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4.5 Fundamental Interactions
intensive development in various directions. The deviation
of the free electron g-factor from the Dirac value g =
2 has become the most significant QED test. The magnetic
moment anomaly a =(g−2)/2 is the only possible
extension of the electromagnetic interaction of a spin 1/2
particle, which does not violate parity and time reversal
symmetries. It has been calculated very accurately over
many years including all 4-loop diagrams and partially
the 5-loop diagrams. The comparison with recent precise
measurements of the electron anomaly in a Penning
trap performed at Harvard University has led to the
most accurate value of the fine structure constant α.
The magnetic moment anomaly of the muon has been
measured with 0.5 ppm precision at the Brookhaven
National Laboratory. Since the muon is 200 times heavier
than the electron, its anomaly is much more sensitive
to the existence of as yet unknown heavier elementary
particles, which may significantly contribute to a µ . It is
also sensitive to the so called hadronic contribution,
the major part of which can be obtained from the e - - e +
annihilation or hadronic τ-decays. However, a small part,
the so called light-by-light hadronic correction, can only
be obtained from theory. Both hadronic corrections limit
the present accuracy of theoretical prediction, which
somehow deviates from the experimental value by more
than 3σ. This might be due to new physics and therefore
a new experiment at the Fermilab accelerator complex
is in preparation with the aim of a fivefold improvement
of the muon g−2. The hadronic corrections need more
precise experimental input and thorough theoretical
scrutiny. Here European experimental and theoretical
work is playing a central role. If at the end of the next
round experiment and theory would happen to agree,
this would provide best limits for numerous parameters
in theories beyond SM. Therefore the muon g-2 value
is a crucial calibration point for speculative theories as
well as for the SM itself.
Light hydrogenic ions
Within the direction toward high precision tests with
light hydrogenic ions, various QED effects such as one-,
two- and three-loop contributions to the Lamb shift and
to the hyperfine splitting have been calculated using
both analytic and numerical approaches, and in general
good agreement between different calculations has been
achieved. Also, by combining experimental and theoretical
efforts, the charge radius of halo nuclei (e.g. 8 He,
11
Li and 11 Be) were recently determined for the first time
and model-independently. Further on, the finite nuclear
mass effects, which are significant for such systems as
positronium, muonium, muonic and pionic hydrogen,
and even hydrogen, have been studied intensively during
recent years as their evaluation was found to be the
most challenging. Theoretical predictions for positronium,
its energy levels and decay rates, were found to be in
agreement with results from the most recent experiments,
although significant discrepancies were present with early
measurements, in particular with the ortho-positronium
decay rate. This has stimulated development of various
speculative theories, as the ortho-positronium decay is
sensitive to an admixture of new interactions, which are
not accommodated in the Standard Model. Theoretical
results for another very interesting pure QED system,
i.e. muonium e - + µ + , are so accurate that they have the
potential of determining physical constants, like α or the
muon mass, provided the measurements reach a similar
level of accuracy. Such experiments are being considered
for example at PSI, where high intensity muon beams are
available. Interestingly, in hydrogen-like ions theoretical
predictions for the bound electron g-factor have led to the
most accurate determination of the electron mass from
precise measurements of the ratio of Larmor to cyclotron
frequencies of a single hydrogen-like C 5+ ion stored
in a tandem Penning trap. Regarding hadronic atoms,
although pure QED effects can be obtained as accurately
as for hydrogen, the mixed QED and strong interaction
effects cannot at present be consistently calculated, an
example of this being the pion self-energy in the pionic
hydrogen. The problem of mixed QED and QCD corrections
may therefore deserve further consideration.
Light few-body atoms
The third direction in the development of QED has been
the light few-body atoms helium, lithium and exotic
counterparts, such as antiprotonic helium. Comparing
theoretical predictions with experimental results, such as
the recent measurement of the helium ionisation energy,
provides high precision QED tests. Further on, accurate
theoretical predictions, as for the helium fine structure,
allow for the determination of the fine structure constant
α. At present however, this determination is not as
accurate as that from the electron g-factor. Nevertheless,
measurements of α by different methods provide a sensitive
test of consistency of theory across a range of
energy scales and physical phenomena. Particularly
interesting in this respect is antiprotonic helium, where
one of the electrons is replaced by an antiproton. This
is the hadronic system that allows the highest precision
tests of long range interactions between hadrons
to be performed. The agreement of QED predictions
with experimental results of the ASACUSA collaboration
demonstrates the universality of QED theory and will
soon make possible the accurate determination of the
antiprotonic mass and the magnetic moment or even
the electron mass. This requires, however, evaluation
of challenging higher order QED effects, which so far
have been investigated only for the simplest systems,
such as the hydrogen atom.
168 | Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010