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A broad experimental programme has been explored
over the past years at several facilities and experiments:
at JLab with a 6 GeV electron beam, at HERMES with a
27 GeV electron and positron beam, and at H1 and ZEUS
with 820 GeV protons colliding with 27 GeV electrons or
positrons. Available DVCS data already allow us to make
some comparisons to models and are providing insights
into the nucleon GPDs. For example, with the help of
Ji’s sum rule, one can make a first model-dependent
estimate of the orbital momentum contributions of the
u and d quarks to the nucleon’s spin, see Figure 4. This
hints at a nucleon where d quark angular momentum
contributes little to the proton’s spin, a large part of it
originating therefore from the u quarks.
In the near future numerous high statistics data
employing many channels and observables – for DVCS
in particular – are expected from the 6 GeV beam at
JLab. New, fully exclusive, beam charge asymmetries
and beam spin asymmetries should be available in the
next couple of years. After 2010, the COMPASS experiment
at CERN also plans to study GPDs with a 200 GeV
muon beam. As at HERMES, a dedicated recoil detector
will be installed in order to detect all the particles of
the DVCS final state and ensure the exclusivity of the
process. Also in the near future, high statistics data on
many channels and observables are expected from the
6 GeV beam at JLab.
In the longer term (> 2013), the JLab upgrade, with a
12 GeV beam, promises to yield a wealth of new experimental
data that will reach into new kinematical domains.
In both Europe and the USA, high luminosity polarised
electron-nucleon/ion collider projects (ENC / EIC) are
under discussion. Whilst fixed-target experiments
explore mainly the valence region, a collider experiment
could significantly extend the leverage in Q 2 , thus
providing a test of the underlying scaling behaviour in
both unpolarised and polarised observables, required
for extracting GPDs. Furthermore, it could also probe the
region where gluons as well as quarks play a significant
role in the nucleon’s structure.
A further generalization of the GPD concept has been
proposed in cases where the initial and final states are
different hadronic states. When these new hadronic
objects are defined through a quark-antiquark (respectively,
three quark) operator (meson to meson or meson to
photon transition), they are called mesonic (respectively
baryonic) transition distribution amplitudes (TDA), The
study of hard exclusive lepton pair production accompanied
with a pion in antiproton-proton annihilation at
FAIR e.g. will allow extracting such TDAs.
Lattice QCD
The next round of lattice QCD (LQCD) simulations should
result in calculations of several of the hadron-structure
observables discussed above, close to the physical point
and with carefully controlled uncertainties. The hadron
spectrum calculation already mentioned demonstrates
that it is only a matter of time before LQCD leads to
the evaluation of many hadron-structure quantities with
similar accuracy. In particular, the combination of experiment,
perturbative QCD and LQCD is already providing
a powerful framework for understanding the rich physics
of hadron structure. During the coming decade, developments
combining these three elements will further
intensify.
The fact that in LQCD calculations several fermion
lattice actions is an illustration of the non-trivial technical
challenges in this area. The goal is to provide results
with the smallest overall error. With given computational
power, this can entail a trade-off between statistical and
systematic errors. Theoretical progress over the years
has allowed for a reduction cut-off effects and restoration
of chiral symmetry on the lattice without unwanted
fermion species, at the expense of more complicated
actions that require greater computer resources. The
best strategy at present is to use a number of improved
actions and regard the spread of predictions as a measure
of the systematic errors. Only when lattice artefacts
are correctly accounted for, can comparisons with continuum
physics be meaningful.
Up to now the extrapolation to physical light-quark
masses (or equivalently pion masses) has been a major
source of uncertainty. This extrapolation was needed
because LQCD simulations at unphysically large lightquark
masses are much less demanding of computer
resources. With increasing computer power, combined
with algorithmic improvements and steadily improving
input from chiral effective theory (ChPT), it is expected
that the gap between lattice simulations and the physical
point will be bridged in the next couple of years.
Lattice calculations at the physical quark masses will
still need corrections for finite volume and discretisation
effects. ChPT can provide insights into the volume and
cut-off dependences of lattice quantities, and these
can be very valuable for carrying out the infinite-volume
and continuum extrapolations. Current LQCD simulations
make use of lattices with spatial sizes L such that
Lm π ≥ 3.5 and spacings smaller than 0.1 fm. These make
it extremely important to determine finite-volume corrections
and cut-off dependences from effective field. Only
then will it be possible to draw rigorous conclusions from
lattice QCD for quantities like orbital angular momenta,
moments of GPDs, or distribution amplitudes.
Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010 | 67