No. 9] Proc. Jpn. Acad., Ser. B 84 (2008) 363
Review Two alternative versions of strangeness
By Kazuhiko NISHIJIMA 1;y
(Contributed by Kazuhiko NISHIJIMA, M.J.A.)
Abstract: The concept of strangeness emerged from the low energy phenomenology before the entry of quarks in particle physics. The connection between strangeness and isospin is rather accidental and loose and we recognize later that the definition of strangeness is model-dependent. Indeed, in Gell-Mann’s triplet quark model we realize that there is a simple alternative representation of strangeness. When the concept of generations is incorporated into the quark model we find that only the second alternative version of strangeness remains meaningful, whereas the original one does no longer keep its significance.
Keywords: strangeness, Sakata model, quark model, algebra of weak currents, generation
phenomenology. Then, in the second half we 1. Introduction introduce the quark model and show how the In the late forties the so-called V particles were properties of strange particles in low-energy phe- discovered, and the investigation of their properties nomenology can be accounted for in terms of this led us to the establishment of the concept of flavors model. The contents of this article are organized to and generations later. As we now know; particles of realize the strategy described above. higher (second and third) generations decay quickly In Sec. 2 we introduce charge independence into those of the first generation so that the former (CI) which is one of the most important symmetries could not be observed unless they were produced by in hadron physics and interpret properties of V accelerators or cosmic rays. We realize, therefore, particles on the basisofthissymmetry. that we are normally surrounded by particles of the The constituents of matter are hadrons and first generation alone. This set-up provided us with leptons and in Sec. 3 we focus our eyes on the boundary condition for the natural laboratories leptons. From the experimental studies of leptons in which experimental studies of V particles had it had been suggested that there would be two been performed. kinds of leptons, one belonging to the electron In the early fifties cosmic rays were the main family and the other to the muon family. This tool for studying V particles, but there was a was an important forerunner of the concept of technical cut-off for cosmic ray energies in order to generations that would be clarified later in the observe their decay tracks within the cloud cham- quark model. bers. Thus this constraint made it impossible to In Sec. 4 we advance our considerations to observe particles of higher flavors except for the V various models of hadrons by Fermi and Yang, by or strange particles, and at that time our hadronic Sakata and by Gell-Mann. It is at this level that we world consisted of hadrons of the first generation find two alternative representations of strangeness, and strange particles. one for low energy phenomenology and the other for In the first half of this article our reasoning of the quark models. the structure of the hadronic world is developed on In Sec. 5 we concentrate our attention on the the above assumption that we may call low energy algebraic properties of weak currents that are the richest source of information about the family 1 Member of the Japan Academy. structure of elementary particles. Then we lift the y Correspondence should be addressed: K. Nishijima, 1-21- 8-604, Nakamachi, Musashino, Tokyo 180-0006, Japan (e-mail: energy constraint imposed on low energy phenom- [email protected]). enology so as to introduce the charm quark that doi: 10.2183/pjab/84.363 #2008 The Japan Academy 364 K. NISHIJIMA [Vol. 84, changes our interpretation of strangeness complete- Table 1. ly. nucleon doublet pion triplet þ 0 2. Charge independence and V particles pn 1 1 I3 2 2 10 1 Charge independence (CI) is one of the most Qe 0 e 0 e important concepts in particle physics. It is an old symmetry recognized in the early days of nuclear physics but persisted in playing a major role in the Table 2. gauge theory of electroweak interactions. (3,3) resonance From elucidation of the level structure of þþ þ 0 mirror nuclei it had been recognized that the 3 1 1 3 I3 2 2 2 2 proton-proton (pp) and neutron-neutron (nn) in- Q 2ee0 e teractions are approximately equal except for the difference due to Coulomb interactions. This prop- erty was called charge symmetry. Furthermore, violated only in weak interactions. from the pp and pn scattering experiments at low The nuclear forces are mediated by