Event Shapes and Power Corrections in e e Annihilations

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Event Shapes and Power Correctionsin ee-
Annihilations

• Guenther Dissertori
• CERN , EP-Division
• DIS99, Berlin
• April 1999

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Outlook

• Introduction
• Variables
• Power corrections for
• mean values of event shapes
• distributions
• Comparison with MC corrections
• Shape Functions

Many of the results based on a study by
H.Stenzel, shown at Moriond QCD 99
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Introduction

• Observables in ee- -gt Hadrons receive
  non-perturbative corrections of the type 1/Qp,
  QECM
• fully inclusive observables (e.g. total
  x-section) p4
• semi-inclusive observables (e.g. event shapes)
  p1
• Non-pert. effects are sizeable for event shapes
  which are used for as measurements
• e.g. at LEP1 5-10
• Corrections obtained from Monte Carlo Models
• model dependence, systematic uncertainties
• New calculations of power corrections could lead
  to improvements in this respect

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Variables

• These are infrared and collinear safe variables
• standard event shapes for which predictions exist
  at 2nd order resummations of leading and
  next-to-leading logarithms

• T Thrust
• MH Heavy jet mass
• Bt Total jet broadening
• Bw Wide jet broadening
• C C-parameter
• y3 transition value between 2 and 3 jets
  (Durham)

• Available published(!) measurements
• For T and MH from 14 to 161 GeV
• PETRA,PEP,TRISTAN,LEP
• For Bw,Bt and C from 35 to 161 GeV
• PETRA,LEP
• Experiments
• TASSO,JADE,MARKII,HRS,AMY,TOPAZ,SLD,ALEPH,DELPHI,L
  3,OPAL

some preliminary measurements up to 189 GeV
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Experimental Technique
theoretical prediction ( parton level
) ? corrections for hadronization effects (via MC
or power laws)
Corrections ? Event Selection ? Data
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Predictions from pert. QCD

• theoretical uncertainties because of
  uncalculated higher orders
• ambiguity in the choice of the renormalization
  scale m2
• typically for the central values m2/s 1
• variation of the scale allows for estimation of
  these errors
• eg.
• Further ambiguity in the matching of the fixed
  order and
• resummation predictions -gt test several
  matching schemes

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In case of mean values.

• theoretical uncertainties because of
  uncalculated higher orders
• ambiguity in the choice of the renormalization
  scale m2
• typically for the central values m2/s 1
• no resummation !

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Power Laws
New Ansatz by Dokshitzer, Webber et al Power
corrections have their origin in infrared
divergencies in the perturbative expansion
(renormalons) when Q -gt L. In the calculations a
new phenomenological parameter is introduced
Separates pert. from non-pert. region,
typically set to 2 GeV
Parametrizes low-energy behaviour of the
coupling (i.e. soft gluon radiation)
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Power Laws for Mean Values
For mean values of event shapes one finds
2 , Thrust 1 , Mh 3p, C-par
Milan-factor _at_ 1.8
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Case of Broadening
Recent calculations have shown that in the case
of jet broadening the factor ax is not a
constant, but the non-perturbative
contribution becomes proportional to

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Latest results by Delphi
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Fit results
Stat.error
Scale error

• Note
• For ECMgtMZ, only DELPHI measurements are
  included in the fit
• Scale error determined by varying renorm. scale
  xm2/ECM2
• from 0.25 to 4.

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Similar results by Dokshitzer et al.
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Case of distributions
For Thrust, MH,Cpar exactly the same terms as
for mean values
For Broadenings shift depends also on the value
of the event shape
See hep-ph/9812487
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Broadening Distribution is shifted and squeezed
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Results

• Open questions
• quark (or hadron) mass
• effects
• difference of results
• obtained with MC and
• power corrections
• other variables
• -lny3
• EEC, AEEC

Related?
Milano group is working on it
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Other approach Shape functions
Korchemsky and Sterman (hep-ph/9902341) have
shown that the leading power corrections can be
resummed into non-perturbative shape
functions. The event shape distributions are
then given by a convolution of the perturbative
spectrum with those shape functions (done for
Thrust and Heavy Jet Mass)
Ansatz L 0.7 a 1.5
eg. for Thrust
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Conclusions

• Significant progress in the understanding of
  power corrections for event shapes in ee- has
  been made
• The universality of a0 is obtained at the level
  of 20 with improved calculations for the jet
  broadenings
• spread of as measurements obtained with MC and
  with power corrections has to be understood
• the interplay of power corrections and mass
  corrections has to be studied
• calculations for -lny3 and EEC are awaited for
• Shape function approach works nicely for thrust,
  not so well for heavy jet mass