Weak Interaction of Elementary Particles

Citation preview

weak: in t e r a c t io n

of

ELEMENTARY PARTICLES

Weak Interaction of Elementary Particles BY

L. B. OK UN’ T R A N S L A T E D FROM THE R U S S I A N BY

S. AND M. N IK O L IC T R A N S L A T I O N E D I T E D BY

J. B E R N S T E IN

P E R G A M O N PR ESS O X F O R D L O N D O N • E D I N B U R G H • NEW YO RK TO R O N T O • PARI S • F R A N K F U R T

A D D IS O N -W E S L E Y P U B L IS H IN G C O M PA N Y , INC. R E A D I N G , M A S S A C H U S E T T S • PALO ALTO • L O N D O N

Copyright © 1965 Pergamon Press Ltd.

Sole distributors in the U.S.A. ADDISON-WESLEY PUBLISHING COMPANY, INC. Reading, Massachusetts • Palo Alto • London

PERGAMON PRESS International Series of Monographs in Natural Philosophy Volume 5

Library of Congress Catalog Card No. 65-13072

This book is a translation of CnaSoe B3anMOAeficTBHe ajieMeiiTapHBix Hacrau, by L. B. Okun\ published by Fizmatgiz, Moscow, 1963, and incorporates revisions supplied by the author during translation towards the end of 1964

CONTENTS F oreword F oreword

to the

E nglish E dition

1. P articles. I nteractions. M odels

1

Classification of elementary particles (1). Types of interactions (1). Are elementary particles actually elementary? (4) Composite models (5). Iso­ topic multiplets (5). Schemes of isomultiplets in the Sakata model (7). Quasiparticles in the Sakata model (8). Universal, unitary-symmetric strong interaction (10). Isotopic invariance in the Sakata model (11). Conservation of fundamental particles (12). Universal weak inter­ action (13). Table of weak interactions (15). Neutral currents? (17) Two neutrinos (18). Minimal model (20). 2. S pinors . A mplitudes . C urrents

22

Scalars and vectors (22). Wave function (23). Spinors (23). Dirac equation (24). ^-matrices (25). y-matrices (26). Some relations (27). Calculation of traces (27). Operations *, and + (29). Conjugated spinor (29). Five bilinear covariants (30). Electromagnetic inter­ action (30). Strong interaction (31). Weak interaction (32). y5-invariance (33). Lagrangian and amplitude (34). S- and T-matrices (37). Probability and cross section (37). 3. C-, P-, ^

40

transformations

Charge conjugation (40). Space inversion (42). Combined inversion (44). Time reversal and CPT-theorem (45). Intrinsic parity of the fer­ mion (47). P-inversion and V-A-interaction (48). Charge conjugation for fermions (49). Charge conjugation and ^-^-interaction (50). Parity of the antifermion (50). Instrinsic parity of the boson (51). Charge parity of the boson (51). 4. W eak I nteraction

between

L eptons

Muon decay (53). Fierz relation (54). Expression for the probability (55). Approximate estimate of the decay probability (55). Integration over phase space (56). Expression for \M \2 (58). Projection operators A 45* and A (59). Reduction to traces (60). Calculation of traces (60). Inte­ gration with respect to neutrino momenta (61). Spectrum of decay electrons (63). Asymmetry and polarization of electrons (63). Neutrinoelectron scattering (65). Muon-pair production in the neutrino beam (67). v

53

C O N T EN T S

VI

5. Leptonic D ecays P roperties

of the

of S trongly I nteracting P articles. G eneral A mplitudes

68

Problem of strong interactions (68). General form of the amplitude (69). Three types of matrix elements (70). Decays of the first type (71). Decays of the second type (72). Decays of the third type (73). Reality of the functions / and g (74). 6. S trangeness C onserving L eptonic D ecays. A nalogy with E lectro­

