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4.5.4 Properties of Known
Basic Interactions
The weak interaction has been dealt with extensively in
the previous sections. This contains a number of fundamental
constants, several of which have recently been
determined with improved precision, e.g. a new measurement
of the muon lifetime has recently provided a more
precise value for the Fermi coupling constant G F , while
measurements of the muon capture on protons have
provided the pseudoscalar coupling constant g P . In the
following sections we will concentrate on the other basic
interactions, which also allow for the determination of
a number of fundamental constants and searches for
physics beyond the Standard Model.
Figure 7. Progress in the proton-to-electron and antiproton-toelectron
mass ratio over time.
tion. This comprehensive and consistent framework is
called the Standard Model Extension (SME). It consists
of the SM (coupled to general relativity) extended with all
possible operators that violate Lorentz invariance. The
minimal version of the SME includes only the Lorentzviolating
operators of mass dimension three or four,
about half of which violate CPT invariance. The coefficients
multiplying these operators are dimensionless or
have positive mass dimension. Many of the experiments
have been analysed within the framework of this minimal
SME (see Figure 5). So far, no deviation from Lorentz and
CPT invariance has been found, and several experiments
have put stringent upper limits on the SME coefficients.
However, a large part of the parameter space has not
been investigated experimentally yet.
QED and fundamental constants
Quantum electrodynamics (QED), the quantum theory
of electromagnetic interactions, is a cornerstone of the
Standard Model. It has been intensively tested and
verified by comparison against precise measurements
on free elementary particles, the hydrogen atom, and
other simple atomic systems. The measurement of the
2S 1/2 - 2P 1/2 transition frequency in hydrogen by Lamb
and Rutherford in 1947, which according to Dirac theory
vanishes, stimulated the development of the covariantly
renormalised QED. Recently, precisions at the 10 -13
level were achieved in direct measurements of optical
transitions, such as the 1S-2S or the 2S-nS hydrogen
transitions. At this level of sensitivity, apart from verifying
QED theory, fundamental physical constants can
be obtained with a very high accuracy. This, however,
requires a good understanding of the proton and in general
nuclear structure effects, such as charge radii or
polarisabilities. In fact all QED tests with the hydrogen
atom are limited by the uncertainty in the proton electric
or magnetic radii. Since, at present, no QCD implementation
allows for their accurate evaluation, these radii
have to be determined experimentally, for example by
low energy electron scattering or through the measurement
of the Lamb shift in muonic hydrogen (at PSI). At
the time of writing this report, these experimental results
are not yet officially available, but preliminary results
indicate intriguing discrepancies for the proton charge
radii. Nevertheless, accurate determinations of these
quantities are of utmost importance for improved tests
of QED with the hydrogen atom.
g–2 measurements
Since the original calculations of Bethe, Feynman and
others of the hydrogen Lamb shift, QED has been under
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