ANNUAL REPORT 2006

Annual report 2006 30
in a large class of granular packings. We show that the force network ensemble generates
networks belonging to the same universality class, while other simple models
do not. Finally, the effects of external shear stresses on the geometry of forces are
investigated within the framework of the force ensemble. While the shear stresses
do not modify the scaling exponents, they induce an anisotropy, which remarkably
appears to be universal.
Pijlman, F. (VUA)
thesis title: Single spin asymmetries and gauge invariance in hard scattering processes
advisor: prof. dr. P.J.G. Mulders
date: 12 January 2006
present position: research scientist, Philips, Eindhoven, the Netherlands
In the thesis effects are studied that appear in hard scattering processes when one
accounts for transverse momentum of partons. The hard scattering processes that
are treated are semi-inclusive lepton-lepton, lepton-hadron, and hadron-hadron scattering.
The processes are called hard because the momenta of the initial particles
and the measured particles (or jets) in the final state are well separated by large
momentum differences. The partons that are studied are quarks and gluons which
form the constituents of hadrons. This research has investigated effects that arise
from transverse momentum of partons. Since these partons only appear in hadrons,
the transverse momentum of partons is defined with respect to the parent hadron
momentum.
The thesis studies the scattering process from a theoretical viewpoint. The main assumption
is that in certain kinematical regions the cross sections can be determined
from cross sections of the elementary partons folded with parton distribution and
fragmentation functions (these connect the partons with hadrons). In other words,
the distribution of partons or their fragmentation into hadrons is at some stage supposed
to be independent of the scattering process; this is also known as factorization.
The investigation has its focus on (color) gauge invariance. of the theory. The relation
of transverse momentum dependent effects and gauge invariance is of increasing
interest after the publications of Brodsky, Hwang, Schmidt; Collins; and Belitsky, Ji,
Yuan, who show the possibilities of nonvanishing single spin asymmetries in particular
model calculations. The interesting point here is that such single spin asymmetries
would be absent if quarks and gluons would not be part of a gauge theory. In that
sense these QCD-effects are like the Aharonov-Bohm effect in QED.
In the investigation mathematical tools are developed, enabling one to express the
cross sections in experiment independent quantities. These tools have successfully
been confronted with fundamental issues like unitarity to the first few non-trivial orders.
The results we found is that the way in which distribution and fragmentation
functions are encountered in an experiment depends in a subtle way on the process,
but without violating factorization, at least at tree level. However, the results do
raise questions on the issue of factorization that still need to be addressed. In order
to clarify these questions, we made several predictions for cross sections that can
be tested in the next years. Those measurements will contribute to our understanding