Neutrino Mass and Mixing – the Beginning and Future

Nuclear Physics B Proceedings Supplement Nuclear Physics B Proceedings Supplement 00 (2012) 1–4

Neutrino mass and mixing – The beginning and future –

M. Kobayashi High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan

Abstract The early history of neutrino mixing will be discussed with a focus on the birth of the MNS theory. Keywords: two neutrinos, MNS matrix

1. Sakata Model Another important aspect of the Sakata model is the fact that the weak interactions of hadrons can be ex- The first evidence of strange particles was found in plained by two types of transitions among the funda- cosmic ray events in 1947. Much progress in under- mental triplets: standing these particles was made in the early 1950’s, in particular after the operation of accelerators started. p The discovery of strange particles made it difficult to ↑↓-& . (1) regard all of the known hadrons as fundamental objects n Λ since there were so many. This pattern of the weak interaction is similar to the In 1956, Sakata proposed a model known as the weak interaction of the leptons, Sakata model [1], in which all the hadrons, both strange and non-strange, are composite states of a fundamental ν triplet formed from the proton, the neutron, and the Λ ↑↓-& . (2) particle. e µ Shoichi Sakata was born in 1911. He was a collabora- tor of Yukawa for some time. He was appointed profes- At that time the neutrino was thought to consist of a sor of Nagoya University when its physics department single species. This similarity of the weak interaction was established in 1942. was called B-L symmetry by Gammba, Marshak, and Sakata was deeply impressed by the fact that the dis- Okubo [2]. covery of the neutron resolved mysteries of the atomic In 1960, Maki, Nakagawa, Ohnuki, and Sakata de- nucleus at that time. I think that he expected the Λ par- veloped the idea of B-L symmetry and proposed the so- ticle to play a similar role in this case. called Nagoya model [3]. In this model, they considered In the Sakata model, however, the strange baryons Σ the triplet baryons, p, n and Λ, as composite states of a and Ξ have a structure different from the fundamental hypothetical object called B-matter and the three lep- ν e µ triplets. Eventually it turned out that this was not com- tons, , and , respectively. patible with experimental data and the Sakata model p = (Bν), n = (Be), Λ = (Bµ). (3) was replaced by the quark model, where the triplet quarks, u, d and s, replace p, n and Λ. We can say, The idea is that the strong interactions of the triplet however, that the roots of the fundamental triplet idea baryons come from the B-matter and the weak interac- lay in the Sakata model. tions from the leptons inside. The composite picture of M. Kobayashi / Nuclear Physics B Proceedings Supplement 00 (2012) 1–4 2 the Nagoya model did not make remarkable progress, but the ideas of the Nagoya model made for interesting developments nonetheless.

2. Discovery of Two Neutrinos

In 1962, it was shown that νe and νµ are different particles [4]. Just before the results of this discovery at Brookhaven were to come out two interesting papers were published. The first was written by Katayama, Matsumoto, Tanaka, and Yamada [5] and the other by Maki, Nakagawa and Sakata [6]. The latter is known as the MNS paper. Both papers discussed modification of Figure 1: S. Sakata, Z. Maki and M. Nakagawa (left to right). Cour- the Nagoya model to accommodate two neutrinos. tesy of Nagoya University. The paper by Katayama et al. was received on June 5, 1962 and that by Maki et al. on June 25, while the BNL result appeared in Phys. Rev. Letters on July 1 [4]. They started with the bare lepton fields Considering the state of communication at that time, I ! ! think that they wrote those papers without seeing the µ0 νµ0 ψ0 = , ϕ0 = . (7) published results of the BNL experiment. e0 νe0 Since I was still a high school student at that time, the following is what I heard from active scientists of the Then they considered the following interaction, 0 ∗ era. There was a workshop sometime before these pa- Lint = [(ψ¯ 0Λψ0) + (ϕ ¯0Λ ϕ0)]X X. (8) pers were written where there were rumors of the BNL result. The implication of the result was discussed at the They assumed that the masses of the leptons are gener- workshop and these papers were written after they went ated from interactions with an unknown field X. How- 0 back home. ever, apart from a normalization factor, Λ and Λ are In the course of the argument to associate leptons essentially mass matrices for the charged leptons and and baryons MNS precisely formulated the lepton fla- neutrinos, respectively. 0 vor mixing. Let us look at their arguments more closely. They made some assumptions about Λ and Λ so the Denoting the neutrinos associated with the electron and explicit form of the relations they obtained thereafter are not useful from the present viewpoint. However, they muon as νe and νµ, respectively, they assumed that the diagonalized the mass matrices and identified the mass proton is composed of a superposition of νe and νµ, eigenstates e, µ, ν1, and ν2. They also determined the p = (Bν1), (4) mixing angle δ from the difference of the charged lepton and neutrino diagonalization transformations. with Of course, identifying the mass eigenstates ν1 and ν2 as constituents of the baryons is an assumption which is ν1 = cos δνe + sin δνµ, (5) not a necessary conclusion in the context of the Nagoya

