261 ATOMIC ELECTRIC DIPOLE MOMENTS AND CP VIOLATION S.M.Barr Bartol Research Institute University of Delaware Newark, DE 19716 USA Abstract The subject of atomic electric dipole moments, the rapid recent progress in searching for them, and their significance for fundamental issues in particle theory is surveyed. particular it is shown how the edms of different kinds of atoms and molecules, as well Inas of the neutron, give vital information on the nature and origin of CP violation. Special stress is laid on supersymmetric theories and their consequences. 262 I. INTRODUCTION In this talk I am going to discuss atomic and molecular electric dipole moments (edms) from a particle theorist's point of view. The first and fundamental point is that permanent electric dipole moments violate both P and T. If we assume, as we are entitled to do, that OPT is conserved then we may speak equivalently of T-violation and OP-violation. I will mostly use the latter designation. That a permanent edm violates T is easily shown. Consider a proton. It has a magnetic dipole moment oriented along its spin axis. Suppose it also has an electric edm oriented, say, parallel to the magnetic dipole. Under T the electric dipole is not changed, as the spatial charge distribution is unaffected. But the magnetic dipole changes sign because current flows are reversed by T. Thus T takes a proton with parallel electric and magnetic dipoles into one with antiparallel moments. Now, if T is assumed to be an exact symmetry these two experimentally distinguishable kinds of proton will have the same mass. But we know that there is only one type of proton in the world, as otherwise the chart of nuclides would look very different. Thus either the proton has no edm or T is not an exact symmetry. The same argument applies to any other elementary particle (that is not "CP doubled" , which includes all the known ones). The same kind of argument shows that edms violate P. Now, CP violation is not well understood. That it is violated has been known since the classic experiment of Christenson, Cronin, Fitch and Turlay in 19641) for which Cronin and Fitch received the Nobel Prize in 1980. What that experiment showed was that CP was violated in the neutral Kaan system; in particular that KL decayed about two times in a thousand into two pions rather than three. It is remarkable that from that time until now - thirty years - CP violation has been observed in the laboratory in no other system than the neutral Kaons. I put in the qualifier "in the laboratory" because according to the currently standard picture of cosmology the cosmological baryon asymmetry (OBA), which is the fancy name for the fact that the matter in the universe is almost entirely matter rather than antimatter, is due to CP­ violating processes in the early universe.2l However, this fact, while it almost certainly points to OP-violating physics beyond the standard mode!3l, is of little help in understanding CP violation because there are so many possible scenarios of cosmological baryon generation. From the neutral kaon system there are two OP-violating quantities which can be measured, and has been known for thirty years [= 2.3 x 10-3), while the situation with 1 ([ E remainsE • murky,E with one experiment showing aE definitely non-zero value4l and the other6l fl being consistent with zero. The Particle Data Book gives the average of the two as 1 / [ = [ E E 2.2 ± x io-3. Withu so little data to work with it is not surprising that CP violation is poorly understood. Our other information about CP violation is in the form of null results. The most important of these is the limit on the neutron edm,6) which is d,. � 1.2 x lQ-25 e-cm. As we shall see, this leads to a major puzzle for particle theory called the Strong CP Problem. As we shall also see, the limits on the edms of atoms and molecules are also theoretically very important and will become greatly more important as they are pushed further, unless, of course atomic or molecular edms are seen, which would be epoch-making. It should be emphasized that the subject of CP violation is not some obscure corner of particle physics. It is a central topic of inquiry. It touches on such diverse issues as the edms of elementary particles and the origin of matter in the universe (as already noted), as well as on the nature of dark matter ("axions" are a prime candidate), the origin of galaxies, and the structure of physics beyond the so-called Standard Model of particle physics, as we shall see. And, of course, it is a question of fundamental interest in itself whether the laws of physics are T invariant and if not why. Fortunately, there are good prospects of learning more about CP violation over the next ten years. The main hope lies in the direction of further progress 263 in atomic and molecular edm experiments and in the study of neutral B mesons (a heavier analogue of the neutral kaons) at either "B factories" or at the LHO. There is also a large and promising effort being made to detect dark-matter axions by a variety of techniques, as is being discussed in other talks at this conference. II. CP VIOLATING PHASES OP violation arises, essentially, because of the presence in the underlying particle theory of non-trivial, physical, complex phases. Not all phases are physical. Some can be "rotated away"; that is, they can be absorbed by field redefinitions. Take, for example, QED, the theory of photons and electrons. In that theory the electron mass parameter can be complex: m.e'8eLeR+ h.c .. The phase Bis not physical as it is possible to eliminate it by redefining the righthanded electron field: ek e'8eR m.eLek+ h.c .. In simple theories there are often few enough parameters that= all the =>phases can be rotated away, as in QED. Such theories automatically conserve OP. But as a theory becomes more complicated the number of OP-violating phases tends to proliferate rapidly. III. CP VIOLATION IN THE STANDARD MODEL The Standard Model of particle physics is so simple that there are only two possible OP­ violating phases in it. They are called ti (or {jKM) and 8. ti is the Kobayashi-Maskawa phase which appears in the charged weak interactions, while 8 is the QOD vacuum angle which appears in the theory of the strong interactions. Let us discuss the latter first. A. The Strong CP Problem The Strong OP Problem, or B Problem, arises due to the fact that the neutron edm gets a contribution of order (10-16 e-cm) x sin 8. The experimental limit, therefore, implies that 8 10-9. The problem is to explain why, given the presumed fact that the weak interactions badly� violate OP (suggested by the neutral Kaon system), the strong interactions conserve OP to at least a part in a billion. Any explanation of this requires going beyond the Standard Model. There are two main approaches to solving this problem, the Peccei- Quinn mechanism7l and models with spontaneous OP breaking8l. The Peccei-Quinn mechanism involves the existence of the particles called "axions" . (Al­ ternatively there could be massless quarks. For example, it is much discussed whether the up quark could in actuality be massless.) In the axion models Ii comes out to be of order 10-15, generally. (In exotic variants it could be different.) This would give a value of order 10-31 e-cm for the 8 contribution to d,., far too small to be interesting experimentally. Axion models are not without difficulties. They are highly constrained by laboratory searches, and astrophysical and cosmological limits. Moreover there are potential problems with cosmic domain walls and with possible quantum gravity effects that have to be faced in constructing such models. Nev­ ertheless, the axion idea still has to be considered the most attractive solution to the strong OP Problem. The alternative approach is based on the idea that 8 is small as the consequence of some symmetry. The most likely possibility is that this symmetry is OP invariance itself. The idea is that OP is a good symmetry of the Lagrangian which is "spontaneously broken" by a OP-non-invariant ground state. In this way some OP-violating parameters may be small as a consequence of the underlying symmetry of the theory, while others may feel the spontaneous 264 OP breaking more directly and have larger values. In many of these models there is some difficulty in making 1J come out as small as 10-9. This may be even more of a problem in the context of supersymmetry. However, this idea has attractive features and quite viable and relatively simple models exist. One would expect that if this solution of the Strong OP Problem is the correct one that would be not far below present limits. We see, therefore, 1Jthat edm experiments already have had a major impact on particle theory. And it should be emphasized that the limits on 1Jcoming from searches for the edms of diamagnetic atoms and molecules are competitive with that coming from the neutron, and it is quite likely that may eventually first be seen in atomic experiments. If an edm of the neutron1J or a diamagnetic atom or molecule is observed, how will we know that it is a consequence of IJ? With just this kind of experiment we will not. There are many kinds of new OP-violating physics that could give rise to these effects.