Fixed-target experiments permit the study of hadron production in the target
fragmentation region. It is expected that the tagging of specific particles in
the target fragments can be employed to introduce a bias in the hard scattering
process towards a specific flavour content. The case of hadrons containing a
heavy quark is particularly attractive because of the clear experimental
signatures and the applicability of perturbative QCD. The standard approach to
one-particle inclusive processes based on fragmentation functions is valid in
the current fragmentation region and for large transverse momenta $p_T$ in the
target fragmentation region, but it fails for particle production at small
$p_T$ in the target fragmentation region. A collinear singularity, which cannot
be absorbed in the standard way into the phenomenological distribution
functions, prohibits the application of this procedure. This situation is
remedied by the introduction of a new set of distribution functions, the target
fragmentation functions. They describe particle production in the target
fragmentation region, and can be viewed as correlated distribution functions in
the momentum fractions of the observed particle and of the parton initiating
the hard scattering process. It is shown in a next-to-leading-order calculation
for the case of deeply inelastic lepton-nucleon scattering that the additional
singularity can be consistently absorbed into the renormalized target
fragmentation functions on the one-loop level. The formalism is derived in
detail and is applied to the production of heavy quarks. The renormalization
group equation of the target fragmentation functions for the perturbative
contribution is solved numerically, and the results of a case study for deeply
inelastic lepton-nucleon scattering at DESY (H1 and ZEUS at HERA), at CERN
(NA47) and at Fermilab (E665) are discussed. We also comment briefly on the
case of an intrinsic heavy-quark content of the proton.Comment: Habilitationsschrift, Universitaet Hamburg, submitted in April 1996.
118 pages (LATEX); figures are included via epsfig; The AMSTEX fonts are
required. See also http://wwwcn.cern.ch/~graudenz/publications.html for a
complete (compressed) postscript fil