the pion or energies it had also been recognized that the pp and the Yukawa meson so that the pion-nucleon inter- pn interactions are approximately equal. Thus, in actions must also respect this symmetry. Kemmer the angular momentum states not excluded by the formulated such a symmetrical theory4) accepting Pauli principle we have an approximate equality of Pauli’s suggestion in 1936. nuclear potentials: Then we can pick out the most fundamental charge multiplets in Table 1. V V V : ½2:1 pp pn nn We can give many other multiplets but here we The independence of the two-body nuclear forces on shall choose just one example in Table 2. the nuclear charge is called CI.1)–3) The (3,3) resonance states are realized in pion- 3 This symmetry corresponds to the invariance nucleon scattering and they carry I ¼ J ¼ 2. of the nuclear system under the following SU(2) In these examples we find by comparing the transformation: charges and the third components of the closest p0 p neighbors the following relationship: U ; 2:2 0 ¼ ½ n n Q ¼ e I3: ½2:6 where U is unitary and unimodular, namely, By integrating this difference equation we obtain UyU ¼ UUy ¼ 1; ½2:3 Y Q ¼ eI3 þ ; ½2:7 det U ¼ 1: ½2:4 2 Since this group of transformations is isomorphic to where Y is a constant of integration called hyper- the group of space rotations, we may introduce charge. Each multiplet carries a definite hyper- isospin I corresponding to the angular momentum charge and we recognize later that it is an impor- J. tant quantum number in the gauge theory of I is a vector in charge space with three electroweak interactions. components I1, I2 and I3 satisfying the commuta- Now we switch to V particles. In the late forties tion relations Rochester and Butler5) observed two new events in the cloud chamber operated at the sea level. They ½I ;I ¼i I ; ½2:5 a b abc c were the celebrated V particles named according to which are identical with those of J.CIisan the shapes of the decay tracks of these particles. approximate symmetry since the Coulomb inter- This was indeed the dawn of the flavor physics actions and the proton-neutron mass difference developed later. Soon it became clear that V break this symmetry. It is important to realize, particles are produced at high altitude and decay however, that the third component I3 is conserved quickly. Therefore, it is more effective to go up to in strong and electromagnetic interactions and is mountains to observe them before they decay, and No. 9] Two alternative versions of strangeness 365 for this reason the Caltech group6) went up to the be controlled artificially in the latter and the White Mountain and the Manchester group7) went intensity of particle beams is much higher in the up to Pic du Midi to observe several tens of V latter than in the former. events. There were also some early contributions The following two processes had been observed from the French group, including Leprince-Ringuet by the Cosmotron experiment:12) and others, but they were not well recognized since þ p ! 0 þ K0; ½2:8 their work was not easily accessible to us. We shall þ skip the historical details, but we stress the þ p ! þ K : ½2:9 experimental findings that V particles are produced There are various V particles and they are distin- by strong interactions but decay by weak interac- guished by proper names. Here, 0 and are tions with the lifetimes of the order of 10 10 sec. baryons and Kþ and K0 are heavy mesons. The two Then a question was raised of why V particles do processes alone clearly confirm the pair production not decay through strong interactions. In order to hypothesis. avoid strong decays there must be a selection rule to There had been still some problems left un- forbid them. solved. In response to this question a number of 1. Observed charged K mesons were almost authors8)–10) published their theories in 1951 in a exclusively positive and the problem then meeting held at the University of Tokyo. There was was how to interpret this positive excess.13),14) one aspect common to all these theories. In 1952 2. A new baryon which undergoes cascade Pais came up with a similar idea.11) All of these decays was discovered.15) It decays in two steps authors assumed that V particles are produced in as pairs by strong interactions. Then we may intro- ! 