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In order to describe the non-perturbative features of hadronization
processes, we usually assume two generalities ; one is the local
parton-hadron duality and the other is the universality of
in low
energy region. With these assumptions we can construct models for
hadronizations resulting in various jet generating algorithms such as
HERWIG from cluster model, JETSET or UCLA from string
model, PYTHIA, PANDORA, ISAJET, SUSYGEN etc. with appropriate
corrections. For these algorithms, one important point is that there
exist differences between quark jet and gluon jet. These differences
could be critical in analyzing many jet systems resulting from
high energy,
*e*^{+} *e*^{-} linear collider.
Another point to be considered in analyzing many jet systems
is jet overlapping. For 2 jet system, there exists no problem
since the configuration of 2 jets is linear. For 3 jets, the
differences between quark jet and gluon jet turn out to be string
effects with slight overlapping effects. However, for 4 jet system,
the overlapping probability becomes significant. For example, let's
estimate the probability to overlap by assuming jet shapes of cone
structure with subtending solid angle
,
which corresponds
approximately to a cone with side angle
.
For a fixed cone,
the total solid angle for another cone to overlap becomes
.
Then the probability for 3 fixed cones to overlap with the
remaining one is
,
which is larger than
.
This
probability becomes
for 5 jet system and increases to
for 6 jets. Since
processes in linear collider correspond
to 6 jet system, it becomes problematic to analyze
by just
counting particle trajectories. The situation becomes worse if
we want to get some information about particle polarizations.
Moreover, the
processes result in 8 jets for which the
overlap probability becomes
.
In our simple estimation, jets
cannot be separately observed in 8 jet system so that it is
meaningless to follow particle trajectories to define jets.
Since we have to be prepared to account for many jets
such as 10 or 20 jets in high energy linear collider, we need
to construct new theoretical models which can be used to analyze
jet overlapping. One possibility is the momentum space flux-tube
model which will be explained in the following sections. We can
classify flux-tubes and construct topological spaces and then it is
possible to define probability amplitude to have quark pairs which
can be used to predict particle multiplicities in jets. In this
way, we can account for string effects in 3-jets by considering
appropriate differences between quark and gluon jets.

** Next:** 5.4.2 Flux-Tube Model
** Up:** 5.4 Non-perturbative Topics
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*ACFA Linear Collider Working Group*

E-Mail:acfareport@acfahep.kek.jp