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4.1 Hadron Physics
Elastic scattering and inclusive DIS processes are
time-honoured tools to access hadron form factors and
structure functions respectively. The space-like electromagnetic
form factors reveal the spatial distribution of
quark charges in a hadron, whereas the structure functions
measure the longitudinal momentum distributions
of partons in a hadron. However, a full 3-dimensional
exploration of the nucleon structure, in position and
momentum space, has only just begun. For this purpose,
several correlation functions encoding the quark-gluon
structure have emerged in recent years. The correlation
between the quark/gluon transverse position in a hadron
and its longitudinal momentum is encoded in generalized
parton distributions (GPDs). The information on the
quark/gluon intrinsic motion in a hadron and several
correlations functions that describe this 3-dimensional
structure have been devised in recent years.
Over the last few years a rich experimental programme
has developed to measure these different correlation
functions, and significant advances are anticipated in the
future. This field is based on a fruitful interplay between
experiments, phenomenological treatments of the relevant
matrix elements, and ab initio calculations of these
matrix elements from lattice QCD.
In the following we describe in more detail the stateof-the-art
of the different hadron structure observables
and spell out the open issues in these fields.
Electromagnetic Form Factors
The electromagnetic form factors (FFs) of hadrons, most
prominently of nucleons, have been studied with ever
increasing accuracy over the last 50 years. The main
tool has been elastic lepton scattering, which probes
negative (space-like) momentum transfers. Positive (timelike)
momentum transfer is accessible in annihilation
processes. Due to their analyticity in the 4-momentum
transfer q 2 , space-like and time-like FFs can be connected
through dispersion relations. In the space-like
region, they allow for a spatial imaging of quarks in a
hadron, whereas in time-like region, they encode the
excitation spectrum of spin-1 (vector) mesons. These two
complementary aspects of hadron structure demand a
determination of the electromagnetic FFs over the full
kinematical range of q 2 .
On the theory side, a wide variety of models based
on effective degres of freedom has been used to estimate
the nucleon’s FFs. Form-factor data also provide
benchmarks for lattice gauge theory, in particular, for
systematic studies of the approach to physical values
of the quark masses. Furthermore, space-like FFs yield
the first moment (over the quark longitudinal momentum
fraction) of GPDs (see below). Dispersion relations are
used to analyse the structure of the FFs in the spaceand
time-like region simultaneously.
As well as revealing information on the spatial structure
of hadrons, FFs provide vital input for interpreting
precision experiments in other fields of physics. A wellknown
example is the hydrogen hyperfine splitting, where
the main limiting theoretical uncertainty lies in proton
structure corrections. A further example for the need
of precise FFs are the experiments on parity violating
electron scattering, where the uncertainty in the extraction
of strange FFs via axial and electromagnetic FFs
limits the current experimental precision.
For electric and magnetic FFs of the proton and neutron
at space-like momentum transfers, there are active
experimental programmes at MAMI (at lower momenta)
and at JLab (with higher momenta). The availability of
CW electron beams at high current and high polarisation
allows measurements with unprecedented accuracy up
to high energies due to the large available luminosities
and – for experiments with polarisation – large figures of
merit. The interest in the nucleon FFs has been renewed
especially by recent mea surements at JLab using the
polarization transfer method. These show that the ratio
of electric and magnetic FFs for the proton deviates
from unity, in contrast to the results derived from the
Rosenbluth separation technique. While this discrepancy
is most likely connected with two-photon exchange
amplitudes, it has been shown that the polarization transfer
method is much less sensitive to those effects and
therefore yields clean FF extractions.
The question of the importance of the two-photon
exchange amplitude in elastic scattering has triggered
a whole new field of research. Several dedicated programmes,
comparing elastic scattering of electrons with
elastic scattering of positrons from protons are underway
at JLab, at the Novosibirsk e + e − collider VEPP2000, and
at the Doris ring at DESY.
In the time-like region, where the FFs are complex
functions of q 2 , the most precise experimental data
have come from the B-factory e + e − colliders, where the
centre-of-mass energy is fixed at a bottonium resonance,
and from antiproton annihilation experiments at
LEAR. The limited statistics of current data mean that
an independent extraction of the time-like electric and
magnetic FFs is not possible. The present error of the
ratio of electric over magnetic FF in the time-like domain
is of order 50%, in contrast to the space-like regime,
where the precision is almost two orders of magnitude
better. At B-factories, radiation of a photon from one of
the particles in the initial states is used to vary the q 2 of
the virtual photon that probes the nucleon. The BESIII
experiment at Beijing has recently started data taking.
The PANDA experiment at GSI/FAIR offers a unique
64 | Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010