A four-state theory of the neutrino

A four-state theory of the neutrino

Nuclear Physics 5 (1958) 11--10; 1~) North-Holland Publishing Co., Arasterda~ lqot to be reproduced by photoprint or microfilm without written permi...

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Nuclear Physics 5 (1958)

11--10; 1~) North-Holland Publishing Co., Arasterda~

lqot to be reproduced by photoprint or microfilm without written permission from the publish




P. E. C A V A N A G H , C. F. C O L E M A N , B. W. R I D L E Y a n d J. F. T U R N E R

Atomic Energv Research Establishment, Harwell, Didcot, Berks Received 29 A u g u s t 1957 A scheme of coupling c o n s t a n t s for t h e beta-decay interaction is p r o p o s e d explain a wide r a n g e of e x p e r i m e n t a l results. The scheme a s s u m e s a f o u r - s t a t e n e u t r i n I t implies t h a t all electron polarization m e a s u r e m e n t s will yield one or the o t h e r of t] values +v/c, w h a t e v e r the values of the ratios Cr/CA and CslCv.


1. I n t r o d u c t i o n

It appears t h a t the two component theory of the neutrino of Lee an Yang m a y be incapable of explaining some of the phenomena of r-decal Unfortunately the issue is still obscured by uncertainties in the experiment: data, particularly in regard to the experiments on electron polarizatio~ This situation is hardly surprising, since a variety of new experiment techniques have had to be developed, and it takes time to evaluate tl possible causes Of inaccuracy. It is still too early to come to any defini conclusion about the validity of any of the results. One major discrepam appears in Au 198, for which Frauenfelder et al. 1) and de Waard et al. obtain a small or zero polarization, while Wu et al. 3) and Cavanagh et al. obtain a full (--v/c) polarization. In the case of Ga ss a value for the electr polarization of ~ ( + v / c ) obtained by Deutsch et al. s) disagrees w: t h a t of Frauenfelder et al. s), which is given as (O.l±0.3)v/c. In what follo we will assume t h a t the 4-(v/c) values of the polarization are correct The data on which we will base the theory will be derived from th~ sources, primarily. These are (i) electron polarization (ii) electron-neutri correlation (iii) Fierz terms. (i) E L E C T R O N


The polarization of negatons from a pure G.T. emitter is --v/c. Th is a large measure of agreement on this particular point, though none of t Supporting this choice are the measurements of H. Langevin-Joliot and N. M; ( C o m p t e s R e n d u s 245 (1957) 670) on 128 keV electrons f r o m S s5 (3/2 -* 3/2), w h o ob a polarization - - ( 0 . 4 + 0 . 1 4 ) b y M o t t s c a t t e r i n g f r o m a 260 /~ g m / c m 2 gold foil, a n , F. B o e h m , T. B. N o v e y , C. A. B a r n e s and B. Stech ( p r e p r i n t ) on p o s i t o u s f r o m m i r r o r t r a n s i t i o n N z3 -* C is. T h e y o b t a i n a polarization + (0.93~:0.20) v/c f r o m t h e circ polarization of t h e high-energy q u a n t a formed b y annihilation in flight of N xs posit 11




experiments are accurate and only a few transitions have been studied. The polarization of positrons from a pure Fermi emitter is +v/c. This is based on the results of Deutsch et oJ. for Ga 66. If these results are interpreted in terms of the two component theory it implies that T >> A and S >> V. (ii) E L E C T R O N - N E U T R I N O


Here again it appears that all the experimental results cannot be made compatible. This matter will be treated fully by Ridley in a separate paper. Here we will say merely that the He 6 result of Rustad and Ruby v) is difficult to reconcile with those for the neutron (RobsonS)), Ne 19 and A a5 {Allen et aL 9)). Moreover Ridley's measurement on another {essentially) pure G.T. emitter, Ne 2s,shows that T is not the dominant term, as indicated by the H e s measurement, but that T and A are present in roughly equal amounts. The limits quoted are 0.9 < ICAI/ICTI< 1.4.The A 88 measurement shows that the Fermi interaction is predominantly vector, [Cvl/[Csl> 1.8. These two results taken in conjunction with those from electron polarization present a major difficulty for the two component theory. (iii) F I E R E T E R M S

A n y theory must be compatible with the Fierz terms in both allowed and first forbidden decays being small. W e shall take them to be zero. For a theory in which invariance under the parity and time reversal operators m a y be violated, they are Re (CTCA* + C ' T C ' A * ) = 0 allowed Re (Cs Cv*-t- C's C'v*) = 0 / Re

(CsCA*q-C'sC'A*) = 0


Re (CT Cv*-}- C'T C'v*) -----0


first forbidden

in t h e notation of Jackson et ad.x°). 2. Rleetron P o l a r i z a t i o n

Let us turn now to the expression derived by Jackson a aL ao) for the electron polarization for allowed transitions (but neglect for the moment Coulomb terms) viz. P=--{-2---

IMGTI~ Re ( C T C ' T * - - C A C ' ^ * ) + I M F I ~ Re ( C s C ' s * - - C v C ' v * )

IMo I'(IcTI'+ Ic' l'+l c,,18+ Ic',.l')+ tM,,ls(Icsl'+ IC'sl'+ Ic,.l'+ lc'¢) The two component theory requires that neutrinos arising from T and A interactions and also S and V interactions should all have the same spin direction, either parallel or antiparallel to the direction of motion, depending on the sign of the emitted electron. This is expressed b y CT = --C'T,

C A = --CtA,

C$ = - - C t s ,

C v = - - C ' V.







