STABLE AND SEMI-STABLE

The : Particles and Until 1932 the only elementary particles known in physics were the , the and the which we called stable particles. In that year two new elementary particles were discovered, viz. the and the positron. The existence of a positron had been predicted by Dirac in 1930 in his relativistic theory of the free electron. Dirac set up the relativistic wave equation for the electron and showed that solutions were possible for all values of the total energy Et whenever

where m is the actual mass of the moving electron and c is the velocity of light. According to the Dirac theory there exists a set of mathematically possible positive energy states with energies greater than mc2 and also a set of possible negative energy states with energies less than - mc2. the following simple argument may help the reader. The relativistic equation connecting the momentum and total energy of a moving is

where mo is the rest mass of the moving particle and p is its momentum. Thus

and for any given value of the momentum p the energy Et can be positive or negative. In the case of the electron there are therefore positive energy states corresponding to observable energies, but the negative energy states have no simple physical meaning and can only be interpreted mathematically. Since in the positive states would make radiative transitions to the negative states, and since this is not observed, Dirac proposed that all the negative energy states in a perfect vacuum were completely occupied by electrons, whereas all the positive states were normally empty. The negative states are therefore completely filled and are unobservable until a vacancy occurs in one of them by the removal of an electron to a positive, observable, energy state by the interaction of the electron with the electromagnetic field. This leaves a positively charged hole or vacancy which is manifest as a particle with the same mass as its companion electron but with opposite and (conservation

9

of angular momentum). The energy required for this upward transition will be, since two particles are created, which means that a positron-electron pair cannot be created by bombarding particles or of less than the threshold energy of 1·02 MeV, see Fig. 26.5.

Negative·· electron O observable Energy E

/ E•mc2 i I AE•2 mc2

)0 }E=-mc2 0 0 0 0 0 0 0 0 0 Electrons 0 0 0 0 0 0 (. ) 'J 0 0 0 of negative mass 0 0 0 0 0 0 l.J .) � 0 0 unobservable 0 0 0 0 (_) 0 0 (.,21 0 0 0 l J to Continuous -: distribution + Vacancy a positron extends to Infinity Fig. 26.5 Creation of a positron-electron pair. according to Dirac.

The above is a simplified description of the formation of a positron-electron pair. In free flight most are slowed down to low energies before annihilation and many of these are then captured by electrons to give so-called . A positronium is a short-lived positron-electron pair.

The relativistic equation for E, holds for all free particles of spin fh/21t, so that all such particles have 'antiparticles'. When a.particle and its meet, great energy is created by their mutual annihilation. As we have seen, the positron-electron pair requires about 1 Me V for its creation so that we can expect the creation of a proton- pair to require at least 1836 x 1 MeV, i.e. an energy of nearly 2 Ge V relative to the centre of the mass of the pair. Calculation shows that the initial kinetic energy of the bombarding proton in a proton• proton collision producing an antiproton by p" +p+ -+(p+ +p+)+(p+ +p+) is 6mPc2 = 5·6 GeV, when allowance is made for conservation laws and relativistic effects at these high energies.

10

Particles and antiparticles have opposite charges but always have the same mass. They interact strongly in pairs where they create great energy from the annihilation of particle . The existence of the antiproton and the as well as the positron gives strong support to the Dirac theory of free particles.

Fig. 26.7 Emulsion photograph showing annihilation of anti proton. The antiproton enters from the top left-hand corner and is annihilated at the end of its range. The annihilation energy is then distributed among the secondary charged particles of which four and two are shown. (From Powell, ibid.)

