event shape distributions at lep
DESCRIPTION
Event shape distributions at LEP. Marek Taševský (Physics Institute Prague) for all LEP collaborations 21 April 2006 KEK-Tsukuba, Japan. Outline. - Data samples and Event selection - Definitions & Properties of Event shape observables - Event shape observables at LEP1 and LEP2 energies - PowerPoint PPT PresentationTRANSCRIPT
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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
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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)
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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
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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
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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
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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
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Thrust Thrust
Thrust axis nT chosen to
maximise the expression
1-T=0: 2-jet event
1-T=1/2: spherical event
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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
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Thrust minor Thrust minor
Tmin =0: 2-jet event
Tmin =0: 3-jet event
Tmin =1/2: spherical event
- 4-jet observable
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Oblateness Oblateness
O=0: 2-jet and spherical event
O=Tmaj for 3-jet events
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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
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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
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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)
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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
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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:
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Heavy jet mass Heavy jet mass
- never zero due to finite masses of individual particles
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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
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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
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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
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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]
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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.
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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
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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
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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.