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4.1 Hadron Physics
Dedicated experiments (HERMES@DESY, COMPASS@
CERN and JLab) have provided important new results,
showing transverse spin effects. Future results in this
field are expected from COMPASS and from JLab
experiments, either running or planned at an upgraded
energy of 12 GeV. The spin structure of the proton is also
being investigated at RHIC, with polarised proton-proton
scattering. New electron-nucleon (ENC) or electronion
colliders (EIC), with polarised beams and targets,
planned in Europe and the USA, will be dedicated facilities
for accessing TMDs.
The transversity distribution, being a chiral-odd quantity,
can be measured only when coupled to another
(unknown) chiral-odd quantity; this has been recently
achieved by combining SIDIS and e + e − data. More precise
experiments, spanning different ranges of x and
Q 2 are essential. The “golden” channels for this would
be double-tronsverse-spin asymmetries in Drell-Yan
processes with polarised antiprotons, as proposed by
the PAX Collaboration at FAIR.
A non-vanishing “Sivers” effect (relating the intrinsic
motion of unpolarised partons to the parent nucleon
spin) has been observed in SIDIS by the HERMES for
the proton. Similar measurements by COMPASS on the
deuteron yield asymmetries compatible with zero. A
confirmation of the HERMES findings for the proton is
therefore vital, since this would provide a clear indication
of parton orbital motion. Furthermore, the Sivers function
is predicted to contribute with opposite signs to singlespin
asymmetries in SIDIS and Drell-Yan processes.
The Drell-Yan measurements could be performed in a
hadronic run (pions scattering off transversely polarised
protons) at COMPASS. A transversely polarised target
in the future PANDA experiment could also access such
processes.
The Collins effect (relating the transverse spin of
a fragmenting quark to the transverse motion of the
resulting hadron) has been independently observed by
three different experiments, HERMES, COMPASS and
Belle. One remaining theoretical issue related to the
Collins functions, and TMDs in general, is their QCD
evolution.
Generalized Parton Distributions
In recent years, much progress has also been made
in a different direction by developing a broader framework
of so-called Generalised Parton Distributions
(GPDs). These structure functions can be probed in hard
exclusive leptoproduction of a photon (deeply virtual
Compton scattering, DVCS) or a meson. In the forward
limit they reduce to the PDFs. GPDs extend the twodimensional
transverse spatial picture of the nucleon,
accessible through the form factors, to a third dimension,
by correlating it with the longitudinal quark momentum
components. This dependence on the transverse
spatial motion means that GPDs can provide, through
a sum rule derived by Ji, a handle on the contribution
of the orbital angular momentum of the quarks to the
nucleon’s spin.
Determination of the GPDs forms a long-term
experimental programme, requiring measurements of
observables for various channels over a wide kinematical
range. Including constraints from dispersion theoretical
techniques, one can reduce the model dependence in
the extraction of GPDs. In order to test the scaling limit,
it is also, in particular, necessary to reach Q2 values as
large as possible so that the leading-order GPD formalism
applies.
Figure 4. Model-dependent constraints on the u-quark total
angular momentum J u vs. d-quark total angular momentum J d
obtained by comparing JLab and HERMES DVCS experimental
results and theoretical model calculations.
66 | Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010