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muon intensities. These could be achieved for example
at the European Spallation Source that is due to be built
in Sweden. Another particle considered for a ring EDM
experiment is the deuteron, for which a sensitivity of 10 -29
e cm might be achievable. Design studies, particularly
on spin dynamics in a ring and on deuteron polarimetry
using nuclear scattering, are presently being performed
at the COSY facility in Jülich, with the aim of performing
a deuteron EDM experiment in the near future.
Decay correlations
Observables for testing time reversal violation in particle
decay or reactions can be constructed by combining
appropriate vectors and axial vectors. Time reversal
violation in nuclear strong interactions can usually be
addressed with more sensitivity from limits on neutron
and nuclear EDMs.
Important TRV observables are available in β decays
of leptons and hadrons (e.g. muons, neutrons, nuclei,
hyperons). Experimentally accessible are triple correlations
of parent particle spins, J, and decay lepton
momenta, p, and spins, σ. The triple correlation between
parent spin, β particle momentum and neutrino momentum
is conventionally referred to as the D coefficient,
while the R coefficient labels the correlation between
parent spin, β particle momentum and spin:
〈J → 〉 p → e p → ν
〈J → 〉 p → e
D ∝ ⎯ . ⎯ × ⎯ and R ∝ → σ . e ⎯ × ⎯
J E e E ν J E e
The TRV contribution in D would be from a phase
between vector and axial vector coupling, in R from
tensor and scalar couplings.
The best limits on D come from 19 Ne decay, D Ne =
(0.1 ± 0.6) × 10 -3 (Princeton), and from neutron decay,
D n = (0.4 ± 0.6) × 10 -3 (NIST, ILL), on R from β decays of
8 Li and neutrons (both PSI): R Li = (0.9±2.2)×10 -3 and R n
= (0.8 ± 1.5 ± 0.5)×10 -2 .
Further improvements of the sensitivity in D and R
correlation experiments appear possible, both with
neutrons as well as with light nuclei, eventually using
trapped radioactive atoms or ions at radioactive beam
facilities.
Investigating TRV observables in other than nucleonic
systems remains of interest for various reasons;
for example, the pure leptonic character of the muon
system and the absence of electromagnetic final-state
interactions. Superior sensitivity could be obtained by
improved positron polarimetry at existing facilities or
via improved counting statistics at future production
facilities for muon neutrinos.
CPT and Lorentz invariance
The principle of relativity in four-dimensional space–time
implies that the laws of physics are Lorentz (Poincaré)
invariant, that is, they are invariant under translations,
rotations, and boosts (velocity transformations). Lorentz
invariance is a cornerstone of modern physics: when
combined with the principles of quantum mechanics,
it leads to the framework of relativistic quantum
field theory for the description of the interactions of
elementary particles. Lorentz invariance is at the basis
not only of the SM, but also of extensions of the SM,
such as supersymmetry, that are formulated in terms
of a local quantum field theory. Lorentz invariance is
intimately connected to CPT invariance: Lorentz invariance
is needed to prove CPT invariance in a quantum
field theory, and, equivalently, CPT violation implies the
violation of Lorentz invariance. CPT invariance is valid
in a local and causal Lorentz-invariant quantum field
theory; to break it, one must give up locality, causality,
and/or Lorentz invariance. Numerous experiments so
far have confirmed that Lorentz and CPT invariance are
valid at presently accessible energies and precisions;
violations, if they exist, must be very small. Nevertheless,
there are excellent reasons to test their validity as exact
symmetries as accurately as possible. All the symmetries
of physics are based on a priori theoretical assumptions
that Nature may not respect and that therefore need to
Table 3. Status of electric dipole moment searches.
Particle Experimental method Limit
(e cm)
SM value
(factor to go)
New physics
(factor to go)
electron thallium beam 1.6 x 10 -27 10 11 1
muon magnetic storage ring 1.9 x 10 -19 10 8 200
neutron ultracold neutrons 2.9 x 10 -27 10 4 30
proton thallium spin resonance 3.7 x 10 -23 10 7 10 5
199 Hg atom spin precession in external E and
B fields
3.7 x 10 -26 10 5 various
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