Assume a jet system, in its c.m. frame, with the quark moving out in the direction and the antiquark in the one. We have discussed how it is possible to start the flavour iteration from the end, i.e. pick a pair, form a hadron , etc. It has also been noted that the tunnelling mechanism is assumed to give a transverse momentum for each new pair created, with the locally compensated between the and the member of the pair, and with a Gaussian distribution in and separately. In the program, this is regulated by one parameter, which gives the root-mean-square of a quark. Hadron transverse momenta are obtained as the sum of 's of the constituent and , where a diquark is considered just as a single quark.

What remains to be determined is the energy and longitudinal
momentum of the hadron. In fact, only one variable can be selected
independently, since the momentum of the hadron is constrained by
the already determined hadron transverse mass ,

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The fragmentation function , which expresses the probability that a given is picked, could in principle be arbitrary -- indeed, several such choices can be used inside the program, see below.

If one, in addition, requires that the fragmentation
process as a whole should look the same,
irrespectively of whether the iterative procedure is performed
from the end or the
one, `left-right symmetry',
the choice is essentially unique [And83a]: the `Lund symmetric
fragmentation function',

In the program, only two separate values can be given, that for quark pair production and that for diquark one. In addition, there is the parameter, which is universal.

The explicit mass dependence in implies a harder
fragmentation function for heavier hadrons. The asymptotic
behaviour of the mean value for heavy hadrons is

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In principle the prediction is that , but so as to be able to extrapolate smoothly between this form and the original Lund symmetric one, it is possible to pick separately for and hadrons.

For future reference we note that the derivation of as a
by-product also gives the probability distribution in proper
time of
breakup vertices. In terms of
, this distribution is

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Many different other fragmentation functions have been proposed, and a few are available as options in the program.

- The Field-Feynman parameterization [Fie78],

(245) - Since there are indications that the shape above is too
strongly peaked at , instead a shape like

(246) - Charm and bottom data clearly indicate the need for a
harder fragmentation function for heavy flavours.
The best known of these is the Peterson/SLAC formula [Pet83]

where is a free parameter, expected to scale between flavours like . - As a crude alternative, that is also peaked at , one may
use

(248) - In [Edé97], it is argued that the quarks responsible for the
colour fluctuations in stepwise diquark production cannot move along the
light-cones. Instead there is an area of possible starting points for the
colour fluctuation, which is essentially given by the proper time of the
vertex squared. By summing over all possible starting points, one obtains
the total weight for the colour fluctuation. The result is a relative
suppression of diquark vertices at early times, which is found to be of
the form
, where
and
. This result, and especially the value
of , is independent of the fragmentation function, , used to
reach a specific -value. However, if using a which implies
a small average value
, the program implementation is
such that a large fraction of the
attempts
will be rejected. This dilutes the interpretation of the input
parameter, which needs to be significantly enhanced to
compensate for the rejections.

A property of the Lund Symmetric Fragmentation Function is that the first vertices produced near the string ends have a lower than central vertices. Thus an effect of the low- suppression is a relative reduction of the leading baryons. The effect is smaller if the baryon is very heavy, as the large mass implies that the first vertex almost reaches the central region. Thus the leading-baryon suppression effect is reduced for - and jets.