ν2 = − sin δνe + cos δνµ. (6) model. This assumption leads to a common flavor mixing angle for the lepton and hadron sectors, which is not This is necessary to explain the existence of both transi- supported by the current experimental data. tions p − n and p − Λ. An important fact, however, is that they formulated Here the MNS paper raised the question ”Under what the neutrino mixing correctly and derived the mixing conditions should the parameter δ be determined?” and angle from the mass diagonalization of the charged lep- they wrote, ”It is tempting to suppose that the ques- tons and neutrinos. They were aware of the implication tion mentioned above may be closely connected with of their argument in the purely leptonic sector. They the problem of µ − e mass difference.” This reasoning correctly pointed out that if the mass difference of the is not necessarily sufficiently clear, but what they have neutrinos is sufficiently small, the mixing effect would done is to derive lepton flavor mixing by introducing not be seen in the ordinary setup of experiments because neutrino masses. the oscillation length becomes too long to observe. M. Kobayashi / Nuclear Physics B Proceedings Supplement 00 (2012) 1–4 3

It is hard to say that the Nagoya model was successful as a model of fundamental particles. Hence, we cannot take the model itself seriously. However, we can say that the Nagoya model prompted Maki, Nakagawa, and Sakata to think over the mass eigenstates carefully, and in comparing hadrons and leptons led them to the cor- rect formulation of lepton ﬂavor mixing. To recognize their contributions we call the lepton ﬂavor mixing matrix the “MNS matrix.” We will not discuss the experimental discovery of the neutrino oscillation in this article except to say that the discovery of atmospheric neutrino oscillations was re- ported by Kajita at one of the conferences in this series held in Takayama in 1998.

3. Fourth Fundamental Particle

Another important outcome of the modiﬁed version of the Nagoya model is the possible existence of a fourth fundamental particle in the hadron sector,

0 Figure 2: Cosmic ray event (from Ref.[8]) p = (Bν2). (9)

Both groups adopted the stance that the fourth particle may or may not exist. Katayama et al. investigated 4. Third Generation it in some detail though they did not discuss the neutrino mass. Although the fundamental particles were I received my Ph.D. from Nagoya University and still considered to be baryons at that time, the structure moved to Kyoto University in 1972. Masakawa also of the weak interaction discussed at that time was essen- received his Ph.D. from Nagoya and moved to Kyoto tially the same as that of the Glashow-Illiopoulos-Miani a little before I did. Soon after I moved to Kyoto, we scheme [7]. wrote a paper on CP violation in which we proposed a An interesting development related to the fourth six quark model to explain CP violation in the frame- baryon is that in 1971 Niu and his collaborators found work of renormalizable gauge theory [9]. In order to a new kind of event in emulsion chambers exposed to violate CP symmetry, the system must be complex to cosmic rays [8]. Figure 2 shows one of the events they a certain extent; The existence of a third generation is found. There are kinks on two tracks, indicating the de- essential for CP violation. cay of new particles produced in pairs. The estimated This was before the discovery of the J/ψ particle and mass of the new particle was 2 ∼ 3GeV and the esti- therefore the existence of the fourth quark, c, was not mated lifetime was several times 10−14 s. yet widely accepted. However, we were thinking about When this result came out Ogawa, one of the mem- the fourth element as a realistic possibility based on the bers of the Sakata school, immediately pointed out that study of Niu’s events. This may have lowered the barri- this new particle might be related to the fourth element ers to multi-quark models. expected in the extended version of the Nagoya model. The first experimental evidence of the third genera- At that time the Sakata model had already been replaced tion came from the lepton sector. The τ lepton was dis- by the quark model so what he meant was that those covered shortly after the publication of our paper. The new particles might be charmed particles in the cur- discovery of the b-quark followed. Later the existence rent terminology. Unfortunately, Sakata-sensei passed of ντ was confirmed. What we see in the atmospheric away a little before this discovery. However, following neutrinos is essentially oscillations between νµ and ντ. Ogawa’s suggestion a few groups of the Sakata school B-factory experiments at SLAC and KEK confirmed discussed these events. I was among them. that CP violation observed in the K- and B-meson sys- M. Kobayashi / Nuclear Physics B Proceedings Supplement 00 (2012) 1–4 4 tems is caused by flavor mixing among the six quarks. There is experimental interest in CP violation in the lepton sector. It is possible that CP violation occurs in the lepton sector through flavor mixing just as in the quark sector. This attracts attention because the matter dominance of the universe could be caused by CP violation in the lepton sector. This is known as the lep- togenesis scenario. Recent measurements of the mixing angle θ13 are encouraging in this context. From the theoretical point of view, the origin of mass and mixing is a longstanding problem. Additionally, a problem related to neutrino oscillation is that the observed mixing angles are very different from those of the quark sector. In the quark sector the mixing angles are rather small, while in the lepton sector two of the mixing angles are almost maximal. Of course, the mass generation mechanism of the neutrino could be different from that of the charged particles. It is afterall possible that neutrinos have a Majorana mass and could therefore be connected to a very large mass scale.

References

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