In order to generate the quark-antiquark pairs
lead to string breakups, the Lund model invokes the idea of
quantum mechanical tunnelling, as follows. If the and
have no (common) mass or transverse momentum, the pair can
classically be created at one point and then be pulled apart
by the field. If the quarks have mass and/or transverse momentum,
however, the and
must classically be produced at a
certain distance so that the field energy between them can be
transformed into the sum of the two transverse masses .
Quantum mechanically, the quarks may be created in one point
(so as to keep the concept of local flavour conservation) and then
tunnel out to the classically allowed region. In terms of a
common transverse mass of the and the
the tunnelling probability is given by
The factorization of the transverse momentum and the mass terms leads to a flavour-independent Gaussian spectrum for the and components of pairs. Since the string is assumed to have no transverse excitations, this is locally compensated between the quark and the antiquark of the pair. The of a meson is given by the vector sum of the 's of the and constituents, which implies Gaussians in and with a width that of the quarks themselves. The assumption of a Gaussian shape may be a good first approximation, but there remains the possibility of non-Gaussian tails, that can be important in some situations.
In a perturbative QCD framework, a hard scattering is associated with gluon radiation, and further contributions to what is naïvely called fragmentation comes from unresolved radiation. This is used as an explanation why the experimental is somewhat higher than obtained with the formula above.
The formula also implies a suppression of heavy quark production . Charm and heavier quarks are hence not expected to be produced in the soft fragmentation. Since the predicted flavour suppressions are in terms of quark masses, which are notoriously difficult to assign (should it be current algebra, or constituent, or maybe something in between?), the suppression of production is left as a free parameter in the program: : : = 1 : 1 : , where by default . At least qualitatively, the experimental value agrees with theoretical prejudice. Currently there is no production at all of heavier flavours in the fragmentation process, but only in the hard process or as part of the shower evolution.