Introduction
Theoretical Motivation
Detecting an EDM
Experiments
| Theoretical Implications | Mercury Experiment Data |
system, because the theories usually predicted too large a dipole moment.
The currently accepted Standard Model of Particle Physics predicts
unobservably
small dipole moments. Therefore, EDM experiments are an ideal probe for
new physics beyond the Standard Model, such as supersymmetry, in which
the natural size of EDMs of neutrons, atoms and molecules lies within a
detectable range.
In a general field theory, CP violation is caused
by the presence of a complex phase between different fundamental fields.
Thus CP violation in the K
system is accommodated within the Standard Model by allowing some elements
of the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be complex. For three
generations of quarks exactly one complex phase is allowed, which turns
out to have a value of order unity, 
.
The phase cannot be determined more accurately from measurements on the
K system because of the hadronic uncertainties.
Although the CP violation is explained naturally by the CKM matrix, it is not possible at present to check the self-consistency of this explanation. To address this problem, the B factory is being build at SLAC to study CP violation in the neutral B meson system. Many different decay modes of the B mesons can be studied, and it will be possible to measure asymmetries in which the hadronic effects cancel. Enough measurements can be performed to over-constrain the elements of the CKM matrix and thus check the consistency of this explanation. The B decays will also allow one to test for other sources of the CP violation. First data from the B factory are expected around the year 2000.
Any extension of the Standard Model which introduces additional particles also allows for additional physically observable phases. The general classes of models that have been considered are supersymmetric models, left-right symmetric models, and multi-Higgs models. At present, the limits on the EDM from measurements in paramagnetic atoms, diamagnetic atoms and the neutron all place comparable constraints on the models, and these constraints are already becoming significant. For example, if supersymmetry were broken near the electroweak scale it would solve the gauge hierachy problem, but then it would also very naturally generate EDMs close to currently observable sizes.
The role of CP symmetry in the theory of strong
interactions is also not well understood. The QCD Lagrangian naturally
contains a term which violates CP, parameterized by 
.
The limits on neutron and 
Hg
EDM put a limit on 
,
while the natural value of
is of order unity. Several mechanisms have been proposed to explain the
smallness of .
One of the most popular, Peccei-Quinn symmetry, predicts the existence
of an additional pseudoscalar particle, the axion. Many searches for the
axion have been conducted with negative results.
Some evidence for CP violation beyond the Standard Model comes from Cosmology. Astronomical observations indicate that our Universe is mostly made of matter and contains almost no anti-matter. In the Big Bang cosmology this asymmetry has to be generated dynamically during cooling of the universe, a process called baryogenesis. CP violation is one of the requirements for baryogenesis. One of the most attractive scenarios of baryogenesis involves the electroweek phase transition at the energy scale of 100 GeV. Because the interactions at this energy scale are well known, one can make relatively reliable estimates of the baryon asymmetry. These estimates indicate that if the only source of CP violation is in the CKM matrix, the baryon asymmetry is smaller than the observed value by many orders of magnitude. However, extensions of the Standard Model, such as supersymmetry or multi-Higgs theories, which involve additional sources of CP violation, can naturally produce the baryon asymmetry of the correct magnitude.
| EDM violates time reversal symmetry. By the CPT theorem, it also violates CP (charge and parity) symmetry. |
|
Under time reversal the direction of the spin changes, since it is an axial vector, while the charge distribution does not change. The electric dipole moment, which is a vector, has to be parallel to the spin, since it is the only available vector in the rest frame of the particle. Therefore, if time reversal is a good symmetry, the electric dipole moment must be zero. |
One measures the Larmor precession frequency of the spins in parallel electric and magnetic fields and alternates the relative orientation of the two fields. |
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The change in frequency is proportional to the electric dipole moment and the applied electric field.  |
A particle with electric and magnetic dipole moments d
and 
interacts with external electric and magnetic fields 
and 
by the following Hamiltonian
where 
is the total angular momentum. The violation of T is evident when we note
that
does not change sign under 
,
whereas
and
both do. In all experiments, the search for an EDM consists of measuring
the precession frequency of the particle in parallel electric and magnetic
fields and looking for a change of this frequency when the direction
of
is reversed relative to .
EDM measurements are carried out either on a beam of the atoms or
molecules
or on a sample of them held in a bottle. Beams are the method of choice
for such atoms and molecules as Tl and TlF which undergo rapid spin
relaxation
in a bottle. Bottles are usually chosen for those systems which have a
long spin relaxation time, 
,
such as Cs, Xe, Hg, or the neutron. The long
obtainable in a bottle means a sharp resonance line and high precision.
The bottle also has the advantage of averaging the 
motional magnetic field nearly to zero. However, bottles cannot support
as large an electric field as beams, and bottles usually have larger high
voltage leakage currents.
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[1] K.F. Smith et al., Phys. Lett. B 234,
191 (1990).
[2] I.S. Altarev et al., Phys. Lett. B 276,
242 (1992).
[3] J.P. Jacobs, W.M. Klipstein, S.K. Lamoreaux, B.R.
Heckel, and E.N. Fortson, Phys. Rev. A 52, 3521 (1995).
[4] D. Cho, K. Sangster, and E.A. Hinds, Phys. Rev. Lett.
63,
2559 (1989).
[5] E.D. Commins, S.B. Ross, D. DeMille, and B.C. Regan,
Phys. Rev. A 50, 2960 (1994).
[6] S.A. Murthy, D. Krause, Z. L. Li, and L.R. Hunter,
Phys. Rev. Lett.
63, 965 (1989).
There are extensions of the above experiments, either now underway or expected to begin shortly, that aim to significantly improve the sensitivity to EDM. These include the Berkeley atomic beam experiment that will compare Tl and Na atoms, a cryogenic neutron EDM measurement proposed at LANL, our mercury experiment using a frequency-quadrupled laser diode for optical pumping and a YbF experiment at Sussex. There are also efforts underway at Austin, Stanford and here to apply the techniques of atom cooling and trapping to EDM experiments, as well as a 129Xe-3He spin maser experiement being developed at University of Michigan and Harvard - Smithsonian.
The table below gives limits on some of the CP violating parameters
set by our measurement in Hg
(J.P. Jacobs, W.M. Klipstein, S.K. Lamoreaux, B.R. Heckel,
and E.N. Fortson, Phys. Rev. A 52, 3521 (1995)) compared
with best limits from other work.
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[1] D. Cho, K. Sangster, and E. A. Hinds, Phys. Rev. Lett.
63,
2559 (1989).
[2] K. F. Smith, et al., Phys. Lett. B 234,
191 (1990).
[3] E. D. Commins, S. B. Ross, D. DeMille, and B.C.
Regan,
Phys. Rev. A
50, 2960 (1994)