0 þ ; 0 ! p þ : ½2:10 duce a sort of parity tentatively called V parity PV and assume that PV is conserved in strong and The problem was to assign a proper V parity to electromagnetic interactions but is violated even- . If it is positive it would decay quickly into tually in the weak interactions just like space n þ , and if it is negative it would decay into parity. Then let us postulate that V particles carry 0 þ by strong interactions. Thus, the negative V parity whereas stable or semi-stable meta-stability of cannot be accounted for hadrons around us carry positive one. in terms of the multiple quantum number PV Under these assumptions it is clear that V alone. particles are produced always in pairs by strong For the resolution of these questions we shall interactions and decay through weak interactions introduce an additive quantum number with the since the V parity has to change its sign in decay help of CI. For this purpose we shall check the processes. Later we shall find a close connection hypercharges of various hadrons. between this pair production mechanism and the Y ¼ 1for(p,n); quark model. Unfortunately, it was difficult to Y ¼ 0forð þ; 0; Þ; ½2:11 confirm this pair production hypothesis by cosmic þþ þ 0 ray experiments since it was not easy to observe two Y ¼ 1forð ; ; ; Þ: decay tracks simultaneously in one picture. We recognize that the hypercharge in these cases An experimental confirmation of this hypoth- agrees with the baryon number B,namely, esis came from the Cosmotron experiment at Y ¼ B: ½2:12 Brookhaven in 1953. This was certainly shocking to cosmic ray physicists and in July 1953 the Next we examine strange baryons. 0 seems to be a 0 Bagne`res de Bigorre Conference on cosmic rays had charge singlet so that we assign I ¼ I3 ¼ 0 to , been held, and C. F. Powell made an alarming then the formula [2.7] yields speech there: ‘‘Gentlemen, we have been invaded. Y ¼ 0for 0: ½2:13 the accelerators are here.’’ It was a critical time for cosmic ray physicists and some of them switched Since B ¼ 1 for 0 the formula [2.12] does not their experimental means from cosmic rays to hold and we introduce the difference between Y and accelerators since the experimental conditions can B 366 K. NISHIJIMA [Vol. 84,
Table 5. Y ¼ B þ S: ½2:14 doublet 16),17) Nakano and the present author called S the 0 18) charge, but Gell-Mann called it strangeness and 1 1 I3 2 2 this naming persisted. Then we find Q 0 e S ¼ 1for 0: ½2:15 The strangeness S is equal to zero for all the old In this case we find S ¼ 2. hadrons obeying [2.12]. The quantum numbers Q, I3 and B are The production process [2.8] takes place conserved in strong and electromagnetic interac- through strong interactions so that we can apply tions and so is S, but in the decay processes S is not conservation of I3,namely, necessarily conserved and we postulate a selection 0 0 rule for S in weak processes, namely, S ¼ 0, 1 þ p ! þ K ; which is illustrated by 1 1 I3 ¼ 1 þ ¼ 0 þ : ½2:16 i S 0:n p e ; 2:18 2 2 ð Þ ¼ ! þ þ ½ 0 1 0 ðiiÞ S ¼ 1: ! p þ : ½2:19 Thus we find I3 ¼ 2 for K and consequently I3 ¼ 1 0 2 for its antiparticle K . Then we recognize Later we shall find a theoretical ground for them based on the quark model. K 0 6¼ K0: ½2:17 Now we are ready to resolve the problems that In the case of neutral bosons so far known, such as could not be accounted for on the basis of the 0 and , antiparticles are identical with the original multiple quantum number PV alone. particles so that this example gave us a strange 1. As we have already seen all the strange feeling. Then, K0 and K 0 cannot belong to the same baryons carry negative strangeness. If K charge multiplet, but they belong to two separate mesons are produced in association with the multiplets as shown in Table 3. excitation of nucleons into strange baryons the In this case S ¼ 1 for ðKþ;K0Þ and S ¼ 1 for K mesons should carry positive strangeness as ðK 0;K Þ. is clear in the processes [2.8] and [2.9]. Thus at Then by studying the process [2.9] we find that such low energies only Kþ of positive S can be carries I3 ¼ 1, B ¼ 1, S ¼ 1,anditisa produced thereby excluding K of negative S. member of a charge triplet in Table 4. There are processes in which K mesons are For we do not know its partners, but we produced but the threshold energies are much assume that it is a member of a charge doublet in higher and in this way we can understand the order to avoid extraneous complications. It is shown reason for the positive excess of K mesons. in Table 5. 2. The selection rule [2.19] forbids the decay ! n þ so that [2.10] is the only possible weak decay mode for . Apparently PV is Table 3. related to S by K doublet K doublet S PV ¼ð 1Þ : ½2:20 Kþ K0 K 0 K I 1 1 1 1 3 2 2 2 2 3. Two neutrinos and two families of leptons Qe 00 e In the preceding section we have discussed the nature of hadrons in connection with CI. Matter Table 4. consists of hadrons and leptons, however, so that it is also important to clarify the properties of leptons. triplet They do not interact strongly and they have been þ 0 studied mainly through weak interactions. The I3 10 1 leptons known in the fifties had been the electron Q e0 e (e), the muon ( )andtheneutrino( ). No. 9] Two alternative versions of strangeness 367