78

dynamics

Conservation of the vector current (78). Electromagnetic properties of the proton (79). Electromagnetic properties of the neutron (82). Isotopic spin (83). Isotopic form factors (84). Relationship between weak and electromagnetic form factors (85). Matrix element of the n p transition (85). Vector coupling constant (86). “ Weak mag­ netism” (87). “ Effective scalar” (88). Interaction of the 7z+-meson with the photon (88). n +^7t° + e+ + v decay (89)1. Analogy with electro­ dynamics—a consequence of the minimal model (91). 7. Strangeness C onserving L eptonic D ecays. Isotopic P roperties the

of

N ucleonic C urrent

93

Nucleonic current—isovector (93). Isotopic rotation and charge conjugation (93). TVrotation and nucleons (93). T2-rotation and jr-mesons (94). (/-transformation (95). Lee-Yang theorem (95). G-parity of the nucleon? (96) G-parity of the nucleon-antinucleon system (96). G-parity and annihilation (97). G-parity of the a>°-meson (98). G-parity and ^-decay (98). Other decays (100). 8. S trangeness C onserving Concrete P rocesses

L eptonic

D ecays.

C alculations

of

101

7re3-decay (n+ -> n° + e+ + v) (101). ^ 2-decay -* fi+ + v) and ne2decay (tz+ ->■ e+ + v) (103). Polarization of muons in the tt^2decay (105). Neutron /3-decay (106). Polarization of electrons (109). Decay of the polarized neutron (110). //“-meson capture by the proton (111). Decays of strange particles (112). 9 . Strangeness C hanging L eptonic D ecays. G eneral P roperties

114

Hyperon decays (115). ^-decays (116). |zl£|== 1 rule (118). A Q - A S rule (118). A T = ■£rule (120). Vector current zip is not conserved (121). Hyperon-decay probabilities (123). Unitary symmetry and weak inter­ action (125).10 10. Strangeness C hanging L eptonic D ecays. A'-decays

Kp 2 -decay (126). ^Tc2-decay(128). X^-decay (129). Pion spectrum (130). Total decay probability (131). Electron spectrum (132). Neutrino spectrum (133).

126

VU

CONTENTS

11. S trangeness C hanging L eptonic D ecays. Ke3-

and

A ^ - decays

135

( continued )

Electron polarization (135). Electron spectrum at given pion energy (136). Dalitz plot for Ac3-decay (138). “ Sliding ray” dia­ gram (141). A^-decay (142). 12. N on -leptonic D ecays deration .

0-

Strange P articles. Q ualitative C onsi­

of

145

a n d t- decays

Interaction of the iip and A p currents (145). /1-hyperon decay (146). 27- and is-hyperon decays (147). A-decays (148). A*2-decay (150). A^-decay (151). Dalitz plot (153). A?- and A§-mesons (156). 13. N on - leptonic D ecays

of

H yperons

159

Amplitudes of hyperon decays (159). Switch off the scattering (161). Reality of + n° (0+) decay (181). A? -> n+ + tT and A? n° + n° decays (182). A„3decays (182). Lifetime of the A^-meson (184). 15. D ual P roperties

of

N eutral A- mesons

186

Analogy with angular momentum (186). Why not tii and n2rl (187) Muonium (188). Pais-Piccioni Gedanken experiment (189). A? —A§ mass difference (190). Oscillations of leptonic decays (194). 16. D ual P roperties

of

N eutral A- mesons ( continued ) ^

195

Three types of the regeneration (195). Piccioni’s experiment (196). Which is heavier, A? or A§? (198) 17. P arity N on - conservation

in

N uclear F orces

201

Contribution of weak interaction (201). Can parity non-conservation in strong interactions be large? (202) 18. W eak I nteraction

at

S mall D istances

Statement of the problem (203). A local four-fermion interaction (204). Anon-local four-fermion interaction (205). Intermediate bosons (206). Equality of the vector constants of /?-decay and //-decay (210). Absence of the //+ 2e+ + e~ decay (211). Absence of the //-► e + y decay (212).

203

viii

C O N TE NT S

19. W hat

is to be

M easured ,

and

W hy?