H o w e v e r the above formula for the electron polarization shows that if electrons emitted in T interactions have the same sign of spin as the neutrino, those emitted in A interactions will have the opposite sign of spin. So electrons emitted in an interaction in which C T = C A would be essentially unpolarized, contrary to the assumed data. A w a y out of this difficulty is to require that neutrinos emitted in a T interaction have the opposite sign of spin to those emitted in an A interaction. This is expressed b y CT = --C'T,

CA -= C'A,

and for the Fermi interaction Cs=--C's,


With this assumption the electron polarization = +vie irrespective of the ratio of T to A, or S to V. This enables one to reconcile the electronpolarization and electron-neutrino correlation data. Moreover it is at once seen that the Fierz terms for both allowed and first forbidden decays become identically zero. It will be of interest to examine some of the further consequences of this theory. 3. T i m e R e v e r s a l T e r m s In what follows we shall again make extensive reference to the paper b y Jackson a al. lo). Their expression (A.10) includes the Coulomb terms in the electron polarization. These are of the form ~Z Im (CsC'v*+Cs'Cv*), and become identically zero on the basis of the new theory. Similarly the time reversal terms in every one of the expressions derived b y these authors, except that for D~, become identically zero. The expression for D~ reduces to


= ~yj[MF[IMGT[ ~ J 4 Im (CsCT*--CvCA*). J+l

This only vanishes for certain special relations between the amplitudes and phases of the various coupling constants. From this it follows that no experiment which involves the measurement of the electron spin can succeed in detecting time reversal terms. The one experiment which can do this is a recoil experiment with oriented nuclei emitting p-particles in a mixed transition. In this case also the issue would not be clouded b y the presence of Coulomb terms, since these vanish identically. The recoil experiment with polarized neutrons, of course, falls into this class. 4. S T and VA Interference T e r m s In the expression for A t (A.7), which gives the parity violating terms determined b y Wu et al. 11) in their orientation experiment, the first term is the same as the G.T. part of the expression for the electron polarization, while the second appears only for a mixed transition, and contains inter-




C. F .


B . ~V. R I D L E Y





ference terms between S and: T and between V and A. For the present theory

A ~ = [MGTiZ ~jj,[ ={22{[CTI2-~ ICAI2}] --~Jj'IMFI [MGT[ V J

[4 Re (CsCT*+Cv CA*)].

A similar interference term appears in the expression for the circular polarization of ~,-rays, first investigated b y Schopper 1~). The first orientation measurements made on a mixed transition viz. Co 5s (Wu et al.13), Postma et al. 14)) were compatible with a zero value for the interference term. However the measurements on y-ray circular polarization b y Schopper 15) on Na 2., Zr 9~, and Sb TM, and b y Boehm and Wapstra 16) on Sc 46 and Au 198, appear to require the presence of large interference terms. The failure to observe such terms in Co 5s m a y be due to the Fermi part of the matrix element being very small (Grace, private communication). The smallness of the interference terms in this case is confirmed b y the measurements of Boehm and Wapstra 1T). Both the present theory and the two component theory predict the presence of these terms.

5. Inverse •-Decay Lee and Yang have pointed out that a consequence of the two component theory,, on the assumption that the E-disintegrations in a nuclear reactor are predominantly G.T., is that the antineutrinos emitted should be largely polarized, and that if this were so the cross-section for inverse E-decay measured: b y Reines and Cowan is) should be twice the value they actually observed. It was suggested then that there is an incompatibility between the parity measurements on Coe° and Reines and Cowan's measurement, independent of any detailed theory. We would like to suggest, instead, that the result of the Reines and Cowan experiment indicates that the neutrinos from a reactor are largely unpolarized. If we also make the reasonable assumption that Fermi transitions are unimportant, this conclusion is in agreement with the theory we have put forward here and suggests, in agreement with Ridley's electron-neutrino correlation measurement, that the T and A interactions are roughly equal.

6. Double ~-Decay The two component theory of the neutrino could still be made compatible with the relations between the coupling constants suggested here, provided that lepton conservation is dropped; i.e. it is suggested that in r - d e c a y antineutrinos are emitted in T interactions and neutrinos in A interactions. It can however be shown that this would lead to neutrinoless E-emission in






double r-decay, since antineutrinos emitted in the T part of the interactio~ in the first decay could be absorbed in the A part of the interactions in the second. Although in recent years the theoretical estimates of half life of double r-decay for Majorana and for Dirac neutrinos have become much closer it still appears t h a t the results of Awschalom on Ca~ 19) and Reines and Cowan on Nd 1~° 20) exclude the possibility of neutrinoless ~tecay.