11

Pions, and We have mentioned that primary cosmic rays consist largely of protons. When such fast protons encounter the nuclei of atoms in the atmosphere, high-energy -nucleon collisions take place which cannot easily be reproduced in the laboratory. It is not surprising, then, that many new particles were discovered in cosmic ray events, particles with very strange properties compared with the early elementary particles known to physicists (stable particles). As we have said the first new particle to be found was the positron, soon to be followed by the -, which has a mass lying between that of the electron and the proton. Many other have since been discovered, and now we know that when a fast cosmic ray proton strikes a nucleus it reacts strongly with the and in the ensuing rearrangement a shower of many mesons can be ejected. The discovery of the first meson as an was made in 1937 by Neddermeyer, Anderson, Street, and Stevenson in Wilson cloud chamber cosmic ray observations. This particle was then called a mesotron and could be either positive or negative. We now call this particle the -meson or . Its mass was estimated to be about three hundred times the mass of the electron. The existence of a particle with these peculiar characteristics had been predicted by Yukawa in 1935. Yukawa put a theory of nuclear attraction forces which required the existence of a particle, with either positive or negative charge, and of mass equivalent to two or three hundred electronic masses, to give the correct distance over which the short range forces act, viz. about 1 fm. These mesons of Yukawa are the quanta of the nuclear force-field and it was natural to identify the 1937 experimental meson with Yukawa's nuclear photon. This was then interpreted as the strong force-carrier within the nucleus, shuttling backward and forwards among the nucleons and so binding them together. One of the properties of the negative meson, as predicted by the theory, was that when stopped by ordinary solid materials it should be absorbed very rapidly, showing strong nuclear interaction, but in time it was found that -mesons have only a weak interaction with nuclei, a result incompatible with Yukawa's requirements. Experimentally it was found that fast -mesons could pass through thick plates of lead without being absorbed, showing their weak interactions with nuclei of solid substances. Hence the possibility of identifying the experimental • meson with Yukawa's particle was open to doubt, and when in 1947 the first nuclear emulsion plates exposed to cosmic rays at high altitudes were examined by C. F. Powell and his team at Bristol, and the existence of another meson of mass about 300 me was suspected, this doubt was strengthened, since the Yukawa theory did not postulate two different mesons. In the early nuclear emulsion plates some of the mesons were

12

found to decay at the end of their range. These were later identified as positive -mesons which decay when stopped in the emulsion to secondary mesons. The new -mesons were also shown to be produced in disintegration processes and it was found that they reacted very strongly with the nucleons of the emulsion nuclei.

I_ I I..,. _I I

Fig. 26.2 First observation of a-meson decay in a nuclear emulsion. The enters the plate at the bottom left-hand corner and reaches the end of its range at the top. A secondary µ-meson is ejected nearly backwards along the line of approach of the pion. Note the increase of grain density of these particles at the end of their respective ranges: (From PowcH, ibid.)

We have mentioned that -mesons (pions), which have mass about 273 me, are created when primary cosmic ray protons collide with atmospheric nuclei and cause energetic nuclear disintegrations. Pions are radioactive and have a very short lifetime T: They can exist in all three states:

n ", with T= 25 ns 1t , with T-25 ns n°, with T'=O·l fs.

13

These lifetimes, which refer only to mesons at rest, are so short, that only a fraction of cosmic ray pions can reach sea-level. They are attenuated in the atmosphere because of the strong nuclear interaction. The charged pions decay to muons and as follows:

n+ --.µ+ +v+33 MeV n---.µ-+v+33 MeV.

The charged muons are also unstable, emitting electrons:

µ±--.e± +2v+ 105 MeV.

The radioactive decay of -mesons can be followed easily in the nuclear emulsion plate. The above equations are of great importance. Since the muon decays from rest, the conservation of linear momentum requires that two particles must be ejected. The only particle observed is the electron with its continuous energy spectrum. Since the charge is conserved, one expects the second particle to be a . However, since the spin of the muon is ½ and the sum of the electron and neutrino spins can only be 0 or 1, but never! The conservation of angular momentum requires another particle of opposite spin 1/2 to be ejected at the same time. This must be an antineutrino so that the muon decay equation should read µ±--.e±+v+v+105 MeV� Spins i--.t -+ o

This raises another difficulty. If the neutrino and the antineutrino are ejected simultaneously, one would expect that they would occasionally annihilate in flight to produce a -ray by v + v--+Y, i.e. the apparent decay an event which would be recognizable by the -ray conversions. This has never positively been found; so we conclude that v and v- are not antiparticles to each other. As they must be neutrinos, they can only be neutrinos of a different species. Two types of neutrino are therefore postulated:

14

(a) that associated with electrons and positrons, which we have previously called simply neutrinos, \I and v- , but which we now write as and 흂̅̅풆; (b) that associated with muon decay, which The muon decay equation should now be written µ--+e-+v£+vµ+105 MeV, µ+ -+e+ +ve+i\, + 105 MeV.

