A question of interest for LEP 2 is that of how well the characteristics
of QCD events are understood at large energies. By QCD events, it is here
meant those that are produced through the s-channel decay of a Z
into quark and gluon jets. This question is of interest
because W
W
events lead to multi-jet states for
which one of the principal backgrounds will be QCD events,
because QCD events will also form a principal source
of background for higgs, chargino and other particle searches,
and because QCD events will be interesting in their own right
as a means to test perturbation theory in a regime
with particularly small hadronization uncertainties.
The principal tools to test how well QCD event
characteristics are understood are Monte Carlo generators.
The main generators,
ARIADNE, COJETS, HERWIG and PYTHIA,
have been tuned by the LEP experiments or by the Monte Carlo
authors to describe global features of hadronic Z
data.
In many cases,
the generators have proven able to describe
detailed features of these data as well.
It is thus relevant to extrapolate the predictions of
the QCD generators to LEP 2 energies and
to compare their level of agreement for
distributions likely to be of importance at LEP 2.
In this section, such an extrapolation and
comparison is presented.
For this study, members of each of the LEP experiments generated Monte Carlo
event samples at 
=175 GeV using parameter sets determined within
their Collaboration. The Monte Carlo parameter sets used at LEP 1 are
continually revised in order to yield as accurate a description of the Z
data as possible. Therefore, the parameter sets employed for this study do
not necessarily represent official versions which will be published by the
Collaborations. The parameter sets used for ARIADNE, HERWIG
and PYTHIA are given in
tables 3--5. For COJETS, L3
and OPAL results were made available using the parameter values given in
table 6. There are numerous parameters and strategies
involved in the optimization of the parameters. Comparison of the results
obtained using the parameter sets of the different Collaborations therefore
provides a systematic check of effects associated with the optimization
choice. Samples of 100,000 events were generated without initial-state photon
radiation or detector simulation, treating all charged and neutral particles
with mean lifetimes greater than 
s as stable.
Table 3: Optimized parameter sets for ARIADNE, version 4.06
(for ALEPH, version 4.05), from the LEP Collaborations.
The parameters listed are those which were changed from their
default values by at least one of the groups.
The ARIADNE events were generated using PYTHIA
version 5.7 to describe the hadronization and hadron decays.
The DELPHI Collaboration implements its own procedure to
specify the relative rate at which mesons are produced in
different multiplets [9],
in place of the PYTHIA parameters PARJ(11)-PARJ(17).
Table: Optimized parameter sets for HERWIG, version 5.8,
from the LEP Collaborations.
The parameters listed are those which were changed from their
default values by at least one of the groups.
Table 5: Optimized parameter sets for PYTHIA, version 5.7,
from the LEP Collaborations.
The parameters listed are those which were changed from their
default values by at least one of the groups.
The DELPHI Collaboration implements their own procedure to
specify the relative rate at which mesons are produced in
different multiplets [9],
in place of the PYTHIA parameters PARJ(11)--PARJ(17).
Table 6: Optimized parameter sets for COJETS, version 6.23,
from the L3 and OPAL Collaborations.
The parameters listed are those which were changed from their
default values by at least one of the groups.
The following distributions were examined using charged particles only:
,
,
, and
.
The following distributions were examined using both charged and neutral particles:
[115],
[115],
defined using the 
jet finder [116],
[117],
,
[118],
[118],
[121], with four-jet events
defined using the 
jet finder with 
=0.01,
and
.
, 
and 
were examined as a function of 
.
The results for 
, 
and 
as a function of 
are shown in Fig. 7.
Figure:
The mean values of 
, Thrust 
and 
predicted by ARIADNE, COJETS,
HERWIG and PYTHIA as a function of 
in comparison with measurements from
PEP, PETRA, TRISTAN and LEP 1.
The LEP 2 point is indicative only,
based on the PYTHIA prediction.
The total uncertainty expected at LEP 2 assuming
QCD events is smaller than the symbol size.
For those cases in which the results of at least three Collaborations are similar to each other, the Monte Carlo predictions are shown as shaded or hatched bands. The widths of the bands show the maximum deviations between the results found by the different Collaborations. The widths of the bands are generally much larger than the statistical uncertainties. In a few cases, the Monte Carlo prediction obtained by one of the Collaborations differs significantly from those obtained by the other three groups and is shown as a separate curve. The COJETS predictions are likewise shown as separate curves for purposes of clarity. The results found by the four LEP experiments are labelled A, D, L and O in the figure legends.
Representative measurements from PEP, PETRA, TRISTAN
and LEP 1 are included in Fig. 7.
