* text on FRAGMENTATION FUNCTIONS *

content of this page:

text on fragmentation functions (this page)
parton distribution functions (PDFs)
unintegrated PDFs
fragmentation functions (FFs)
unintegrated FFs
multiple-hadron FFs
model calculations
target fragmentation and fracture functions

back to the sitemap

parton distribution functions (PDFs):

The internal structure of hadrons can be studied in hard perturbative processes by means of the factorization theorems of QCD separating soft from hard physics. For inclusive reactions the experimental cross sections are given by convolutions of process-independent parton distribution functions (PDFs) and elementary partonic cross-sections which are process-dependent, but calculable in perturbative QCD.

The PDFs have a formal definition via hadronic matrix elements of (non-local) quark and gluon field operators. They encode the information on the structure of the initial state hadron(s) and acquire a simple interpretation in the QCD-improved parton model, where they give the probabilities of finding a parton with a certain momentum fraction inside the parent hadron.

Experiments with polarized beams and/or targets give access to information on the spin structure of the hadrons in terms of polarized PDFs. To leading order (in an expansion in inverse powers of the hard scale) there are three different functions in the quark sector:

interpretation of PDFs

Of genuinely non-perturbative nature the DF's have to be taken from experiment or calculated in models. Parametrizations of DF's from global fits to experimental data are available for f₁(x) and g₁(x).

unintegrated PDFs:

Taking into account the effects of the transverse momentum partons can have relative to the momentum of their parent hadrons a richer structure arises. Accordingly, there are more functions parameterizing this information. Nevertheless, to leading order there is an intuitive probabilistic interpretation of the functions. New are those functions describing, for instance, the preference of a certain transverse polarization of quarks inside a longitudinal polarized hadron. Those functions vanish for simple geometrical symmetry reasons, if the relative transverse momentum is zero.

interpretation of PDFs (incl. transv. momentum effects)

fragmentation functions:

Complementary information on the internal structure of hadrons is contained in fragmentation functions (FFs) involved in the description of semi-inclusive processes with one or more hadrons of the final state detected. Like the PDFs also the FFs are universal in the sense that they are process independent. They parameterize the unknown mechanism how partons (quarks or gluons) turn into confined hadrons in the final state which are observed in the detectors.

In principle, although experimentally difficult, detection of polarization for final state hadrons gives access to information on spin correlations in the hadronization process in terms of polarized FF's.
Like the PDFs, to leading order the FFs have an intuitive probabilistic interpretation.

interpretation of FFs

The inclusion of QCD loop corrections leads to a scale dependence of the FF's (again similar to the DF's) such that they obey integro-differential evolution equations of the GLDAP (Gribov-Lipatov-Dokshitzer-Altarelli-Parisi) type. Logarithmic scaling violations may be utilized to determine the strong coupling.

unintegrated fragmentation functions:

... (text still to come)

multiple-hadron FFs:

... (text still to come)

Useful classification of (spin-dependent) FFs:

talk presented by R. Jakob at the European Workshop on the QCD structure of the Nucleon - QCDN'02 - Ferrara, Apr. 3-6 2002.

model calculations:

Some model calculations for FF's are available
and can be compared with
experimental information on FF's and parametrizations obtained from global fits.

target fragmentation and fracture functions

Since the information encoded in PDFs and FFs is complementary (distribution of partons in hadrons -- hadronization of partons) only the knowledge of both will enable us to finally understand confinement.

back to the sitemap up to the list of content

Since these pages are (and always will be) under construction, there is a list of items relevant to the subject, but not yet (or only partly) contained or wrongly sorted ...

transverse momenta between partons and produced hadrons
`T-odd' fragmentation functions
power corrections / renormalons
text on current versus target fragmentation
FF's in Monte Carlos
interference FF's, multiple hadron FF's
multiplicities
...