Gnther Dissertori

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What have we learnt about QCD at LEP?

• Günther Dissertori
• ETH Zürich
• Laboratoire de Physique Corpusculaire de
• Clermont-Ferrand, 21.2.2003

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LEP 1989 - 2000
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Anatomy of the process ee- Z Hadrons
Quantum Chromo Dynamics
pert.
MZ
Scale ? R(proton)
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Outlook

• Introduction
• Measurements of
• Measurement of the b-quark mass
• Transition pert./non-pert. regime
• Hadronization/Particle correlations
• Not covered colour factor measurements, gluino
  limits, detailed studies of particle production,
  Monte Carlo models, photon-photon interactions,
  ...

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Introduction
before LEP...
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Introduction
The huge statistics (4 million events per
experiment) has allowed a plethora of detailed
studies of pert. and non-pert. QCD.
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Part 1 Studies of perturbative QCD
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Measurements of the strong coupling constant

• from inclusive observables
• (counting experiments)
• from semi-inclusive observables
• (distributions of topology-dependent variables)

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as from inclusive Z or t decays
quarks hadrons
q
q
q
1
...


q
q
q
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Higher Order Corrections
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R from Z decays
Hadrons
Rl
Muons
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Rt Study the decay Z to tt-
e
t-
Z
t
e-
Rt
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Hadronic mass spectrum
s(invariant mass)2 of hadronic decay products
r resonance
?s from moments of this distribution
pp
ppp
s (GeV/c2)2
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Without phase space factor and taking moments, in
order to average out resonances
Rt(non-strange states)
only quarks, no gluons
Example non-strange moments Rt00 3.484
0.024 Rt12 0.203 0.003
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Results

• Rl as(mZ) 0.123 0.005
• Rt as(mt) 0.323 0.030
• as(mZ) 0.118 0.003

energy evolution
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Less inclusive quantities Event Shapes, Jet
Rates
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General Structure of the Cross Section
Calculable for the class of observables,
which are infrared and collinear safe,
i.e. IR-singularities from real and virtual
radiative corrections cancel
Examples Jet Rates, Thrust, C-Parameter, .
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Example Thrust (invented around 1978, used at
Petra/DESY)
Thrust Axis parallel to vector n for which
maximum is obtained
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Z decays
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Thrust..
1/2
1
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Results from NLO Fits

• First measurements showed
• indication that missing higher order terms are
  large
• typical results
• as(Mz) 0.120 /- 0.010
• (0.115 - 0.130)

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An attempt to calculate higher order
correctionsResummation of Large Logs
Example Jet Rates
Have to define resolution criterion in order to
distinguish particles (and finally) jets
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Perturbative Predictions
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Resummation of logarithmic terms in all orders of
pert. theory
For a particular class of observables it is
possible to resum log. terms in all orders of
pert. theory
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Example Recent result by OPAL
Analysis of ee- data from 35 GeV
JADE to 91 GeV OPAL, LEP1 to 189 GeV
OPAL, LEP2
as(Mz) 0.1187 0.0034-0.0019
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Very recently new analysis by ALEPH using the
4-jet rate

• predictions known at NLO resummation
• note
• ALEPH
• as(Mz) 0.1170 ? 0.0001 (stat)
• ? 0.0009 (exp)
• ? 0.0003 (had)
• ? 0.0008 (scale)
• 0.1170 ? 0.0013

fit range
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World Average( summary by S.Bethke,
hep-ex/0211012)
LEP
DIS, HERA
PETRA/PEP
SPS, TEVATRON
LEP
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The of as
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Measurements of the b-quark mass
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What is mq?

• Two schemes
• Running mass scheme ( )
• The mass is a renormalizable parameter in the
  Lagrangian, depends on renormalization scheme and
  scale
• Pole mass scheme
• The mass is defined as the position of the
  pole of the quark propagator, does not depend on
  a scheme or scale

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• In inclusive quantities at high energies you
  dont see an effect

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Idea of the measurement

• 1) Charged particles radiate if accelerated
• 2) Under the influence of the same force, heavier
  particles are less accelerated than lighter ones
  
• F m a

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The Theory
Dynamical as well as phase space effects
reduce radiation in b-quark events
1 for incl. Obs. b0 gtgt
1 for semi-incl. Obs. e.g.
3-jet rate
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The Measurements