Experimentally many processes were known to In 1962 the existence of two neutrinos was be forbidden and in order to account for the confirmed by the Columbia group23) by using the selection rules Konopinski and Mahmoud19) intro- AGS machine at the Brookhaven National Labo- duced a hypothesis of the lepton number conserva- ratory. tion in 1953. They postulated that e , þ and be A neutrino beam is generated by decay in flight leptons and eþ, and be antileptons. Assuming of pions and eventually of kaons. This beam consists that the neutrino is massless we decompose it into predominantly of muon-neutrinos. They are pro- the right-handed and the left-handed components duced by 15 GeV protons striking a Be target and as ¼ R þ L, then the lepton number` a la the resulting flux of particles strikes a 13.5 m thick Konopinski and Mahmoud is given by iron shield wall at a distance of 21 m from the target. Neutrino interactions are observed in a 10 l ¼ nðe ; þ; ; Þ nðeþ; ; ; Þ; ½3:1 KM R L R L ton Al spark chamber located behind this shield. where n denotes the particle number. After subtracting possible backgrounds they have Later in 1957 Lee and Yang20) proposed an concluded that practically only muons were pro- alternative definition of the lepton number by duced. If there were only one kind of neutrinos, electrons would have been observed with compara- l ¼ nðe ; ; ; Þ nðeþ; þ; ; Þ: ½3:2 LY L L R R ble rates. Thus the most plausible explanation for These definitions have been modified from the the absence of electrons is that the neutrino coupled original version so as to comply with the later to the muon and produced in decay is experiments. It is interesting to recognize that different from the one coupled to the electron and conservation of both types of lepton numbers seem produced in nuclear decay. This is precisely the to be consistent with experiments. prediction of the hypothesis of two neutrinos. Then in 1957 the present author21) assumed that both versions of the lepton number are 4. Models of hadrons separately conserved and took their sum and differ- As the entry of hadrons discovered by accel- ence to find new quantum numbers, namely, erators increased rapidly it was important to make þ a distinction between elementary and composite Nef ¼ nðe ; LÞ nðe ; RÞ; ½3:3 particles. For that purpose attempts have been N n ; n þ; ; 3:4 mf ¼ ð LÞ ð RÞ ½ made to pick out basic hadrons of which all other where Nef denotes the number of leptons belonging hadrons are made. to the electron family since it does not depend on 1. The first attempt had been made by Fermi and 24) the number of muons. Similarly, Nmf denotes the Yang before the wide recognition of strange number of leptons belonging to the muon family. particles, to compose all the hadrons of nucle- Now we may change the notation of the neutrinos to ons and antinucleons by regarding them as the clarify the two family structure of leptons as basic elementary particles. In particular, the newly discovered Yukawa meson or pion was ! ; ! ; ! ; ! ; ½3:5 L e R e L R considered to be composed of a nucleon and an and call e and as the electron-neutrino and the anti-nucleon. Thus p and n are the basic muon-neutrino, respectively, and reexpress [3.3] particles in this model. and [3.4] in the following form: 2. After the discovery of strange particles 25) þ Sakata modified their model by adding Nef ¼ nðe ; eÞ nðe ; eÞ; ½3:6 to the set of basic particles. Thus p, n and N n ; n þ; : 3:7 mf ¼ ð Þ ð Þ ½ form the Sakata triplet. As a natural extension In this way we find that leptons are divided into two of CI or the SU(2) symmetry based on the families, the electron family and the muon family isospin doublet (p,n), Ikeda, Ogawa and and they are separately conserved. The family Ohnuki26) introduced the SU(3) symmetry for concept for leptons has been generalized to gener- the Sakata triplet (p,n, ). Once a symmetry is ations by accommodating hadrons (quarks) much introduced we can study the multiplet struc- later. A similar proposal was made also by ture of the composite hadrons. Let t represent Schwinger22) independently. one of the fundamental triplet (p,n, ), then 368 K. NISHIJIMA [Vol. 84,
Fig. 1. Pseudoscalar meson octet. Fig. 2. Baryon octet.