The annihilation y-rays are not produced, since v e $ v u and v e $ v w The decay equations we have previously discussed are therefore rewritten as: n°-+p+ +e- +Ve) free decay p + -+n° + e + + v, within nucleus 7t+ -+µ+ + Vµ 1t--+µ-+vµ µ+-+e+ +vc+vµ µ- -+e- +i\+vu. The muon itself (i.e. u>, not the antimuon µ +) is a very interesting particle. In all respects it behaves as a superheavy electron, and most electron decay schemes Have a corresponding muon decay scheme. Negative pions react strongly with nuclei (e.g. C, Nor O in the emulsion of the nuclear emulsion plate) to give characteristic star patterns; see Fig. 26.10. The basic reaction in the nucleus is 1t - + p + -+ n + Q, where the energy Q is very large and causes the star. It is this strong interaction.with nucleons which provides the nuclear binding forces, whereas the interaction of muons with nucleons is so weak that they can find their way readily down to sea-level in a cosmic ray burst. There they are observed as the penetrating component of secondary cosmic rays. Their weak reaction with protons is by µ-+P+-+n°+vw All three types of pion can be produced artificially by high-energy protons or photons on metal targets. Muons are then available from the decay of the pions in flight. Many other unstable particles have been observed in cosmic ray studies and subsequently confirmed in the accelerator experiments. Examples are the K• mesons (mass -970 me), and the which have masses greater than that of the nucleon. K-mesons (kaons) were first discovered in high-altitude cosmic ray experiments with emulsions but now are readily available from the accelerators. Kaons exist as K + and its antiparticle K - , and also as KO and its antiparticle KO• Their masses are slightly different, as shown in Table 26.1. They are similar to

15

Fla. 26.10 Creation or a n-meeon in a nuclear emuleion. The pion is created in the lower diaintearation and proceeds to the upper where it reactiee the end ofite range and is captured by a liaht clement caueina a eecond disintcaration. (From Powell. lbld.) pions but have many more decay possibilities. Common modes of decay are K ± -+n± + n° K+-+µ++v µ - K + -+n+ +n+ +n- with T= 12·4 ns. K + - and K - -mesons have masses of about 966 m. while K 0-mesons have masses of 975 m., and decay by K0-+n+ +n-. All kaons and pions have zero spin.

16

:::-; >u :=E :=E ...... � ·+ + + • . ' u ...... + + + +.... +...... T T T ..c .. ' < ""

-1 ..... -i_ = 0 Q Qi � ...... _...... ""-� ------00 - .... ::z ...... :;.i ..... � I ;Q � ...... ,.. Ew -22 ..... � ..... -� � - - I -- • ii � co: 0 I ]- :=E i:z: :cl

17

Hyperons Hyperons are unstable particles, having masses greater than that of the nucleon, and the first were discovered in cosmic rays by Rochester and Butler in 1947. They have lifetimes of the order of 0· 1 ns, and three groups are now known: AO (lambda) particles, zero charge only; l: (sigma) particles, with +, 0, - charges; S (xi) particles, with 0, - charges only. The A 0-particles were so named from .the fork-like tracks produced by the secondary charged particles (Fig. 26.11). Some possible modes of decay are: Ao-+p+ +1t• r+ -+p+ +n° Ao-+no+1to :::- -+A0 +n• r- -+n° +n• r+ -+n0 +n+. I:0-+Ao +y Hyperons are produced in the laboratory by pion or interactions with protons. Energies greater than 1 GeV are required for these reactions. Typical reactions are: n-+p+-+Ao+Ko, n- +p+-+�- +K+, K- +p+ -+E0+K0, K-+p+-+�++1t-, K-+p+-+E-+K+. All hyperons have spin iii =ih/2n.

,.,.. - .. ··------i I ! 'i i

iI '! i

F"".._. 26..1 l(b) I.n.c.e-rpretatio-n oC Fi.,a.. 2�1 l(a

18

Fig, 26.1 l(a) The decay ol two fundamental particles by a \'11,cak-iotcraction pcoccu i..s illustrated in the bubble chamber photograph above, made by Luis W. At,,a..-czand his oollcagucsat the Univc..-si1y ol California. "Tbc events in the photoaraph arc tr-aced in the drawifl.i: on the next paa.c. A hi&h-c-nc.ra,y ncgati'\ol'C pion (x "), pr-oduccd by the Berkeley Bcvatr0n,, cn1ers the' ctuunbe.r- at lower right. It tl'ikcs a proton in the liquid hydl'ogcn of the bubble chamber. gjvioa rtse 10 a neutral K-mcson (K°) and a lambda particle (/\0). Bcina unchara;cd. these two particles teave no track. The ncuual K-rncson decal'$ into a ncpti,t< pion and a po&,itivc pion; the lambda pan.iclc into a proton (p) and a nqative pion. (Taken Crom Sci�"•if,c Am:,rican. t-.ia.l'ch 1959. "'The Weak lntcl'actions". by S.. B.. Tn:iJn.an.)

