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4.5 Fundamental Interactions
be tested experimentally. The validity of Lorentz and CPT
invariance ultimately rests on experiment.
A concrete motivation to search for violations of
Lorentz and CPT invariance is found in modern attempts
to unify the SM with the fourth fundamental force, gravity.
In such unified theories, formulated at the Planck
scale, plausible mechanisms have been identified that
result in a violation of Lorentz invariance at low energy.
For instance, in string theory, spontaneous breaking
of Lorentz invariance can occur, resulting in vacuum
expectation values for Lorentz tensors. Hence, the fascinating
possibility exists to detect such suppressed
signals from the Planck scale in dedicated, high-precision
experiments at low energy. In the context of cosmology,
Lorentz and CPT violation could have major implications
as well. CPT violation can replace two of the three
Sakharov conditions that are required to generate the
matter–antimatter asymmetry of the Universe (viz. violation
of CP invariance and the deviation from thermal
equilibrium), and thereby offers an alternative scenario
for baryogenesis.
CPT invariance implies that particles and antiparticles
have related properties, in particular the same mass
and opposite signs for internal charge-like quantities
such as electric charge, colour, and lepton and baryon
number. A direct sensitive test of CPT invariance is to
measure these properties for both particles and antiparticles.
The masses of the neutral kaon and antikaon
are presently the most precise such comparison, with
a relative difference at the level of 10 -18 . Figure 6 shows
the comparison of the accuracy reached in such CPT
invariance tests for several quantities of various particles
and systems. The charge-to-mass ratio of the proton
and antiproton was compared at LEAR via measuring
cyclotron frequencies in a Penning trap. The difference
Figure 6. Comparison of several CPT tests in terms of relative
accuracy (blue) and absolute accuracy (red) based on the
Standard Model Extension model of Kostelecky et al. Values for
hydrogen–antihydrogen comparison assume that antihydrogen
will be measured to the same precision that has been achieved for
hydrogen.
was found to be less than about 10 -10 . A similar stringent
CPT test at this level is possible by comparing the
magnetic moments of the proton and antiproton stored
in a Penning trap, as is being prepared at several laboratories.
At present, the only facility to perform such
experiments is the Antiproton Decelerator (AD) facility at
CERN, constructed in 1999 in order to test CPT invariance
for antiprotons and antihydrogen.
The AD experiments ATHENA, ATRAP, and ALPHA
have produced and studied antihydrogen atoms and are
making progress towards confinement and spectroscopy.
The ASACUSA collaboration has produced and
studied antiprotonic helium and measured the mass,
charge, and magnetic moment of antiprotons bound
in atomic orbits by laser spectroscopy. The antiproton-to-electron
mass ratio was found to be equal to
the proton-to-electron one at the 10 -9 level (Figure 7),
implying CPT tests for the relative differences of the
proton and antiproton charges and masses at this level.
Since this community is expanding, it will soon face a
need for antiproton beams. A short-term solution is the
ELENA storage ring at CERN, while possibilities for the
longer-term future are provided by the FAIR facility at
GSI-Darmstadt.
Finally, CPT relates closely to spin-statistics that is
addressed in experiments testing the Pauli principle as
for example at the Gran Sasso laboratory.
The violation of Lorentz invariance generically results
in unique signals, in particular rotational, sidereal, and
annual variations of observables that in Lorentz-invariant
theories, such as the SM and its generally considered
extensions, are constant. Such effects translate e.g.
into the presence of a preferred direction parameterised
by a constant vector in expressions for measurable
quantities. In other words, Lorentz violation results in
a frame dependence of the observables, where the
preferred inertial frame is fixed at a cosmological scale
(this frame might be identified, for instance, with the
frame of the cosmic microwave background). Over the
course of the last decade, there has been significant
experimental activity to search for such signals in various
physical systems. Many of these dedicated experiments,
especially those in electrodynamics and optics, involve
high-precision searches using the sharpest weapons of
atomic physics, such as lasers, atom or ion traps and
storage rings. However, clock comparisons mounted
on space missions have also been proposed. Signals
of Lorentz and CPT violation have also been looked for
in the neutral-kaon system, in neutrino oscillations, in
the muon g-2 experiment, etc.
A model-independent effective field theory has been
developed by Kostelecký and collaborators to quantify
possible signals of spontaneous Lorentz and CPT viola-
166 | Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010