• The ratio of 3-jet rates in b- over uds-events
  has been measured
• have to apply b-tagging
• After corrections one gets a value at the parton
  level

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The Measurements

• First measurement by DELPHI
• they deduced
• then ALEPH, OPAL, SLD
• eg. ALEPH

Running established
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Resumé Studies of perturbative QCD

• consistent as measurements obtained from
      various processes, precision at the 1-2
  level
• uncertainties dominated by theoretical
      uncertainties. Need at least NLO. Resummation
      calculations established
• strong motivation for theorists to invest
  efforts in     NNLO and resummation calculations
  and their     Monte Carlo implementations.
  Useful also for     future colliders

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Part 2 Transition of pert. to non-pert. regime
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Quark vs. Gluon Jets
Simply from couplings one expects a larger
multiplicity in gluon jets of the order CA/CF
9/4 , and a softening of the momentum
distributions for particles coming from the
gluon jet. Also the scaling violations, ie.,
change of multiplicities with scale are different.
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Observations

• Experimental evidence that relevant scale for jet
  comparison is some transverse momentum like
  scale, but not eg. Ejet

• Gluon jets have larger hadron multiplicities than
  quark jets, but lower than naive expectation
  CA/CF9/4

• Gluon jets have softer spectrum. But beware
  b-jets are again similar to gluon jets...

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Inclusive Hadron multiplicity

• pQCD including colour coherence effects, is able
  to describe correctly the energy evolution, up to
  an overall factor a (LPHD)

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Resumé Transition pert. to non-pert. regime

• gluon jets have larger hadron multiplicities
  and     softer hadron spectra than quark jets.
• BUT it is important to use the correct scale
  to     compare different jets. Simply using jet
  energy is     not correct.
• pQCD LPHD can describe certain quantities at
      the hadron level.  Important that coherence
      effects are included in calculation of
  multi-gluon     radiation.

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Part 3 Hadronization
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Tests of phenomenological models
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Models
Parameters have to be adjusted using data!
String Fragmentation ? JETSET/PYTHIA
Cluster Fragmentation ? HERWIG
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Hadron Momentum Distributions
Inclusive
p/pbeam
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Hadron Momentum Distributions
Pions
Kaons
Protons
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Bose-Einstein Correlations
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Theory

• Wave function of like-sign pion pairs should be
  symmetric, ie. obey Bose-Einstein statistics
• Measure for like-sign pion pairs the following
  correlation function (Qmomentum difference)

• Assuming the pion source is gaussian, spherically
  symmetric (further assumptions...), fit this
  simple parametrization

• Obtain thus information on the source size R

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1-dim. Analysis

• However
• measured parameters depend on the details of the
  analysis, eg. choice of (uncorrelated) reference
  sample
• detailed analysis shows that the simple
  parametrization fits badly

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2-dim Analysis

• From this simple picture we expect that
  longitudinal source size is larger than
  transversal one.
• Measure correlation functions for momentum
  difference components parallel/transverse to
  thrust axis

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Resumé Hadronization

• phenomenological models are successful in
      describing many (most) aspects of the
  hadronic     final states. However, many
  parameters have to     be tuned.
• The reliability of these models is important
  for      past/present/future analyses/searches.
• BE-correlations have been observed, together
      with an elongation of the pion source.
  However,     be careful when interpreting
  parameters of (too)     simple parametrizations!

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Conclusions

• Experiments at LEP have performed QCD studies
  with unprecedented precision
• Progress on the theoretical as well as
  experimental side improved confidence in QCD
• major steps forward in the precision of the
• strong coupling constant as
• Also quark masses have been measured directly
  (b,s) or even indirectly (top !)
• Many insights in properties of q/g jets
• Phenomenological hadronization models work very
  well, have been carefully studied/tuned at LEP
• Prospects

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Prospects

• Precise measurements from LEP are important input
  for future colliders, in particular LHC
• many backgrounds to searches are QCD processes
• Big improvements in precision of as , mb ,
  rather unlikely at LHC
• LHC is a discovery machine
• nevertheless LHC offers a rich list of QCD topics
  to study, and LEP has shown that high quality
  data are good stimulus for theorists
• big step forward in precision at future linear
  collider (?)
• e.g. as and mt from tt threshold, mb
  from G(H bb)

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