For 
=175 GeV,
an indicative ``data point'' is also shown,
which is taken to be equal to the mean
of the PYTHIA predictions from the four groups.
The size of the symbol for the LEP 2 point is larger than
the statistical uncertainty for 
QCD events.
Systematic terms were generally found to dominate the
statistical ones for the experimental measurements
shown in Fig. 7.
The total experimental uncertainties at 175 GeV
can therefore be expected to be comparable to those
found for the LEP 1 data.
[BROKEN-IMG]
Figure 8:
Comparison of the predictions of QCD event generators
at 
=175 GeV.
From the distribution of 
versus 
(Fig. 7(a)),
it is seen that,
with the exception of the L3 ARIADNE curve,
the predictions of ARIADNE, HERWIG and
PYTHIA are similar.
The widths of the ARIADNE, HERWIG and PYTHIA bands
are narrow for energies at and below the Z
mass,
showing that the results from the four Collaborations
are in close agreement
(with the exception of the L3 curve for ARIADNE).
For energies above about 150 GeV,
the HERWIG band becomes broader,
indicating that there is some divergence in the predictions
obtained by the different groups.
From Fig. 7(a) it is also seen that COJETS
predicts a substantially larger value of 
than the other models for energies above the Z
mass.
This difference is suggestive of coherence effects
in the parton shower,
which are absent in COJETS but present
in the other three models.
Coherence reduces the mean soft gluon multiplicity
in the parton shower.
It is generally expected that coherence will lead to
a reduction in the mean hadron multiplicity as well.
Thus, a measurement of 
at LEP 2 could help to establish
the existence of coherence phenomena in the data.
Figs. 7(b)--(d)
show the corresponding distributions for the
and 
variables.
Again, ARIADNE, HERWIG and PYTHIA are seen
to exhibit similar behavior.
COJETS agrees well with the other models for T,
but lies below them for 
and above them
for 
in the LEP 2 energy range.
Thus the jets from COJETS are less oblate
than those from ARIADNE, HERWIG or PYTHIA.
(The Oblateness O of an event is given by
.)
The differences between COJETS and the other three
models become larger as 
increases.
Figure 9:
Comparison of the predictions of QCD event generators
at 
=175 GeV.
In Fig. 8,
the Monte Carlo predictions for 
, 
, 
and 
at 175 GeV are shown.
The corresponding results for T, 
,
and 
,
for 
, 
, 
and 
,
and for 
, 
and 
are shown in
Figs. 9,
10,
and 11, respectively.
Overall, the models are seen to be in general agreement
with each other.
Some of the more notable exceptions to this agreement
are discussed below.
and 
distributions
(Figs. 8(a) and (c)).
Smaller but visible differences are observed between
COJETS and the other models for a number of the
other distributions as well.
At the Z
mass,
these differences between COJETS and the other models
are either not present or are much smaller.
This implies that the energy scaling behavior of COJETS
differs from that of ARIADNE, HERWIG and PYTHIA.
distribution is much harder using the L3 parameter set
than it is using the parameter sets of the other Collaborations
(Fig. 8(b)).
This feature is also observed at the Z
energy.
The primary reason for this difference between
L3 and the other groups
is the different treatment of the parameter CLSMR
(see table 4).
values below about 0.02.
Correspondingly, the two jet rate from PYTHIA is smaller.
This difference is also observed at 
=91 GeV.
From this same figure,
COJETS is seen to predict a three-jet rate which
is smaller than that of the other models:
this last difference is not observed at LEP 1 energies.
and 
(Figs. 10(a) and (b)).
Less of a deviation is present for the jet broadening variables,
and 
(Figs. 10(c) and (d)).
This suggests that these last two variables may be less subject
to uncertainties related to the modelling of QCD and hadronization
than the first two variables.
than ARIADNE and PYTHIA
(Fig. 11(c)).
The general conclusion that can be drawn from this study
is that there is relatively little uncertainty in the predictions
of QCD generators for event characteristics at LEP 2.
Such basic features of events as charged multiplicity,
Thrust and Oblateness
are described in an almost identical manner by
ARIADNE, HERWIG and PYTHIA.
Only COJETS deviates significantly from the
predictions of the other models.
On the other hand,
there is modest disagreement between the models for
variables which require use of a jet finding algorithm:
(Fig. 9(d))
and 
(Fig. 11(c)).
This could have some implication for the W mass
determination based on the reconstruction of jets.
Figure 10:
Comparison of the predictions of QCD event generators
at 
=175 GeV.
[BROKEN-IMG]
Figure 11:
Comparison of the predictions of QCD event generators
at 
=175 GeV.