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sponding force acts and α is a strength factor in units
of Newtonian gravity, while G is the gravitational constant.
Most interesting, from the experimental point of
view, are scenarios where the strength of the new force
is expected to be many orders of magnitude stronger
than Newtonian gravitation. Such forces are possible via
abelian gauge fields in the bulk. The strength of the new
force would be 10 6 < α < 10 12 stronger than gravity, independent
of the number of extra dimensions. Theoretical
developments support the original proposal of large
extra dimensions with bulk gauge field. The basic idea
behind another proposal is to modify gravity at small
distances in such a way as to explain the smallness of
the observed cosmological constant.
For the strength α, limits at short distances λ < 10
nm are derived from neutron-scattering experiments.
Other limits on extra forces at larger λ are derived from
mechanical experiments, using Casimir or van der Waals
force measurements or torsion pendulums. It has been
proposed to probe sub-micron forces by interferometry
of Bose–Einstein condensated atoms.
In practice, most of the experimental data are subject
to corrections, which can be orders of magnitude larger
than the effects actually searched for. In micro-mechanical
experiments, gravitational interactions are studied in
the presence of large van der Waals and Casimir forces,
which depend strongly on the geometry of the experiment,
and the theoretical treatment of the Casimir effect
is a difficult task. Currently, atomic force microscope
measurements using functionalised tips determine the
limits on non-Newtonian gravitation below 10 µm. The
best experimental data obtained in this way are at the
same level of accuracy (1–2%) as the numerical calculations
of the Casimir force.
New proposals have been suggested to test the law
of gravitation at small distances using quantum transitions
(GRANIT experiment) or interference (qBounce
experiment) of quantum states of ultra-cold neutrons in
the gravity potential of the earth. These approaches of
probing Newtonian gravity are advantageous because
of small systematic effects. In contrast to atoms the
electrical polarisability of neutrons inducing such Casimir
effects or van der Waals forces is extremely low. This
together with the electric neutrality of the neutron provides
the key to a sensitivity of more than 10 orders of
magnitude below the background strength of atoms.
Finally, limits for hypothetical fifth forces with neutrons
can be easily interpreted as bounds of the strength of
the matter couplings of axions with a range within the
’axion window’, the only existing limit in the axion window
at short distances.
4.5.5 Future Directions
Support to resolve the central and intriguing questions
in fundamental physics is a priority. The future directions
listed below are based upon the available expertise and
European facilities. NuPECC’s focus should be concentrated
on state of the art possibilities to achieve the
goals in the field. Both the availability of skilled researchers
in experiment and theory and the accessibility of
adequate infrastructure are indispensable for efficient
and successful progress toward potentially important
discoveries. The challenging physics goals comprise
the following key issues:
Fundamental symmetries
Time reversal and CP violation
Searches for permanent electric dipole moments constitute
a most promising avenue to new sources of CP
violation required for example to understand the matter–anti-matter
asymmetry of the universe. Searches
in different simple systems like neutrons, atoms and
diatomic molecules, muons and ions should be supported
as they offer large discovery potential and
complementary sensitivities to the underlying sources
of CP violation.
Parity non-conservation in atoms and ions
High precision parity non-conservation experiments in
atoms and ions can lead to the discovery of new physics
beyond the SM. Support for experiments which will
study parity non-conservation with radioactive cesium,
francium and radium or highly charged ions is strongly
recommended. Further, measurements on series of isotopes
would be essential in order to reduce uncertainties.
Improvement in atomic physics calculations of many
electron atoms is crucial.
CPT conservation and Lorentz invariance
Precision experiments will lead to improved limits on or
discoveries of the violation of Lorentz and CPT invariance.
A continuous and close collaboration with theorists
is essential for these activities.
Neutrinos
Nature and mass of neutrinos
The questions of whether neutrinos are identical to their
antiparticles (Majorana) or distinct from them (Dirac) and
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