Classification of the Elementary Particles according to their mass and spin Elementary particles are classified into groups according to their mass and spin properties. These are, referring to their masses: (1) the photon with zero rest mass and spin 1. It is a massless . (2) the or light particles. These are the electrons, muons and neutrinos and their antiparticles, all with masses less than the pions and with spin 1/2. For reasons connected with statistical mechanics they are also called . Leptons interact weakly with other particles.

19

(3) the mesons or intermediate particles, so called because their masses are between those of the muons and the nucleons (this is for particles until 1953). They are the pions and the kaons and have zero or integral spin. (4) the . These are the heavy particles of nucleon mass and above. 392 Hyperons have masses greater than the nucleons. The baryons are therefore the nucleons and the hyperons All baryons have half-integral spins. Mesons and baryons are strongly reacting particles, and collectively they are called . An important concept in all nuclear reactions is the conservation of spin angular momentum and, from a study of this applied to individual events, it is possible to assign a quantum number to each particle in terms of the unit h/2 (ħ). Baryons and leptons with half integral spins are called fermions while mesons with zero or integral spins are called . Thus the muon ( -meson) is really a with spin 1/2 and therefore a , whereas the photon is a fundamental boson with spin 1. Based on these definitions it is possible to classify some 32 of these particles according to Table 26.1. Some particles are shown with their antiparticles which are distinguished by a bar over the symbol. This table is reproduced diagrammatically in Fig. 26.1, except that the muon neutrinos are omitted.

TABL 26.1 M,.....Spin Spoctn,m of Stabk aad Sanl-Stobk Part.ides and their Antiputiclcs Antipartidcs arc shown by� no«alion and 'i7" ._..-

F-.

7 ------· · ·-·- ··--·-·· SUbk ---- Neutrioo "•!� ----·-·----·-----· Stable: ".i-"� • ------Eloc:tr-041 e " :c------·-·------·---SUblc I ----Mw,o,a ,,,_-:µ• ------·----2·214 l'.t-c*-+•+¥+10l McV 11 0 Pioa •• ------·-·----·022 rs ••-2,+1)) McV 2:73 0 Pioll a•: ------··---·---- .. -----ls m •• l't + .. +Jl McV {™ 0 Kaon K •:te. • ------· lO n1 K • -,,,_• + w � 0 Kaon K•�K• -----·---·----·-·-----· 10 n..1 K•-•• +•- {1136 I ------Proton p • :p • Slabk Nuclcoos lllll I Ncu1ron n•i• IOll s n• p• +e" +Y ··------· - La..t,d.a Ao..A• 0-27 as A•-p• +•· +)7 McV i:-:i:· 0-16 n.s �--••+•· +Ill McV Hypcrou Sic,NI �fi I as z· A•+•· +66 McV 2Sl2 ----·------·---Xi J ;.� 0-1 DI E°-A•+ .. +70 McV I

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..... T;,o - Xl -2!IR i I - sio,,,o 2340 ,

21112 ;t -- ••:s.1 � t - 0 ------Ploo -275 0 I 207 t t ... 0 ! t -- 0

Fig. 2�.12 Par1idcs and their tmtipanicles. [From Orear. FwrdameN1al PJ,y,ics, Wiley, 1961.) Muon neutrinos not shown.

Multiplet Structure - and Hypercharges As far as strong interactions are concerned, the neutron and the proton are the two states of equal mass of a nucleon doublet. A glance at Tables 27.2B, C shows that particles can be grouped in multiplets of equal mass but different charges. Examples are shown below: Multiplet number Mass M (MeV) Nucleons N+ No 2 939 1(0 Pions 7t+ 7t - 3 Kaons K Ko, i(o" K- 2 2 496 Xi ...-:o ....-.. - 2 1318

21

TABLE 27.2A Stable Particles with 'T'> > 10- 2> s Rest So= mass Spin Mean obur�d decay Closs Particle (M .. V) J lifetime (s) modes