215

A. Test of the general properties of the theory (215). B. Test of the isotopic properties of the theory (216). C. Accumulation of data that cannot as yet be accounted for by theory. Various problems (217). 20. W eak I nteraction

and

U nitary S ymmetry

218

Test of the general properties of the theory (219). Test of the isotopic properties of the theory (220). From the isotopic properties to the unitary ones (223). Supermultiplets (224). 7T-diagrams (225). Triality (227). Supercharge (228). Additivity of Z and multiplication of unitary representations (231). Scheme for multiplication of representations (232). Tables of supermultiplets (233). Supermultiplets in the Sakata model (233). The eightfold way (237). Quarks (238). Four-baryon model and supercharged particles (239). Other models (242). Models and mathematical formalism (242). T3Y-dia­ grams (243). U-spin (243). Moderately strong interaction (244). Mass formula for decuplet (244). Mass formula for octet (245). Mass formula for any supermultiplet (247). Electromagnetic properties (248). Modified universality of the weak interaction (249). Matrix of eight currents (251). Leptonic decays of mesons (254). Leptonic decays of baryons (256). Hadronic decays (259). 0-dccay (260). Violation of the A T = \ rule (262). Hadronic decays of hyperons (264). Parity non-con­ serving nuclear forces (266). Other groups of rank two (267). Groups of a higher rank (268). Space-unitary symmetries (269). 21. B ibliography

270

Particles. Models. Interactions (270). Weak-interaction Lagrangian (272). Interactions of leptons (274). Strangeness conserving leptonic decays (275). Strangeness changing leptonic decays (277). Non-leptonic decays (279). Neutral tf-mesons (K%, K%) (281). Parity non-conser­ vation in nuclear forces (282). Weak interactions at small distances (282). Weak interaction and unitary symmetry (284). I ndex

289

FOREWORD book is based on lectures delivered by the author in 1960 and 1961 at the Institute of Theoretical and Experimental Physics of the Academy of Sciences of the USSR and at the Joint Institute of Nuclear Research. The book is meant for experimental physicists working in the field of elementary particles and high energies, and for young theoretical physicists specializing in this field. The author has set himself two tasks: first, to make the reader familiar with the basic ideas and problems of the theory of the weak interaction of elementary particles; second, to make the reader familiar with the methods of calculation within the theory and to show him how the methods are to be applied. The overall content of the book is concentrated about two pivotal hypotheses: the universality of the weak interaction, and the composite model of strongly interacting particles. These hypo­ theses allow the contents to be expounded in a more concise way and to retrace the connection between various problems in the theory of weak and strong interactions. Like every extrapolation, the hypotheses of the universality and of the composite model will undoubtedly be improved in the future and in part modified in the light of new experimental facts. In the form in which they are presented in the book, these hypotheses are to be considered as a “ zero approximation”. The author is deeply grateful to A. I. Alikhanov and I. Y. Pomeranchuk, with whose initiative the lectures were delivered and the book was published, to I. Y. Kobzarev for his valuable advice, to V. B. Berestetskii who read the manuscript and made a number of useful remarks, and also to V. A. Kolkunov, E. P. Shabalin, V. V. Solovyev and N. S. Libova for their help in pre­ paring the book for publication. T h is

la

EP

IX

FOREWORD TO THE ENGLISH EDITION I n p r e p a r in g this edition only minor amendments were made in the basic text of the book. To keep up, if only in part, with recent developments in this field, the chapter “ Weak Interaction and Unitary Symmetry” was added. I take this opportunity to express my deep gratitude to Y. B. Berestetskii, V. B. Mandeltsveig, I. Y. Pomerachnuk, J. Prentki, I. S. Shapiro, Y. V. Sudakov, V. V. Vladimirskii and V. I. Zakharov for their discussions on various problems of unitary symmetry, which were very useful to me in writing the chapter quoted. I am in particular grateful to I. Y. Kobzarev, who read the manuscript and made a number of valuable remarks. L. B. O k u n ’

C H A P TE R 1

PARTICLES. INTERACTIONS. MODELS C L A SSIFICATIO N OF EL EM EN TA R Y PARTICLES

All matter around us is made of elementary particles. All known processes and interactions in nature are due to the inter­ action between elementary particles. The present known elementary particles can be divided into four classes. The first class contains only one particle—the photon. The second consists of leptons: electron, muon, neutrino, and their antiparticles. The third one comprises the mesons: three ?r-mesons and four Ai-mesons. The fourth one contains baryons (nucleons, A-, Z- and S'-hyperons) and antibaryons. All these particles are enumerated in Table 1. Beside the mesons and baryons enumerated in Table 1 other particles are known which are not included in the table because of their extremely short lifetimes. These “ particles” live for such a short time that they manifest themselves only in the form of reso­ nances in reactions at high energies. Such resonances are often considered as excited states of the jr-meson, ^T-meson, nucleon, /1-hyperon and so on.f T Y P E S OF IN T E R A C T IO N S