low-lying bosons are bound states of t and tions of the form t . Corresponding representations of tt are ½F ;F ¼if F ; ½4:2 given by i j ijk k where f denotes the structure constant for 3 3 ¼ 8 þ 1: ½4:1 ijk the Lie algebra of SU(3). Furthermore, he Hence we obtain an octet representation and introduced the densities or currents F i ðxÞ eventually a singlet representation of bosons. corresponding to the generators Fi by Each member of this octet is distinguished by Z 3 ðI3;I;YÞ. For instance, for the pseudoscalar Fi ¼ F i0ðxÞd x; ½4:3 mesons the octet is given by Fig. 1. The prediction of the isospin singlet 0 was and tried to express various quantities in terms considered to be a success. We get similar of densities. results for vector mesons. However, the funda- Also, the phenomenological weak Fermi mental triplet alone cannot cover the members interactions are given in the form of baryons and this causes a lot of troubles. 1 ffiffiffi y Experimentally it is favorable to assign an Hw ¼ p GF J J ; ½4:4 octet representation to baryons as shown in 2 y Fig. 2. and the current densities J and J are Furthermore, we find no hadrons belonging assumed to satisfy commutation relations of to a triplet representation among those ob- the SU(2) algebra. served experimentally. It is not possible to ½J ðx;x Þ;Jyðx0;x Þ introduce the baryon octet shown above as 0 0 0 0 3 0 ð3Þ long as we stick to the Sakata model. ¼ 2 ðx x ÞJ0 ðx;x0Þ; ½4:5 3. Recognizing the success of the SU(3) symme- ð3Þ 0 ½J0ðx;x0Þ;J ðx ;x0Þ try and at the same time the difficulty of 0 3 0 specifying the fundamental triplet, Ne’eman ¼ 2 ðx x ÞJ0ðx;x0Þ; ½4:6 and Gell-Mann proposed the Eightfold y ð3Þ 0 ½J0ðx;x0Þ;J0 ðx ;x0Þ Way.27),28) They assumed that low-lying ha- ¼ 2 3ðx x0ÞJyðx;x Þ: ½4:7 drons including baryons belong to the octet 0 0 representation of SU(3) without identifying Although the interaction [4.4] is phenomeno- the fundamental triplet. Thus this is an logical and still without neutral currents the algebraic theory, but not a model, and the above assumption that the current densities fundamental ingredients of this theory are satisfy proper commutation relations is impor- the 8 generators of SU(3) denoted by Fiði ¼ tant in complying with the future adjustment 1; 2; ; 8Þ satisfying the commutation rela- of accommodating the gauge theory. No. 9] Two alternative versions of strangeness 369
An important contribution of the SU(3) and electromagnetic interactions. theory is the prediction of the mass. There NðuÞ¼nðuÞ nðu Þ; is a decimet representation for excited baryons NðdÞ¼nðdÞ nðd Þ; ½4:12 including the resonances and one member called had been missing. Gell-Mann28) and NðsÞ¼nðsÞ nðs Þ: Okubo29) have derived a mass formula for the In this quark model various quantum numbers members of SU(3) multiplets in terms of I and can be expressed in terms of these quark Y by assuming a definite pattern of symmetry- numbers. breaking and predicted the mass of the missing 2 1 1 . Two examples of of the predicted mass Q ¼ e NðuÞ NðdÞ NðsÞ ; ½4:13 3 3 3 were observed at Brookhaven30) and the SU(3) 1 group received a strong support. I3 ¼ ½NðuÞ NðdÞ ; ½4:14 4. Then it was time for Gell-Mann31) and Zweig32) 2 1 to identify the triplet in SU(3) in order to B ¼ ½NðuÞþNðdÞþNðsÞ : ½4:15 proceed a step further. They invented a hypo- 3 thetical triplet called quarks31) or aces.32) The From these relations we can express strange- triplet quarks play a role similar to that of the ness S in terms of the strange quark number Sakata triplet in mathematical sense, but they with reference to Eqs. [2.7] and [2.14] as are considered to be unobservable when they S ¼ NðsÞ: ½4:16 are isolated. This property is referred to as quark