Boson Photon (y) I 0 Stable: infinite - � a v..:v... 0 Stable: infinite - 0 c 0-SI I Stable: infinite ci. - :i .s µ IOS·7 1 2·2 )( 10-6 cv\l .. � 139·6 0 2·6>< ,o-• uv ; ,.o 13S-O 0 8·9x 10-is EM ;-; c � K� 493·8 0 1·24 x 10-• Jrf: 11:x:0: ,nt - se " St c s Ko 497·8 0 1·24 x 10-• 500/.K �: 50°/..K t d! :E Ko - 0 0-87 x 10- •0 n •n-: ffono Ka ffOnO,rO: ,r • ,r - ffo OL - 0 5·3 x 10-• n S48·8 0 3x 10-•• EM iP}O: xo;;· � � p• 938·3 ! Stable: infinite - ...,e � jl � �u ::c ·i :z no 939-6 { 1-01 x 10..1 p•e-v. .... 1\0 11 IS·S 2·52 x 10 ,o p• x-; noxo I:. 1189·S 0-81 x ,o- ,o nOx•; p•,ro l � 1• e :co 1192·S Ix 10- EM AO;· � 1:- 0 0 8. 1197·4 1·66x ,o-• n°,r-; n°c-\•,.. c::- ::c =o 1314·9 2·9 x 10- ,o A0n°: p•n- .;! - - 1321·3 1·73x 10-•0 /\off-: non- n- 1672 I l·I x 10-10 .:,off-: /\oK - The above particles arc well cseablishcd and immune to strong doca)'.

TABLE 27.28 Established Mesons and Meson Resonances Lifetimes: Stable 10-•0 s: Resonances 10-2.:t s

Moss Charge Q Particle and (MeV) -1 0 +I I n,ass (MeV) 1700 1600 .,o ISl4 1500 . 1419 1400 . . � Kv • <..> 1t(A2) 1305 1300 . . . z . < ,,o 1260 1200 :z 0 1100 � .,0 1019 1000 . . "" ,,0 958 900 . . K• 893 800 • ,,o 783 . . ff. 76S 700 • ,- = _I . - 600 - -· = . ,,,0 549 soo . • . K 496 400 _,...... a, 300 ;::= 200 v> . . . 1t 137 100 0 Multiplicities: ,,0 - 1. n- 3. K-4.

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Est.ablished Baryons and Baryon Resonances Liretimes.: Stable 10-•0 s; Resonances 10-2-> s

Moss Charge Q Particle a.n.d (M�V) -I 0 +I +2 mass (MeV) 2200 . . ' 2190 2100 . Ao 2100 . . . � 2030 2000 . . . . 6 1920 1900 � <..., Ao 1830 . z. Ao 1800 . -e 1815 . . . z � 1770 0 .,, 1710 ST . t.U 1700 m . Ao 1690 N 1688 I . 1680 o- 1672 ST . . . . "" 0 1670 L>. 1640 1600 N 1550 . : - I 530 N 1525 1500 Ao 1520 •. . • 1470 Ao 1405 1400 . . . � 1385 . . Stab. - 1318 1300 . . . . Res . 6 1236 1200 . . . � 1193 0 I I I 1100 . t.U =....J ;'.= 1000 .,, . . {n° 939·6 900 N p- 938·3 Muhiplicitics: A0= I� =2. 2=2. �=3. -4 .. .o- I. Antibaryons arc not show n An important outcome of the multiplicity number M of an equal mass group is the concept of Isospin I. This is not a true mechanical spin but its quantum- mechanical derivation follows similar lines to that of electron spin in spectroscopy and obeys similar rules, so that we put M = 2I + 1 for the charge multiplicity, In the case of the nucleon doublet it is reasonable to assume that they are two states of the same nuclear particle. They are distinguished only by their charge and thus by the interaction of the proton with the electromagnetic field. The Isospin I = 1/2 is assigned to all nucleons but with the component I3 = 1/2 for the proton and I3 = -1/2 for the neutron. Here I3 = ±1/2 is the z component of I. Thus the proton and neutron form a doublet with the same Isospin. Similarly, for the pion triplet we have M = 3 and I = 1 giving

[ + 1 for 7[ , /3 = 0 for 7[0 ' -1 for n

The kaons are grouped into two pairs with I3 = ± 1/2 for each pair. These are

23

0,/3 K\l3=+t and K 3=-t, K-,/3=-t and K°",1 =+{. Finally, the delta particle, has four states, viz.,

for which I =3/2 and the I3 values are 3/2, 1/2, -1/2and -3/2 respectively. In general, there are 2I+1 isospin states for a particle of given I Using these data we now obtain isospins as follows:

I 13 +J Nucleons t -2 Pions 1 0, + I 1 Kaons 2 I -2 Xi baryon l +i Delta baryons 2 +2, +t Isospin I is conserved only in strong interactions so that it applies only to hadrons and not to leptons. See Table 27.2A. Continuing our consideration of particles in groups or multiplets the concept of Yis now introduced. This is a charge number equal to twice the average charge Q of a multiplet, so that for the above examples we have the hypercharge numbers shown below, where 1 Q= M(Q. +Q2+ .. · +QM): Q Y=2Q Nucleons N+ No 1/2 l Pions 1t+ 7to 1t 0 0 K+ Ko Ko K- 1 _.l. Kaons 2• 2 1 -1 ':'0 ' ' Xi baryons .:..-- 0 2 -1 6++,6+ 6- 0 6- l. Delta baryons 2 1

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It is found that, like isospin I, the hypercharge number Yis conserved in strong interactions. It is also conserved in electromagnetic interactions, but not in weak interactions. These are strange new ideas of conservation. They can be justified empirically by applying them to established decays and reactions. The strangest quantum number of all is actually called the '' number S. (This is not a spin quantum number.) Various relations between the quantum numbers already mentioned can be derived. Thus we can see that for baryons.

Proton Q--2l +l.2--1 ·, Neutron, Q-- _12 +12--0 ·, !:). + + baryon, Q=1+t=2, etc.

If we extend this to pions, for example, for which B = 0, we have

n ", Q= 1 +0= 1; n°, Q=O+O=O; ti>, Q=-1+0=-1.

0 Now for the baryon A for which J 3 = l O = 0 since it is a singlet (Table 27.2A) we have, from the Q = 13 + 2B formula, Q=O+� i.e. Q". = 1, obviously incorrect. Thus /\ 0 was regarded as a 'strange' particle. Similarly the neutral kaon KO has B = 0 and 13 = -t, from which we get QK• = -t, again incorrect. The KO particle was another 'strange' particle. Difficulties such as this led to the new concept of strangeness. Nucleons, not strange, were assigned S =0 and putting K 0, S = + 1 and A 0, S = -1, where Sis the strangeness quantum number, the charge formula was written giving and as required. Thus we can write Q = 13 +t Y, where Y is the hypcrcharge quantum number given by Y=S+B.

25

Since Y and B are each conserved in strong and electromagnetic interactions S must also be so conserved. As S is a function of the quantum numbers Y and B it becomes redundant if Y and B are used, although it is still frequently used.

S'urnrn ar y of Ne\.v Quanturn Nutnber.s All particles have charge Q and can be arranged in equal mass groups of different charge and �--m�u�l��t p� l-i ci ��i yt �-( ::_/ 3 l _v_:a�-l u _�c )s �- M Total charge per group is f: Q ·1 Average charge per particle in a group is _ f: . Q M' JQ

Hypcrcharge Y 1 Isospin I is given by Y-2Q. is given by M-2I+ 1 M-1 i.e. /--2-

In addition: Baryon number B is given by B = + 1 for all baryons, = 0 for all other particles. Strangeness number S is given by S= Y-B. Lepton number I is given by I . + 1 for all leptons, = 0 for all other particles. The number of possible conservation laws has increased with the number of new particles discovered. Some apply to all three types of reaction while others apply only to parts. They are tabulated in Table 27.3. If these conservation laws are applied to high-energy pion-nucleon collision which often give large quantities of kaons, examples of possible equations are: (i) n++n°-.A0+K+ (ii) n++n°-.K0+K+. Using the conservation of baryons and strangeness, for (i) S=O+O-+ -1 + 1 c5S=0 B = 0 + 1-+ 1 + 0 we get c5B=O (ii) S=O+O-.O+O c5S=0 B=O+ 1-+0+0 we get DB'i"=O So that reaction (ii) violates baryon conservation and therefore cannot occur.

