F EATURE Kavli IPMU Associate Professor Taizan Watari Research Area： Theoretical Physics Impact of Large-Mixing-Angle Neutrino Oscillations 1. Atoms, Electrons, and Mass Everything that we encounter daily is made of atoms. There are as many as some hundred species of atoms, all having different properties. These different species of atoms are named hydrogen, helium, carbon, oxygen, iron, copper, silver, gold, uranium, etc. It is known that all species of atoms Figure 1. A conceptual diagram showing an atom and a nucleus have a structure depicted in Fig. 1, namely, electrons inside it. In this gure, the size of the nucleus is illustrated as if it were about 1/10 of the size of the entire atom, instead of the are circulating around the nucleus which comprises actual ratio of 1/100,000. tightly packed protons and neutrons; the different properties of different species of atoms such as does this signicant difference come from? carbon, hydrogen, and iron solely originate from Hideki Yukawa’s meson theory in 1934 was the different number of protons in the respective motivated to nd, within the framework of quantum nucleus. The properties of various materials such mechanics, the mechanism that enables the nucleus, as chemical changes and superconductivity can be which comprises a number of protons and neutrons, understood based on the properties of these atoms, to be tightly packed. Meson theory claimed that nuclei, and the electron, and in particular, based on if there should be a new particle which was yet the properties of the positively charged protons and unknown at that time, it would do the job, and the the negatively charged electrons. size of the packed nucleus was determined by the Why, then, the protons and neutrons are tightly new particle’s mass. It was expected that the new packed on the one hand, and the electrons circulate particle’s mass had to be about 200 times that of around them on the other hand? Actually, the radius the electron for the radius of the nucleus to be ve of the nucleus that comprises the protons and orders of magnitude smaller than the electron’s neutrons is about ve orders of magnitude smaller radius of activity.1 than the electron’s radius of activity. Suppose that 1 The reason why the meson’s mass should be 2, and not 5, orders of the size of the nucleus is enlarged to 1 cm, then the magnitude heavier than the electron’s mass is that the value of the“ strength of the electromagnetic force” is also to do with the ratio of the nucleus’s electron’s range of activity would be 1 km. Where radius to the electron’s radius of activity. 4 Kavli IPMU News No. 22 June 2013 Figure 2. The sea wave is described by a single number ̶the“ wave height”̶at each point on the surface of the sea. On the other hand, the movement of the chord of a violin is described by the two numbers at each point along the chord, namely“, the position (or deviation) in the two directions shown by the red arrows in the gure.” Therefore, it is described by the wave having 2 degrees of freedom. 2. Discovery of the Muon“: Who day particle physics does not have an answer at all.2 Ordered That!?” An orthodox method to prove the validity of 3. What is the Height of a Wave? meson theory is to show the existence of the new particle that was called the meson. With the The behavior of the“ light = electromagnetic experimental technique in those days, it was difcult wave” is determined by the equations for the waves to create the mesons in the laboratory. There was of electric and magnetic elds. Likewise, the behavior a hope, however, that the mesons could be found of the particles such as the electrons, protons, etc. is among high-energy particles coming down from determined by the equations for the electron waves, the top of the atmosphere. Therefore, experiments proton waves, etc. It is quantum mechanics that to observe the properties of the fast particles gives those equations. coming down in the atmosphere were conducted Even though we put aside the question“, Why in the latter half of the 1930’s. Strangely enough, a new particle called the muon exists?” for the experiments by Anderson-Neddermeyer, Street- time being, it is certain at least that we have to Stevenson, and Yoshio Nishina did nd a new introduce the“ muon waves” newly to describe the particle having nearly the same predicted mass of, behavior of the particles. What are these waves but different properties from, the meson. Later, of electromagnetic elds, electron waves, proton people celebrated the discovery of the predicted waves, muon waves, and so on? Feature meson in such experiments and the unexpected new If we are talking about“ sea waves,” it is a simple particle was named the muon for the time being. story. It goes like this: at any given time, at each Scientists at that time were all puzzled, however. point on the surface of the sea, the sea wave is The muon had exactly the same properties as the high/low according to the extent that the height of electron such as the charge, etc. Only the muon the surface of the sea deviates from the mean sea mass was different from the electron mass. It was level. Also, you may not feel uneasy even if there entirely unknown why such a particle had to exist are different types of waves. For the“ waves of the and for what it would be useful. I. Rabi, who won 2 There might be a close relationship between the fact that muons exist in the Nobel Prize in Physics, said“: Who ordered that?” nature and the fact that antimatter scarcely remains in our universe. It is controversial, however, whether or not it is appropriate to say that it is the It looks too simple a question, but even present- answer to Rabi’s question. 5 Figure 3-1. A dynamical model reproducing the movement of the chord of a violin. Each weight (blue bead) can move into the two directions shown by the red arrows. They are tied to the respective stable position by a spring. Also every adjacent pair of weights is connected by a spring. Figure 3-2. A slightly more complicated dynamical model. A dynamical system sitting at each point is replaced by what is comprised of the two weights and 3 springs shown at the right end. This is called a dynamical system with 4 degrees of freedom, because the conguration of this dynamical system at each point is described by the “4 movements (numbers) shown by the red arrows.” The behavior of this dynamical model as a whole is described by using 4 kinds of waves. chord of a violin,” we can interpret the deviation of assumptions on the properties of the“ complicated the chord in the two directions from its standard dynamical system sitting at each point in space” position as the heights of the two different types of in quantum eld theory, we can explain very well waves as shown in Fig. 2. It is said that the tones all the experimental results on the behavior of the (wave types) of the violin are a bit different depending particles such as the electrons, electromagnetic on the direction to which the chords vibrate. elds, muons, and so on. In a quantum eld theory As a preparation for thinking on a bit more model called the Standard Model, we use 58 kinds complicated example, let me point out that the of waves, namely, 45 kinds of particles = waves behavior of the chord of a violin can be reproduced such as the electron, muon, and so on, 12 kinds by a dynamical model, as shown in Fig. 3-1. If you of electromagnetic waves and other waves having hold and shift one of the weights from the“ normal similar properties to them, and one wave called position” and then release it“, 2 kinds (2 directions) the Higgs eld. Roughly speaking, therefore, the of the deviations from the normal position” of the particle world in our universe is described by“, a set weight will be propagated into the space (horizontal of dynamical systems, each having 58 degrees of axis) through springs. Next, let us consider a bit freedom and sitting at one of the points in space, more complicated model, as shown in Fig. 3-2. In and the adjacent systems are connected to each this model, a certain dynamical system sits at each other (as shown in Fig. 3).” point along the horizontal axis; the adjacent systems In the language of quantum eld theory, this are connected to each other. We now need more means that the question“, Why the particle than one number to describe“ the deviation from called muon is necessary to describe our world?” the stable conguration = that from the normal can be replaced with the question“ Why the position” of the dynamical system at each point. dynamical system sitting at each point in space is so For the model shown in Fig. 3-2, four numbers complicated (multiple degrees of freedom)?” Before are needed. Therefore, the behavior of this model taking on this difcult problem, however, it would be is described by using more than one wave. The an orthodox method to ask“, What is the nature of quantum mechanical version of such a model is the dynamical system sitting at each point in space called quantum eld theory.