CP-violation

After the discovery of the combined charge and space symmetry violation, or CP violation, in the decay of neutral mesons [2], the search for the EDMs of elementary particles has become one of the fundamental problems in physics. A permanent EDM is induced by the super-weak interactions that violate both space inversion symmetry and time reversal invariance [11], Considerable experimental efforts have been invested in probing for atomic EDMs (da) induced by EDMs of the proton, neutron, and electron, and by the P,T-odd interactions between them. The best available limit for the electron EDM, de, was obtained from atomic T1 experiments [12], which established an upper limit of de < 1.6 x 10 27e-cm. The benchmark upper limit on a nuclear EDM is obtained from the atomic EDM experiment on Iyt,Hg [13] as d ig < 2.1 x 10 2 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 24e-cm, was also obtained by Dmitriev and Senkov [14]. The previous upper limit on the proton EDM was estimated from the molecular T1F experiments by Hinds and co-workers [15]. 

As mentioned in the Introduction, the observation of a nonzero EDM of an electron would be a signature of behavior beyond that described by the standard model (SM) of physics [9]. It would be a more sensitive probe of the SM than the neutron EDM, which could have nonzero EDM due to CP violation in the QCD sector of the SM. 

A permanent EDM of a stable atomic or molecular state can arise only when both P and T invariance are broken (see Fig.l). It is often said that polar molecules possess permanent EDMs and exhibit a linear Stark effect. However, the Stark effect exhibited by the polar molecule is not really linear for sufficiently small E at zero temperature, and moreover, it violates neither P nor T symmetry [10]. We emphasize that a permanent EDM that exhibits a linear Stark effect even for an infinitesimally weak is a genuine signature of P and T violation or CP violation... 

DBD experiments with even better sensitivities (of the order of meV) will be essential to fix the absolute neutrino mass scale and possibly to provide information on CP violation. It is therefore evident that next-generation neutrinoless DBD experiments are the next important steps necessary for a more complete understanding of the physics of neutrinos. In the next section, we will describe the CUORE experiment and show how it could reach the required sensitivity. 

As is mentioned in the introduction, the observation of a non-zero EDM would point out the presence of so called new physics (see [30, 1] and references) beyond the Standard Model [2, 3, 4, 5, 31] or CP violation in the QCD sector of SM, SU 2>)c- The discovery of a lepton EDM (electron EDM in our case) would have an advantage as compared to the cases of neutron or proton EDMs because the latter are not considered as elementary particles within the SM and its extensions. 

Masina, I. and Savoy, C. A. Changed lepton flavour and CP violation Theoretical impact of present and future experiments 2004. ArXiv hep-ph/0410382. 

Khriplovich, I. B. and Lamoraux, S. K. CP Violation without Strangeness. The Electric Dipole Moments of Particles, Atoms, and Molecules (Springer-Verlag, Berlin, 1997). 

The new proposed deuteron model is founded on the principles of SLRT and QMT. In Ref. 4, where QMT is presented, it is shown that, if the electron in the hydrogen atom is excited to the state of the potential quantum number, n = 794 then, the electron turns into a positron. The consequence is very unusual the hydrogen atom turns into a system of one proton and one positron, which is undoubtedly a very odd example of CP violation. This has been obtained as a result of theoretical analysis based on the QMT principles. If this is experimentally proved, then atoms with very unusual physical characteristics will certainly be obtained, and a rather exotic regime of matter could be expected. 

Even if allowed by the CPT theorem, the non-conservation of CP symmetry was hard to accept - not least because it was not consistent with the Standard Model. In 1972, Kobayashi and Maskawa predicted that CP violation would be consistent with the Standard Model provided that three generations of quarks exist (and only two were known at the time). The subsequent discoveries of the r lepton by Pearls (1975) and of the top and bottom quarks at the Fermilab confirmed the existence of a third family, this resulted in the incorporation of the CP violation into the Standard Model. 

Even though the CP violation is allowed by the Standard Model, its predicted effect seems to be too small to explain the excess of matter (and the existence of our coino-matter Universe). This means that our way of understanding these CP violations and perheaps the Standard Model itself must be incomplete. Therefore a lot of effort goes into research on fundamental symmetries and setting bounds on their violations. 

The most perceptible experimental reason is the evident asymmetry of the Universe. The CP violation alone, on the level allowed by the Standard model, is not sufficient to explain the excess of matter in the Universe [18]. Finding a suitable extension of the Standard Model is not easy not only do the GUT theories tend to violate CPT invariance but they are also difficult to test. Specifically they can not be tested by means of the particle accelerator experiments, which so far have been very successful in extending our knowledge of Physics. This is because the GUT energy is some 1013 times larger than what we can now days produce in the most powerful accelerators. Consequently we must look for the low-energy manifestations of GUT and CPT invariance. Interestingly some possibilities for such tests lie within the realm of atomic and molecular physics. 

However, the most stringent CPT test comes from a mass comparison of the neutral kaon and antikaon, where the tremendous accuracy of 10-18 has been reached, albeit in a theoretically dependent manner. Not only does the comparison only restrict CPT violation to 1 part in 103 of CP violation, the origin of which itself is not fully understood, but it has been argued [9] that the analysis leading to this limit assumes the validity of the standard model, which in itself does not contain a mechanism for CPT violation. 

The necessary condition for baryogenesis is well documented since Sakharov, although explicit realization for any of these conditions is rather delicate. They are (1) baryon number nonconservation, (2) CP violation, (3) departure from equilibrium. The 3rd condition for the need of the arrow of time is due to presence of the inverse process, which should be possible if there is sufficient time for that to happen. 

Next, I would like to discuss intricacy of CP violation. In gauge theories one may compute the fundamental CP asymmetry, namely the difference of baryon numbers between particle and antiparticle decays using perturbation theory. It is thus given by an interference term of, for instance, the tree and the one-loop contributions. A convenient tool of computing the interference term is the Landau-Cutkovsky rule [19]. The result is like... 

A non-zero value for this difference immediately requires both CP violation / 0 and a non-trivial dynamical phase factor such as the rescattering phase in /2 of a one-loop amplitude. 

One needs some new, fresh idea to establish a link with other low energy CP violation such as observed K and B decays. 

Axions arising from Peccei-Quinn symmetry (1977) as a cure for the strong CP violation problem (46). 

Khriplovich, I. B. and Lamoreaux, S. K. (1997) CP violation without strangeness electric dipole moments of particles, atoms, and molecules. Texts and Monographs in Physics. Springer. 

J. Kiibler Theory of itinerant electron magnetism 105. Y. Kuramoto, Y. Kitaoka Dynamics of heavy electrons 104. D. Bardin, G. Passarino The Standard Model in the making 103. G.C. Branco, L. Lavoura, J.P. Silva CP Violation 102. T.C. Choy Effective medium theory 101. H. Araki Mathematical theory of quantum fields 100. L. M. Pismen Vortices in nonlinear fields 99. L. Mestel Stellar magnetism 98. K. H. Bennemann Nonlinear optics in metals 96. M. Brambilla Kinetic theory of plasma waves 94. S. Chikazumi Physics of ferromagnetism 91. R. A. Bertlmann Anomalies in quantum field theory 90. P. K. Gosh Ion traps... 

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