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Event shape distributions at LEP

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

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Event shape distributions at LEP

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  1. Event shape distributions at LEP Marek Taševský (Physics Institute Prague) for all LEP collaborations 21 April 2006 KEK-Tsukuba, Japan

  2. Outline - 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)

  3. Data 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 fermions for √s > 2mW (2mZ)

  4. Correction 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

  5. Properties 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 emission COLLINEAR SAFE: - not affected by replacing a parton by collinear partons with the same total 4-momentum

  6. Properties of event shape observables 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

  7. Thrust Thrust axis nT chosen to maximise the expression 1-T=0: 2-jet event 1-T=1/2: spherical event

  8. Thrust major 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

  9. Thrust minor Tmin =0: 2-jet event Tmin =0: 3-jet event Tmin =1/2: spherical event - 4-jet observable

  10. Oblateness O=0: 2-jet and spherical event O=Tmajfor 3-jet events

  11. Sphericity 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

  12. Aplanarity 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

  13. C- parameter 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)

  14. D- parameter 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

  15. Hemisphere observables 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:

  16. Heavy jet mass - never zero due to finite masses of individual particles

  17. Light jet mass ML=0: 2-jet and 3-jet events - 4-jet observable - never zero due to finite masses of individual particles

  18. Wide jet broadening BW=0: 2-jet events to O(alphaS): BW=BT=1/2Tmaj=1/2O Spherical event: BW=BN=π/16

  19. Total jet broadening BT=0: 2-jet events to O(alphaS): BW=BT=1/2Tmaj=1/2O Spherical event: BT=π/8

  20. Jets 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]

  21. y23 – 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 LEP have y23 < 10-3.

  22. Event 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

  23. Moments 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

  24. Summary 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.

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