confinement. Gell-Mann assumed that Thus in this quark model we find two alter- there are three kinds of quarks u, d and s which native forms of strangeness. This model is are represented by a common letter q.Low- unique in that it accepts both forms of strange- lying baryons consist of three quarks qqq and ness. In the low energy phenomenology with- low-lying mesons are bound states of a quark out quarks the second form NðsÞ is not and an anti-quark qq . This postulate reprodu- available, but in the next section we present a ces the results of Eightfold Way. quark model which accepts only the second Then the quark triplet inherits the isospin of form of strangeness. the Sakata triplet so that we have 5. Algebra of weak currents and generations uds So far we have discussed hadrons and leptons 1 1 I3 ¼ ; ; 0 ½4:8 separately, but we find a close kinship between 2 2 them in weak interactions. In 1959 Gamba, and p, n and are composed of quarks as Marshak and Okubo33) recognized that weak inter- actions are symmetric under the exchange p ¼ðu; u; dÞ; n ¼ðu; d; dÞ; ¼ðu; d; sÞ: ½4:9 p; n; ; e; : ½5:1 The quarks carry fractional charges as is clear from [4.9]: This means that the weak current J in [4.4] is symmetric under the exchange [5.1]. This operation uds isexpressedintermsofthe Sakata triplet, but it 2 1 1 Q ¼ e; e; e: ½4:10 can easily be reexpressed in terms of the quark 3 3 3 triplet as Since a baryon consists of three quarks the u; d; s ; e; : ½5:2 baryon number of a quark is given by This symmetry is referred to as the Kiev symmetry 1 B ¼ : ½4:11 or baryon-lepton symmetry. In 1962 the second 3 neutrino was discovered and the symmetry was Then we are ready to introduce a new form of modified to a new form by accommodating this new strangeness. In a quark model the quark member as number of a given flavor is conserved in strong 370 K. NISHIJIMA [Vol. 84,
ðhÞ u; d; c; s e;e; ; ; ½5:3 J ¼ iuu ð1 þ 5Þd þ icc ð1 þ 5Þs: ½5:9 which implies introduction of a new quark called This expression is faithful to the symmetry the charm quark. under [5.3]. In Sec. 3 we have introduced the Also, this symmetry makes it clear that the electron family and the muon family, and the weak current J consists of two parts, the leptonic baryon-lepton symmetry makes it possible to and the hadronic weak currents as adopt the concept of family to counter sets of quarks. Thus the set ðu; dÞ forms a family J ¼ JðlÞ þ JðhÞ: ½5:4 corresponding to the electron family, and ðc; sÞ y ð3Þ Since J0, J0 and J0 satisfy commutation relations to that of the muon family. Then combining of the Lie algebra SU(2),34) [4.5]–[4.7], also the the electron family with the corresponding leptonic and hadronic currents satisfy the same set quark family ðu; dÞ, the first generation of of commutation relations, separately. Therefore, fermions, consisting of ð e;eÞ and ðu; dÞ,is the algebra of leptonic weak currents is isomorphic formed. By the same token the second gener- to the algebra of hadronic weak currents. Further- ation of fermions consists of ð ; Þ and ðc; sÞ. more, the baryon-lepton symmetry implies that Now we are going to merge these improvements theremustbeaone-to-onecorrespondence between with one another in constructing the representation irreducible representations of these two algebras. of the hadronic current in terms of the quark fields. These requirements lead us to the concept of Eq. [5.9] does not allow strangeness-changing tran- generations later. sitions so that we replace d and s by d0 and s0, In what follows we are going to construct these respectively in [5.9], where currents in terms of the leptonic and quark fields, d0 cos sin d andforthispurposewestartfromtheleptonic ¼ : ½5:10 s0 sin