Electric Dipole Moment: A clue to what underlies our material world

Soon after leaving his mother’s womb, each of us starts recognizing little by little that a vast space extends around him and numerous objects surround him there. Of what and how are those objects, including himself, composed? This question continues to be borne in his mind, consciously or unconsciously. Natural sciences (and among them physics in the most straightforward manner) have been attempting to answer this question. Achievements of modern sciences including those by the recent experiments obtained at LHC CERN tell us that there exist in our World twelve kinds of fermions (ingredient particles of matter), four kinds of gauge bosons (mediator particles of forces) and (at least) one kind of Higgs boson (background particle).

Then, does this idea, referred to as the Standard Model (SM), work all right? Unfortunately, the answer is NO. First of all, the above set of particles that are enrolled in the SM proves to share only about 5 % of the observed energy content of our Universe, thus lending the other 95 % to some unknown kinds of particles and energies. Second, our Universe contains more matter than antimatter, contrary to the natural consequence of the Big Bang theory of modern cosmology that matter and antimatter should exist in equal amounts. In fact, the observed matter-antimatter asymmetry, as measured with the particles-to-radiations abundance ratio, is by 10⁸⁻¹⁰ times larger compared to predictions by the SM, indicating that the CP symmetry is violated to a far larger extent than in the SM. Third, the SM includes many basic parameters whose values are not determined in the theory itself but need inputs from outside, evoking a view that the SM might be an effective theory that derives from a more fundamental one. Thus, what sort of theory prevails beyond the SM, is the subject of a keen interest among physicists these days.

Many experimental and theoretical studies are actively being conducted, aiming to find evidences for new, CP-violating physics beyond the SM. Essentially there are two approaches: The first one takes a route of producing new particles, detecting them and then studies their properties and interactions. This approach necessarily relies on the ability of a high-energy accelerator, hence is called the energy frontier approach. Another one, the precision frontier approach, focuses on some low energy process which occurs due to new physics (and at the same time is forbidden by the SM, favorably). Such a process inevitably is a higher order one and needs high precision measurements. The former approach is certainly straightforward and is able to provide not only an evidence but also very detailed information on the new physics just discovered, as far as an accelerator capable of delivering the beam of the relevant energy is available. This latter condition, however, is not always fulfilled and, in a case where the expected energy scale for the new physics of interest is very high, this approach is even forbidden. In contrast the latter, the precision frontier approach, does not rely much on the accelerator energy and, although the information provided is rather indirect (or, can only "infer" the existence or properties of new particles and interactions), the tail of its sensitivity to new physics would extend to amazingly high energies.

The electric dipole moment (EDM) is one of the objectives which the precision frontier studies aim to measure. The EDM is a vector quantity representing the particle’s electric charge polarization, accompanying the spin (also a vector, representing the rotation of the particle). It points in the direction of the spin, and its magnitude is given by the spatial separation between the positive and negative charges appearing due to the polarization, multiplied by their charge value, and is scaled in unit of e · cm. Most remarkably, from its definition the EDM violates the CP symmetry, as illustrated in Fig. 1. Furthermore, the EDM is a static moment (or, is not a transition moment that may involve change in flavor), which the Kobayashi-Maskawa type CP violation contained in the SM cannot produce in the tree level. In fact, values of EDM calculated within the SM turn out to be undetectably small for any particles, whereas they can be quite large in most of the theories proposed beyond the SM. Therefore, once a finite value is found experimentally for an EDM, it will constitute an unquestionable evidence for the existence of new physics beyond the SM. Thus, the EDM is entitled to be an exclusive observable that selectively probes new physics beyond the SM.

Nowadays a number of experiments searching for the EDM in various physical sites, such as neutron, diamagnetic atoms, paramagnetic atoms, muon, proton, deuteron and other ions, are planned or actually being carried out. Also, theoretical analyses are in progress, clarifying what CP-violating operators are responsible for which EDMs and so on, as illustrated in Fig. 2. It is worth noting here that, whatever type of theory beyond the SM appears at its characteristic energy scale Λ_BSM, its contribution to the EDM are represented at energies below Λ_BSM by several pieces of CP-violating dimension-6 operators (denoted by in the figure) each of which is constructed using the SM particle and field operators. The operators each generate, through hadronic processes, values on six low-energy parameters d_e, d_N, , , C_T and C_S, which in turn govern the values of the individual EDMs. Evaluation of EDMs for atoms and ions from the global parameters involves nuclear and atomic structure calculations.

Tracing the links from EDMs of various physical sites upward to the global parameters, one sees that the EDM d_para of a diamagnetic atom is generated by d_e and C_S, whereas the diamagnetic atom EDM d_dia comes from , and C_T. Once d_dia for three different diamagnetic atoms are known, for example, individual values for , and C_T are determined. In such a way, the measurement of EDMs for a sufficient number of particles would allow the global parameters to be determined individually, which in turn would disclose the sizes of the Wilson coefficients of the CP-violating dimension-6 operators and thus will provide information on the character of the theory that governs the material world at energies above Λ_BSM.

Currently, the neutron EDM is confined by experiment as |d_n|<2.9x10^-26e・cm. In the site of diamagnetic atoms the experimental limit for the EDM of ¹²⁹Xe is |d(¹²⁹Xe)|<6.7x10^-27e・cm and that for ¹⁹⁹Hg is |d(¹⁹⁹Hg)|<7.4x10^-30e・cm, while in the site of leptons, |d_e|<8.7x10^-29e・cm for electron and |d_μ|<1.8x10^-19e・cm for muon are set by experiments. Although the precision for the electron EDM is quite high, the EDM of a diamagnetic atom ¹⁹⁹Hg is the best confined among all the particles studied up to now. In order to determine the three global parameters , and C_T by taking full advantage of this most stringent upper limit on the Hg EDM as well as that obtained for TlF, the EDM measurement for one more atom in the diamagnetic site with the same level of precision is most eagerly awaited.

Under the circumstances, we aim to measure the EDM of a diamagnetic atom ¹²⁹Xe and to combine the result with those for the other two EDMs for ¹⁹⁹Hg and TlF to determine the three global parameters. Experimentally, a sample of a macroscopic amount (several hundred Torr in pressure, times several cm³ in volume) of the stable isotopes ¹²⁹Xe and ¹³¹Xe gas mixture is used. Since the nuclear spin of a noble gas atom has very long relaxation times, the spin can be highly polarized (up to several tens of %) by means of the spin exchange optical pumping (SEOP) with alkali atoms. Figure 3 shows the principles of a nuclear spin maser with external feedback employed in the measurement.