Symmetry 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]. 

Figure 1. Parity (P) and time (T) reversal symmetry violation.

As mentioned earlier, heavy polar diatomic molecules, such as BaF, YbF, T1F, and PbO, are the prime experimental probes for the search of the violation of space inversion symmetry (P) and time reversal invariance (T). The experimental detection of these effects has important consequences [37, 38] for the theory of fundamental interactions or for physics beyond the standard model [39, 40]. For instance, a series of experiments on T1F [41] have already been reported, which provide the tightest limit available on the tensor coupling constant Cj, proton electric dipole moment (EDM) dp, and so on. Experiments on the YbF and BaF molecules are also of fundamental significance for the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDM de. Accurate theoretical calculations are also absolutely necessary to interpret these ongoing (and perhaps forthcoming) experimental outcomes. For example, knowledge of the effective electric field E (characterized by Wd) on the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron s EDM de in the ground (X2X /2) state of YbF and BaF. 

At this juncture, we note that experiments on the BaF molecule to detect P,T-symmetry violation has not yet been performed but are being planned. Hence the present estimate for Wd as well as the previous calculations [46, 54] will be useful for experimentalists. As the experiments progress, calculations with much higher accuracies will be performed by including effects that are neglected/omitted in the present calculation such as electric field EtJ in Eq.(42). Therefore the accuracy of the present calculation is sufficient at this moment. 

On the most fundamental level, we have shown how this experimental scheme might be used for a fundamental test of CPT symmetry violation [8]. While still somewhat hypothetical, at present, this would constitute the most sensitive currently proposed test on CPT symmetry. The sensitivity expressed as a baryon mass difference Am between particles and antiparticles (with mass m) would be of the order of Am/m = 10"30 [8]. The best currently proposed other experiment is on antihydrogen spectroscopy at CERN (not yet carried out) with Am/m = 10 18, and the best existing result for the proton-antiproton pair is Am/m < 10 9 [9]. 

The conditions required for a non-symmetric Universe were first put forward by Sakharov [16] they include non-conservation of the baryon number, C and CP symmetry violation, and the existence of a period of thermal non-equilibrium during the evolution however, the present limits on the proton lifetime (1033 years) are inconsistent with the first condition, and the small degree of CP symmetry violation displayed by kaons is not compatible with the second condition. 

Another scale of accuracy is set by theoretical considerations regarding the measure of the expected symmetry violations the tests should be sensitive enough to detect the predicted effects. 

Extensions allowing CPT and Lorentz invariance violations [23] lead to atomic models that reflect the symmetry violations as shifts in the atomic energy levels. It has been argued that such effects can be discovered in the fine-structure of Is — 2s transitions and also in the hyperfine structure of Zeeman transitions. 

The notation is defined in ref. [2], where other, CPT even Lorentz-violating La-grangian terms are also given. High precision experiments on muonium (M) can measure or set limits on the parameters of these symmetry violating terms, which are sensitive at the Planck scale level [4]. 

In summary, the model allows for two types of interactions between the mirror spaces, the weak kinematical perturbation and the adiabatic and sudden limits equivalent to Eq. (17) or Eqs. (29)-(34). The overwhelming rate of particles over antiparticles in the Universe is inferred in this picture once the particular particle state has been selected. The Minkowski metric of the special theory of relativity is represented here by a non-positive definite metric, Eq. (8), bringing about a quantum model with a complex symmetric ansatz. Although the latter permits general symmetry violations, it is nevertheless surprising that fundamental transformations between complex symmetric representations and canonical forms come out unitary. 

This contradiction, however, is a merely verbal one, like lhatt)etween a tall wife and a short husband. The contrast is striking, but irrelevant -> since it provides no reason why the contradiction could not go on indefinitely. The notion of a social contradiction has the theoretical function of identifying causes of instability and change, not of locating symmetry violations. 

Physical applications An early application of relativistic molecular theory was to heavy atom collisions, and the production of supercritical fields involving highly stripped ions [234-237]. Studies have been made of parity- and time-reversal symmetry violation in diatomic molecules [74,238,239], and of parity violation in small chiral molecules [240-242]. 

Cs symmetry is not an absolute prerequisite for syndiospecific metallocene catalysts despite its symmetry violation, complex 55 (Figure 12) provides... 

In a separate contribution [11], we have analysed within the present framework an assessment of the various arrows of time and the possible symmetry violations instigated by gravitation including the fundamental problem of molecular chirality [12]. Other related developments involve Penrose s concept of objective reduction (OR), i.e. gravity s role in quantum state reduction and decoherence as a fundamental concept that relates micro-macro domains including theories of human consciousness [13], see also Ref. [3] for more details. Note also efforts to derive quantum mechanics from general relativity [14]. 

There are finally many consequences that follow from the present formulation, i.e. fundamental symmetry violations, scale invariance and the non-probabilistic traits of evolution due to the regulation of self-reference [11]. In principle, the... 

Quack M (2011) Fundeunental symmetries and symmetry violations from high resolution spectroscopy. In Quack M, Merkt F (eds) Handbook of high resolution spectroscopy, vol 1. Wiley, Chichestei/New York, p 1... 

Molecular Parity Violation and Chirality The Asymmetry of Life and the Symmetry Violations in Physics... 

Fig. 3.1 The energies of enantiomers are different because of a symmetry violation. The energy difference Ap Eo = ApyE and the reaction enthalpy Apv/fo = /lApv o for the reaction R = S can be described with the spectroscopic schematic diagram shown here. This is estimated to be 10 J moL for CHFClBr [12]. How important is this energy difference for chemistry What are the consequences for biology (see also [13])...

Pig. 3.4 Symmetry breaking and symmetry violation (After [22]). In the classical limit, the left-hand picture can also be used for illustrating spontaneous symmetry breaking (see text)... 

A further cosmological speculation also points to the importance of the symmetry violations. In Refs. [23, 26], we proposed a world game which is illustrated in Fig. 3.10. 

Quack M (2011) Fundamental symmetries and symmetry violations from high resolution molecular spectroscopy experiment and theory. In Nishikawa K (ed) Abstract book, XVIth international workshop on quantum systems in chemistry and physics (QSCP XVI), Kemazawa, Japan, 11-17 September 2011, p76... 

Cho, D., Sangster, K., and Hinds, EA., Tenfold improvement of limits on T violation in thallium fluoride, Phys. Rev. Lett., 63, 2559, 1989 Cho, D., Sangster, K., and Hinds, E.A., Search for time-reversal-symmetry violation in thallium fluoride using a jet source, Phys. Rev. A, 44, 2783,1991. 

M. Quack. Molecular Parity Violation and Chirality The Asymmetry of life and the Symmetry Violations in Physics. In K. Nishikawa, J. Maruani, E. J. Brandas,... 

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