cos s current that is better known phenomenologically, ðhÞ namely, The new form of J is given by ðlÞ ðhÞ 0 0 J ¼ i e ð1 þ 5Þe þ i ð1 þ 5Þ ; ½5:5 J ¼ iuu ð1 þ 5Þd þ icc ð1 þ 5Þs : ½5:11 corresponding to the electron and the muon fami- which does not change the commutation relations of lies. Then, our problem is to find its hadronic SU(2). Glashow, Iliopoulos and Maiani37) obtained counter expression, and the simplest solution is this form by requesting suppression of the strange- given by ness-changing part in the neutral current in order to ðhÞ suppress the decay rate J ¼ iuu ð1 þ 5Þd; ½5:6 K0 ! þ þ : ½5:12 but this form is incomplete on some accounts and L we are going to improve it in two directions. Indeed, in this case we have 1. It was suggested by Gell-Mann and Le´vy35) ½Jð3Þ;NðsÞ ¼ 0: ½5:13 and also by Cabibbo36) that we have to 0 introduce s in order to describe the strange- Since we have introduced generation-mixing ness-changing transition, thereby respecting for the quarks without changing the commutation universality between decay and decay, and relations for currents we could introduce the same 0 d in [5.6] was replaced by d : modification to leptons by replacing e and in 0 0 ðhÞ 0 [5.5] by e and , respectively J ¼ iuu ð1 þ 5Þd ; ½5:7 ! 0 0 0 d0 d cos s sin ; 5:8 e cos sin e ¼ þ ½ ¼ : ½5:14 0 0 0 where is called the Cabibbo angle. The sin cos current in [5.7] still satisfies the required The generation-mixing of neutrinos causes the so- commutation relations. called neutrino oscillation as predicted by Maki, 2. Adopting the baryon-lepton symmetry under Nakagawa and Sakata,38) and its experimental [5.3] we may add another term: confirmation was made by the Super-Kamiokande group39) much later. No. 9] Two alternative versions of strangeness 371
Finally we shall discuss the impact of the [5.9] and [5.11]. On the other hand, the selection discovery of the charm quark on the concept of rule NðsÞ¼ 1 is obeyed by the transitions strangeness. For a long time and s had been s d; ½5:19 considered to be charge singlets since there had been no isospin partners. In 1974 the charm quark c valid for the weak currents [5.7] and [5.11]. wasobservedintheformofJ= 40),41) (in 1971 a pair There are two s quarks involved in 0 and , of naked charm particles had been observed in 0 ¼ðu; s; sÞ; ¼ðd; s; sÞ: ½5:20 cosmic rays42)), but it was one order of magnitude more massive than s. Then it was natural that the The weak interaction [4.4] induces s ! d, but only presence of c had never been noticed in low energy one s quark makes this transition in one step so that phenomenology. Also, it was a good approximation the transitions obeying NðsÞ¼ 2 are forbidden at low energies to treat s as a charge singlet. Despite and cannot decay directly into n þ . its tremendous success we then had to switch from All the properties of strangeness in the old SU(3) back to SU(2) by regarding c and s as version are described by [5.11] and are inherited by members of a charge doublet, and now we have two its new version. The new version is generic and all sets of quarks ðu; dÞ and ðc; sÞ belonging to the other quark numbers such as NðuÞ, NðdÞ and NðcÞ doublet representation. Then we have share exactly the same set of rules with strangeness. For instance, all of them are conserved in strong 2 1 Q ¼ e; I ¼ for u and c; and electromagnetic interactions. 