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The fluxtube model was originally considered in order to
account for the mass spectra of hadrons and their strong decay processes
which are related to quark pair creations. At first, the creations
of quark pairs were assumed arbitrarily with appropriate operators
resulting in models such as the ^{3}P_{0} or the ^{3}S_{1} model. However, it
was thought later that the quark pair creations were controlled by
gluonic degrees of freedom. It is well known that the gluonic degrees
of freedom in bound state problems are not so simple as to be described
by perturbative calculations only. The nonperturbative feature of
gluonic interactions is one of the motives for consideration of the
simple fluxtube formalism.
The description of gluonic fluxtube was firstly attempted by
a string picture. In quark pair creation model, the created quark
pair breaks a fluxtube with equal probability amplitude anywhere
along the string and in any state of string oscillation. The amplitude
to decay into a particular final state is assumed to depend on the
overlap of original wave functions of quarks and string with the
final two state wave functions separated by the pair creation. For
ground state strings connecting quark and antiquark in mesons, the
amplitude
to break at point
was first assumed to be[28]

(5.19) 
where
and b are parameters and

(5.20) 
with
being the difference between the quark and the
antiquark position vectors.
is the vector with the shortest
distance between any point on the vector
and the pair creation
point, and
measures the ratio of the distances from the original
antiquark and quark positions to the projection point of the created
quark pair along the vector
. The shape of equi
surface
looks like a cigar which is appropriate to describe a fluxtube
of constant width with end caps.
For general shapes, we can introduce a dependent factor
into the exponent of
such that

(5.21) 
Although it has been found that physical results are nearly independent
of
for
,
the arbitrariness of
raises the
problem of theoretical basis for the derivation of fluxtube overlap
function .
In fact, the form in Eq.(423) was derived by
using harmonic oscillator wave functions for discrete string components.
The form was even changed into the spherical one[29]

(5.22) 
which is convenient for calculating physical amplitudes expanded in
the harmonic oscillator wave function basis. The changes in the
form of
indicate the fact that no firm theoretical grounds
exist for treating gluonic fluxtubes.
Next: 5.4.3 Construction of Topological
Up: 5.4 Nonperturbative Topics
Previous: 5.4.1 Jet Overlapping
ACFA Linear Collider Working Group
EMail:acfareport@acfahep.kek.jp