7. ~-v~-e Decay The relations between the parity conserving and parity violating coupling constants in the scheme put forward here are formally the same as those derived by F e y n m a n ~1) from a two component theory of the electron. As he points out, this theory and the two component theory give opposite predictions concerning the spins of the muons and electrons in the n--/z--e decay. Here again the preliminary experimental results differ, t h a t of Lederman et al. being in qualitative agreement with the two component theory, while the value reported by the Liverpool group 22) for the electron polarization is of the opposite sign.

8. The T w i n N e u t r i n o T h e o r y This third scheme of coupling constants has been associated with the name of M. Meyer, and was also put forward at the Harwell Parity Conference by M. A. Preston. It is assumed t h a t in r - d e c a y antineutrinos are emitted in G.T. transitions, and neutrinos in Fermi transitions, and vice versa for r+ decay i.e. CT = - - C ' T , C A = - - C ' A , C s = C ' s , C y = C t v . In this form lepton non-conservation is compatible with the double r-decay experiments. This follows from an argument due to Preston: in all practical cases the initial and final states in double r-decay are both 0% hence a G.T. transition to an intermediate 1+ state must be followed by a further G.T. transition. The same argument m a y be used for Fermi transitions. If the positive result obtained by Davis on inverse r-decay in A 8~ ~3) is substantiated this would provide powerful support for the twin neutrino theory, since it requires both antineutrinos and neutrinos to be emitted from a nuclear reactor. However to reconcile the theory with full v/c electron polarization we must have CA = - - C ' A = 0, Cs = + C s ' = 0, in disagreement with the electron neutrino correlation measurements. Moreover the interference terms which appear in the 7-ray circular polarization measurements are required to vanish, as well as the Fierz terms.

9. Conclusion We have seen that three alternative schemes of coupling constants have been advanced, each of which explains some of the features of the experimental results. The four state neutrino theory, put forward here appears to be in



agreement with a wider range of experiments than the other two. This scheme implies that all electron polarization measurements, at least for allowed transitions, will give one or the other of the values i v / c , whatever the values of the ratios CT/CA and Cs/Cv, and that only one kind of measurement, suggested b y Jackson et al. 10), can reveal breakdown of time reversal invariance, a recoil measurement using oriented nuclei. Many people must be thinking along similar lines at present, and the combination C T ---- --C'T, C A = + C ' A has been specifically mentioned b y Schopper, and b y Wapstra (private communication). It is a pleasure to acknowledge the useful discussions we have had with Dr. T. H. R. Skyrme and Prof. M. A. Preston. References 1) Frauenfelder, Bobone, V. Goeler, Levine, Lewis, Peacock, Rossi and De Pasquali, Phys. Rev. 107 (1957) 909 2) H. de Vv'aard and O. J. Poppema, Physica 23 (1957) 597 3) C. S. Vv'u, private communication 4) Cavanagh, Turner, Coleman, Gard and Ridley, Phil. Mag. 21 (1957) 1105, footnote 5) Deutsch, Gittelman, Bauer, Grodzins and Sunyar, Phys. Rev. (submitted) 6) Frauenfelder, Hanson, Levine, Rossi and de Pasquali, Phys. Rev. 107 (1957) 910 7) B. M. Rustad and S. L. Ruby, Phys. Rev. 97 (1955) 991 8) J. M. Robson, Phys. Rev. 100 (1955) 933 9) Maxson, Allen and Jentschke, Phys. Rev. 97 (1955) 109; W. P. Alford a n d D. R. Hamilton, Phys. Rev. 105 (1957) 673; / Net9 M. L. Good and E. J. Laner, Phys. Rev. 105 (1957) 213; Herrmannsfeldt, Maxson, St~ihelin and Allen, Phys. Rev. 107 (1957) 641 ) A ai 10 Jackson, Treiman and Wyld, Nuclear Physics 4 (1957) 206 11 Wu, Ambler, Hayward, Hoppes and Hudson, Phys. Rev. 105 (1957) 1413 12 H. Schopper, Phil Mag. 2 (1957) 710 13 Ambler, Hayward, Hoppes, Hudson and Wu, Phys. Rev. 106 (1957) 1361 14 Postma, Huiskamp, Miedma, Steenland, Tolhoek and Gorter, Physica 23 (1957) 259 15 H. Appel and H. Schopper, Zeits. fiir Phys. 149 (1957) 103 16 F. Boehm and A. H. Wapstra. Phys. Rev. (in press) 17 F. Boehm and A. H. Wapstra, private communication 18 Cowan, Reines, Harrison, Kruse and McGuire, Science 124 (1956) 103 19 M. Awschalom, Phys. Rev. 101 (1956) 1041 20 Cowan, Harrison, Langer and Reines, Nuovo Cimento 3 (1956) 649 21 R. P. Feynman, Rochester Conference (1957) 22 J. M. Cassels et al., Physical Society Meeting (Manchester, 1957) 23 R. Davis, a b s t r a c t of paper, Unesco Conference (Paris, 1957) Note added in proo[: Since writing this paper we have received reprints of a series of notes b y R. Nataf, in one of which the same scheme of coupling constants is p u t forward as presented here (Comptes Rendus 244 (1957) 1187).