26

Conservation Laws

Interactions Conservation of Symbol Strong E.M. Weak

Mass/energy M.E. Linear momentum j j j Angular momentum J Charge Q !; !; j Hypercharge y J x Total isospin I !; x x z Component of isospin /3 J x Lepton numbers I,../" - Baryon number 8 !; !; Strangeness s '!; J x

Similarly,

is possible, whereas 1t - + p + -+Ao + 11:0 is not, by strangeness violation. Then again, in experiments using free electron-neutrinos as bombarding particles on protons, we could have (i) v.+ p " -+n° + µ+' (ii) v0+p+-+n°+e+. Applying lepton number considerations we have for [i) fe= -1 +0-+0+0 b/e-4=0 �= 0+0-+0-1 ()�¢0 whereas for (ii)

1. = - 1 + 0-+ + - 1 I"= O+O-+O+O showing that the first reaction is impossible. Consider next the collision event illustrated in Fig. 26.6.

p+ +p+ -.2n+ +2n- +n°. Applying various conservation laws, we have Q= -1+1-2-2+0 bQ=O B= -1+1-+0+0+0 bB=O Y= -1+1-+0+0+0 bY=O S= o+o-o+o+o bS=O /3 = -t+t-2-2+0 813=0 so that this event is possible. These are but a few of the many examples we could choose to illustrate the new conservation laws.

27

THE The Mendeleev of elementary was Murray Gell-Mann, who introduced the so-called Eightfold Way in 1961. (Essentially the same scheme was proposed independently by Ne’eman.) The Eightfold Way arranged the baryons and mesons into weird geometrical patterns, according to their charge and strangeness. The eight lightest baryons fit into a hexagonal array, with two particles at the center This group is known as the baryon octet

n p ScO ------__ ,,_ .....,

ro S• -1 - - - .,.. r- • �- The Baryon Octet \ \ \ \ ?:0 \ \ \

Q•- I Q=O

Notice that particles of like charge lie along the downward sloping diagonal lines: Q = +1 (in units of the proton charge) for the proton and the +; Q = 0 for the neutron, the lambda, the o, and the o ; Q = -1 for the - and the  - Horizontal lines associate particles of like strangeness: S = 0 for the proton and neutron, S = -1 for the middle line and S = -2 for the two  ’s. The eight lightest mesons fill a similar hexagonal pattern, forming the (pseudo-scalar) meson octet:

K' S•l

S• 0 - -- - - ,,- •• The Meson Octet \ ' \ s--,------,---...... , \ \ \ \ ' \ \ \ \ 0•-1 O•O 0.'

Once again, diagonal lines determine charge, and horizontals determine strangeness; but this time the top line has S = 1, the middle line S = 0, and the bottom Line S=-I . (This discrepancy is a historical accident; Gell-Mann could just as well have assigned S = 1 to the proton and neutron, S = 0 to the  ’s and the , and S = -1 to the . ’s In 1953 he had no reason to prefer that choice, and it seemed most natural to give the familiar particles proton, neutron, and pion a strangeness of zero. After 1961 a new term hypercharge was introduced, which was equal to S for the mesons and to S + 1 for the baryons. But later developments showed that strangeness was the better quantity after all, and the word “hypercharge” has now been taken over for a quite different purpose.) Hexagons were not the only figures allowed by the Eightfold Way; there Was also, for example, a triangular array, incorporating 10 heavier baryons the baryon decuplet: ,. S 0---- ' �·- � •O r·· ' \ S•-1------\ • \ \ 0•2 ' \ \ S • -2 ---- �·- �-. \ The e,ryon Oecuplc1 ' \ a'• ,

s -J ------n ' \ O•O

a \ -,

Now, as Gell-Mann was fitting these particles into the decuplet, an absolutely lovely thing happened. Nine of the particles were known experimentally, but at that time the tenth particle the one at the very bottom, with a charge of -1 and strangeness -3 was missing: No particle with these properties had ever been detected in the laboratory. Gell-Mann boldly predicted that such a particle would be found, and told the experimentalists exactly how to produce it. Moreover, he calculated its mass and its lifetime, and sure enough, in 1964 the famous omega-minus particle was discovered, precisely as Gell-Mann had predicted (see Fig. 1.10).

. • •I o o;•\ r \�n· ,.

J\pft I.It ��o(thcQ. Th.:.nualbu�':lllt tl".Xbon !he: nchL tl'hatocouni:sy &oolJl.&,'fn N,1�1�1«)'.I Since the discovery of the omega-minus (-), no one has seriously doubted that the Eightfold Way is correct. Over the next 10 years, every new found a place in one of the Eightfold Way supermultiplets.