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Event shape distributions at LEP

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Event shape distributions at LEP

Marek Taševský (Physics Institute Prague)

for all LEP collaborations

21 April 2006 KEK-Tsukuba, Japan

- 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) 1

L3: Phys.Rep.399 (2004) 71

OPAL: EPJC40 (2005) 287, PN519 (Preliminary)

Typical numbers

(ALEPH, 1994-2000)

Main background:

ISR for √s > 91 GeV

- reduced by requiring

- √s - √s,< 10 GeV
WW,ZZ->4 fermions

for √s > 2mW (2mZ)

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

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 emission

COLLINEAR SAFE: - not affected by replacing a parton by collinear

partons with the same total 4-momentum

3-jet observables: sensitive to non-collinear emission of single hard

gluon

4-jet observables: vanish in 3-jet limit

All quantities approach 0 in the 2-jet limit. In experiment, pure 0 is

never reached due to hadronisation.

Measurement of alphaS:

Based on fits of pQCD predictions to the corrected distributions of event

shape 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 axis nT chosen to

maximise the expression

1-T=0: 2-jet event

1-T=1/2: spherical event

Thrust major axis n

chosen to maximise the

expression and to be

orthogonal to nT

Tmaj = 0: 2-jet event

Tmaj =1/2: spherical event

Tmin =0: 2-jet event

Tmin =0: 3-jet event

Tmin =1/2: spherical event

- 4-jet observable

O=0: 2-jet and spherical event

O=Tmajfor 3-jet events

Quadratic momentum

tensor:

has three eigenvalues ordered

such that λ1 < λ2 < λ3. Being

quadratic in pα,β, Sαβis not IR

safe.

Sphericity

cannot be predicted reliably in

pQCD

S=0: 2-jet event

S=1: spherical event

Sphericity tensor

has three eigenvalues ordered

such that λ1 < λ2 < λ3. Being

quadratic in pα,β, Sαβis not IR

safe.

Aplanarity

cannot be predicted reliably in

pQCD

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

- 4-jet observable

Linearised momentum tensor

-linear in pα,β => it is IR safe.

-has three eigenvalues ordered

such that λ1 < λ2 < λ3. M has unit

trace => λ1 + λ2 + λ3 = 1. We can

thus form two indep. combinat.:

2ndFox-Wolfram moment

C low: planar event (one of λ=0)

C=1: isotropic event (λ1=λ2=λ3=1/3)

Linearised momentum tensor

-linear in pα,β => it is IR safe.

-has three eigenvalues ordered

such 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

So far, the variables have been constructed as global

sums over all particles in the event. From now, let’s split

the event into two hemispheres H1 and H2, divided by

a plane orthogonal to the thrust axis.

Invariant mass:

Jet broadening:

- never zero due to finite masses of individual particles

ML=0: 2-jet and 3-jet

events

- 4-jet observable

- never zero due to finite masses of individual particles

BW=0: 2-jet events

to O(alphaS):

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

Spherical event:

BW=BN=π/16

BT=0: 2-jet events

to O(alphaS):

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

Spherical event:

BT=π/8

The aim of jet algorithms is to group particles together such that the

directions and momenta of partons are reconstructed. The jet algos

include 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+pjand 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]

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 LEP

have y23 < 10-3.

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

Another way to study the event

structure – through moments:

Ymax is the max.kinematic. allowed value of observable

Moments always sample all of

available phase space:

Lower moments are dominated by

2- and 3-jet events

Higher moments are dominated by

multi-jet events

All LEP collaborations presented final measurements of event

shape observables and their moments for all available data

(√s = 91-209 GeV).

Satisfactory description of data by Pythia, Herwig and

Ariadne achieved. Discrepancies observed for LEP1 data

in the extreme 2-jet region and for observables sensitive

to 4+ -jet production.