

splitthe event into two hemispheres H1 and H2, divided by

a plane orthogonal to the thrust axis.

Invariant mass:

Jet broadening:

Heavy jet mass Heavy jet mass

- never zero due to finite masses of individual particles

Light jet mass Light jet mass

ML=0: 2-jet and 3-jet

events- 4-jet observable

- never zero due to finite masses of individual particles

Wide jet broadening Wide jet broadening

BW=0: 2-jet events

to O(alphaS):

BW=BT=1/2Tmaj=1/2O

Spherical event:

BW=BN=π/16

Total jet broadening Total jet broadening

BT=0: 2-jet events

to O(alphaS):

BW=BT=1/2Tmaj=1/2O

Spherical event:

BT=π/8

JetsJetsThe aim of jet algorithms is to group particles together such that thedirections and momenta of partons are reconstructed. The jet algosinclude at least one free resolution parameter and Njets depends on its

chosen value.

Durham (or kT) algo defines “scaled transverse momentum” for every

pair of particles: .

The pair with the smallest yij is then replaced by a pseudoparticle

with pij=pi+pj and Eij=Ei+Ej (E-recomb.scheme; two other exist:

P-scheme: Eij=|pi+pj| and E0-scheme: |pij|=Ei+Ej). This is

repeated until all pairs have yij>ycut (fixed value). Remaining

pseudoparticles represent jets.

[small ycut => many jets; large ycut->1.0 => 1 jet]

yy2323 – 2 to 3 jet transition – 2 to 3 jet transition

Measure of how ‘3-jetlike’event is.

Y23 : the highest ycut value

for which the event is resolved into 3 jets.

Events with Njet≥3 have large

y23 values (max. y23=1/3 for

3 identical jets 120° apart),while 2-jet events at LEPhave y23 < 10-3.

Event shapes in radiative hadronic eventsEvent shapes in radiative hadronic events

Measure event shape observables for a boosted qq system after final-state photon radiation.

√s=91 GeV reduces to 20-80 GeV.

Bg from non-rad. events:5% (√s=78GeV) - 15% (√s=24GeV)

- alphaS from radiative events

measured by L3 and OPAL – results

consistent with that from non-rad.events

MomentsMomentsAnother way to study the

eventstructure – through moments:

Ymax is the max.kinematic. allowed value of observable

Moments always sample all ofavailable phase space:

Lower moments are dominated by

2- and 3-jet eventsHigher moments are

dominated by multi-jet events

SummarySummaryAll LEP collaborations presented final measurements of

eventshape observables and their moments for all available

data (√s = 91-209 GeV).

Satisfactory description of data by Pythia, Herwig andAriadne achieved. Discrepancies observed for LEP1 data in the extreme 2-jet region and for observables sensitiveto 4+ -jet production.