3 3 2 We have shown that the interpretation of 1 1 Q ¼ e; I3 ¼ for d and s; ½5:15 strangeness is model-dependent and have given 3 2 two versions of it depending on the absence or and presence of quarks. In this section we have put emphasis on the introduction of the concept of 1 B ¼ for all quarks: ½5:16 generations, and for that purpose we needed at least 3 two generations. Once this concept is established, Thus we find we can introduce the third generation as well. Indeed, Kobayashi and Maskawa introduced the 1 Y ¼ B ¼ for all quarks; ½5:17 third generation in order to accommodate CP 3 violation in the gauge theory.42) The models de- and consequently it follows that strangeness S scribed in this article are phenomenological but vanishes identically for all quarks including the they would serve as the starting point in developing strange quark!! the gauge theory of electroweak interactions. In- Fortunately, we have an alternative definition deed, Eq. [2.7] served as the basis for the gauge of strangeness [4.16], and we identify NðsÞ with theory. the strangeness in the quark models. Interpretation of properties of strangeness discussed in low energy Acknowledgements phenomenology in Sec. 2 can be reproduced by this The author is grateful to Prof. Masud new definition. For instance, pair production of Chaichian and Dr. Anca Tureanu for their interest strange particles is realized by production of the in this work. quark pair s and s , literally a pair production. References Furthermore in low energy phenomenology s com- bines with u’s and d’s to form strange baryons, and 1) Tuve, M.A., Heydenburg, N. and Hafstad, L.R. s combines with u or d to form Kþ or K0,andwe (1936) Phys. Rev. 50, 806–824. 2) Breit, G., Condon, E.U. and Present, R.D. (1936) have positive excess of the K mesons. Phys. Rev. 50, 825–845. In weak interactions the selection rule 3) Cassen, B. and Condon, E.U. (1936) Phys. Rev. 50, NðsÞ¼0 is realized by the quark transitions 846–849. 4) Kemmer, N. (1938) Proc. Camb. Phil. Soc. 34, 354– d u; ½5:18 364. 5) Rochester, G.D. and Butler, C.C. (1947) Nature by any of the hadronic weak currents [5.6], [5.7], 160, 855–857. 372 K. NISHIJIMA [Vol. 84,
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Profile
Kazuhiko Nishijima, a member of the Japan Academy, was born in 1926. He graduated from University of Tokyo in 1948 with a BS degree in physics and started his research career in 1950 at Osaka City University under Prof. Yoichiro Nambu. In 1953 he introduced the concept of strangeness in collaboration with Tadao Nakano. At that time he was interested in the question of how to derive the covariant S matrix elements for reactions involving composite particles starting from the time-ordered Green’s functions. This work was accepted as a dissertation and he received a Doctor of Science degree in 1954 from Osaka University. In 1956 he visited Max-Planck- Institut fuer Physik in Goettingen and he succeeded in formulating reduction formula for composite particles. This is often called Haag-Nishijima-Zimmermann construc- tion of composite particle fields. In 1957 he visited IAS in Princeton and completed the paper on HNZ construction. In 1957 he also proposed the two-neutrino theory from which two separate conservation laws follow, namely, conservation of the electron family and that of the muon family. From 1959 to 1966 he joined University of Illinois. During this period his main interests had been focused on time-ordered Green’s function. One of the important results was a set of identities obtained by taking four-divergence of Green’s function involving conserved current and other field operators. This set happens to be a generalization of the Ward- Takahashi identities connecting the vertex function with the electron propagator in QED. After returning to Japan he had been affiliated with University of Tokyo, Kyoto University and Chuo University, and has been interested mainly in color confinement based on asymptotic freedom. In 2003 he was awarded the Order of Culture by the Government of Japan.