There are four types of elementary-particle interactions, sharply differing from one another: the gravitational, the electromagnetic, the strong and the weak. The gravitational interaction has a very small coupling constant (it is very weak), and, if its character does not change sharply at small distances, its role is insignificant for the phenomena that we are going to consider. Indeed, the energy of gravitational interaction t See tables of baryon and meson resonances on pp. 234 and 235 (note added in 1964).

la*

1

I N T E R A C T I O N OF EL EM E NT A RY P A R T I C L E S

2

of two protons set apart at a distance r is equal to m2 * — r , where %is the Newtonian constant, x = 6 x 10~39/ra2, while m is the proton mass.f When r ~ \jm this energy amounts to ~ 10~38m T able 1. M asses

Class Photon

Spin

Mass (MeV)

Mean life (sec)

y

i

0

oo

Ve e /i

i i i i

< 2 x 10“4 •) (pp) or (up) (pp) in the weak interaction Lagrangian cannot, so far. be excluded. On the con­ trary, as will be seen in what follows, a large amount of data on the non-leptonic decays of strange particles could find a natural explanation on the basis of an interaction including (pp + nn) (/b,), whereas the ordinary non-leptonic interaction (/>/;) (Ap) cannot account for them (we refer here to the so-called J T = + rule). The problem of neutral currents needs further investigation. TWO N E U T R IN O S

Another important problem is whether there are neutrinos of several kinds. We have written the electronic current in the form j e = ev. and muonic current in the form j = fir. assuming tacitly that the neutrinos included in these currents are the same. However, there are no experimental grounds for such an assumption. The assumption that rt, and vft are the same ()•,. = r(i) might be suggested by the symmetry which exists between the three leptons (ji, e and v) and the three fundamental barvons (.1, n and p) in the Sakata model. This symmetry is sometimes called the Kiev sym­ metry (it was first submitted for discussion at the Kiev Conference on High-Energy Physics in 1959). Indeed, the weak interaction

P A R T IC L E S , IN T E R A C T IO N S . MODELS

19

that wc wrote down possesses symmetry with respect to the exchange A p, n e, p «-►v. Introduction of two kinds of neutrinos would violate this symmetry. Unfortunately, the problem of the relation between baryons and leptons is for the present completely unclear. Hence Kiev symmetry cannot be taken as a reliable guide. The assumption that ve and v/t are different particles (ve #= v„) is favoured by the absence of the decays p -> e + y and p 3e (see p. 211). An experiment that would allow one to solve the problem of whether ve and vfl are the same was proposed by Pontecorvo and performed by a group from Columbia University using the Brookhaven accelerator. In this experiment (the results of which were published in the summer of 1962) it was established that the neutrino produced in the tU -*• //* ± v decays does not give rise, in colliding with nucleons, to reactions of the type v + p -*■ n + e* or v + n ->■p + e~ which should take place if ve and v were identical particles. Quite a number of schemes which could account for the results of this experiment are discussed in the literature. One of these is a scheme in which e~, p +, v are leptons, while e+, p~, v are anti­ leptons, and in which the transitions p —e are forbidden by leptonic charge conservation. The ordinary muon decay proceeds in this scheme with the emission of two v’s (and not a v and a v). According to this proposal the neutrino, like other fermions, is a four-compo­ nent particle, its two left-handed components being contained in the electron part, while its two right-handed components belong to the muon part.f This scheme is attractive for it is economic: no special muon charge is introduced in it, and use is made of all four components in the neutrino wave function. If the neutrino mass differs from zero, then, in this scheme, the transition of the electronic components of the neutrino to the muonic ones should exist, so that neutrinos produced in the n~ —>p~ + v decay might give rise to the reaction v + n -> e~ + p. But because of the small neutrino mass this effect would be extremely small. If the neutrino mass equals zero, one cannot devise any experiment which would t In this case the lepton current is unlike the form that is at present uni­ versally adopted (see pp. 33-34), and has the form

vya(i +ys)e +

~ Ys)

v-

20

IN T E R A C T IO N OF ELEM ENTA RY P A R T IC L E S

be able to distinguish this scheme from that in which the muon and muon neutrino have a conserved “ muoniccharge”, and where e~, ve>/ we obtain , -„ y*y* + W = 2