### Discrete Symmetries and CP Violation: From Experiment to Theory

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Applications of the discrete symmetries. Weak and strong phases. The neutralkaon system. Models with vectorlike quarks. Massive neutrinos and CP violation in the leptonic. The strong CP problem. Some experimental issues. The mixing parameters. Heavy neutralmeson systems. Experimental status of BB mixing. The fermions in the standard model. Fundamental properties of the CKM matrix. Weakbasis invariants and CP violation. Mixing in the BjBJ systems. MultiHiggsdoublet models. Spontaneous CP violation. CKM phases and interference CP violation.

Our goal was slightly more modest — to test the hypothesis by exploiting the fact that in this theory the operator product expansion of the currents contained the energy momentum tensor with a known coefficient. Thus we could derive a sum rule for the structure functions that could be measured in deep-inelastic electron-proton scattering [18]. Eventually, however, the current-current Hamiltonian approach was replaced by more traditional Lagrangean formulation-QCD to which Y.

## Presentations

Nambu, 14 G. Veltman, 15 D. Gross and F. Wilczek, 16 H. Politzer, 17 and many other people had contributed. The quark was supposed to be confined dynamically, rather than just being a mathematical object. The current-current Hamiltonian approach turned out to have a rather unexpected, but very interesting application in string theory. I quote the following statement by M.

Around the same time, , after working for five years or so on current algebra, I suggested repeatedly that it would be wonderful if we could express the whole dynamics by means of current algebra, adjoining the energy density to the algebra of the internal charge and current densities, with the energy density expressed in terms of the charge and current densities, particularly in a light-cone frame.

In , in a bar in Ankara, I met Sugawara, who told me he had created such a model. I was delighted, but over time all of us became discouraged when we learned that it had really nice properties only in two dimensions.

## CP Violation: From Quarks to Leptons - Google книги

Today, as David Olive described so eloquently, such two-dimensional systems have turned out to be fundamental. I should say that the current-current construction of the energy-momentum, which is usually called the Sugawara construction, should, in fact, be called Gell-Mann-Sommerfield-Sugawara construction, as all these people contributed to it in their own way.

Most of the particle interactions became understandable within the framework of gauge theories. A surprisingly simple model of the weak and electromagnetic interactions by S. Weinberg 18 and A. Salam 19 turned out to be correct, as the discovery of neutral currents 39 dramatically demonstrated.

From the beginning my own interest was in studying the defects of the Standard Model: the Higgs interaction was not understood as gauge interaction and its origin is left untouched in the Standard Model. As a related problem, the question of the flavor degrees of freedom still remains. It was well known that CP symmetry cannot be violated in gauge interactions and that the Higgs interaction was the only way to violate CP symmetry within the Standard Model. Kobayashi and T. Maskawa investigated this issue and proposed several versions to solve this problem.

Pakvasa and I pursued their three quark version and studied its physical consequences. Maskawa: In their paper, they started by observing the fact that in this scheme with two families, there is no room for a non-trivial phase that could give rise to observable CP violation. The weak charged current for quarks is given by. In Eq. But the three phases can be absorbed into the definition of three quark fields, and only the one mixing angle, the Cabibbo angle remains.

They go on to try various options. One is to introduce a right handed doublet of quarks and leptons to preserve anomaly cancellation.

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- CP violation?

In this case, there is indeed room for an extra phase which cannot be transformed away and can give rise to the observed CP violation in K decay. They observed that there are some phenomenological problems with such a scenario. This possibility was raised and pursued already slightly earlier by Mohapatra, 14 who also found that there needs to be further proliferation of fields in such a model.

They also briefly considered other models with right handed currents and dismissed them as being not satisfactory. The second possibility is to increase the number of scalar fields beyond the minimal single Higgs doublet by one, and have two scalar fields. In this case also there is an extra phase which can give rise to CP violation. A few months earlier, Lee 15 had considered such a model in connection with a theory of spontaneous T violation.

Finally, in the last page of the paper, they raise the third possibility of having three families of quarks and leptons. They give an explicit parameterisation of the matrix. In summer , when Hirotaka Sugawara arrived in Hawaii for his annual two month visit, he suggested that we work on CP violation, and specifically study the proposal in the K-M paper. We found that it was indeed possible to obtain a correct value for the K L decay rate with a reasonable choice of the new Cabibbo-like angles and the phase in the K-M matrix.

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Thus we showed that the K-M proposal was indeed a viable description of the known CP violation at the time. We submitted the paper to Physical Review Letters in September It was eventually accepted for Physical Review and appeared in print in July A paper by Maiani appeared shortly after ours in which he independently reached the same conclusions we did.

None of the papers found any large effects with which the model could be easily and quickly checked. The family or the flavor problem of quarks and leptons is closely related to the symmetry of the Higgs interactions. It does not seem to be related to gauge symmetry, at least in the low energy region.

In such a situation it is natural to consider some kind of discrete symmetry to avoid the appearance of Nambu-Goldstone bosons. Pakvasa and I initiated such an approach to the family problem and we had some limited success. Non-gauge symmetry is destined to be broken at higher energies and the outstanding problem is to find the mechanism of this symmetry breaking. Until then we will not be able to understand the family problem, even if discrete symmetry is the right way to proceed.

Supersymmetry has been introduced into the framework of the standard model to explain the hierarchy problem, and the supersymmetric standard model has become a standard platform for phenomenologists to study. For almost twenty years I was involved in encouraging those experimental projects in various ways, first in managing the KEK physics division and then as director general of KEK, now known as the High Energy Accelerator Research Organization. I hope to be able to talk about that process another time. A related interest of mine was in Grand Unified Theory.

I gave a summary talk on this issue at the High Energy Physics Conference which was held in Madison, Wisconsin in Yoshimura came up with the idea 46 in that the baryon number of the universe can be explained within the framework of Grand Unified Theory, it was clear to me and to many people in the field that the crucial parameter for Grand Unified Theory is the rate of proton decay. I asked M. Koshiba to design such an experiment and he and his group came up with a reasonable project. Nishikawa, then the KEK director, to help us fund this project. He was more than enthusiastic, and, thanks largely to his efforts, the project was funded.

Takahashi and the detector belonged to the University of Tokyo. Initially, J. Arafune and myself were among the members of the Kamiokande Group and our names were on the author list. Later we learned that our names had been deleted from both lists. However, Arafune and I have never lost our interest in the physics of Kamiokande. Common feature of superstring theory, climate change models and the brain models is that they lack sufficient data to support the various models being proposed.

I am trying to address that problem by inventing new ways of collecting more data and by trying to find missing links that connect the models to the data in each of these area. A model becomes a true theory only after being tested a sufficient number of times by the data and after showing the power of predicting the output data from a known set of inputs.

Its relevance to the unification of all interactions, including gravity, has become widely recognized.

It became a fascinating field of mathematical physics, but, unfortunately, without much relevance to the real world, at least for now.