Pais doublets and the universal Fermi interaction

- ~

NuclearPhys,cs 11

(1959) 599---603,

~) North-HoUand Pubhsh,ng Co, Amaevdam

Not to be reproduced by photoprmt or tmcrofflm wtthout written permasmon from the pubhsher

PAIS DOUBLETS AND THE UNIVERSAL FERMI INTERACTION J

c

POLKINGHORNE

Trinity College, Cambridge, England Received 25 F e b r u a r y 1959 Abstract: A universal Fermi interaction responsible for all weak decays is Investigated in t e r m s of Pals's doublet representation of b a r y o n s Some u n d e r s t a n d i n g m a y be g a m e d

of t h e a p p a r e n t l y anomalous hyperon-leptomc decays a n d some of t h e consequences of t h e AI = ~ rule are stmulated One of the two alternative schemes proposed would lead to a direct decay mode for ~ particles into nucleons and plons

1. I n t r o d u c t i o n Pals 1) has discussed a symmetrical form of baryon-meson interactions in winch the baryons are described b y four doublets t. Nl(nucleon), N~ and Ns (composed of combinations of 27 and A particles), and N 4 (cascades). There are two separately conserved strangenesses, $1 and S~, and tins implies selection rules that are not in accord with experiment Accordingly tins symmetrical theory cannot describe the whole of the strong interaction effects, as one might indeed expect from the trlplet-slnglet mass structure of the 27--A system However if, as Pals 2. 3) has suggested m a y be the case, K+ and K ° have opposite parities, the apparent success of conventional charge independence is best understood b y supposing that this symmetrical doublet scheme (DS) represents an important element of structure In the strong Interactions The purpose of this paper is to see if any understanding of weak interactions m a y be obtained b y expressing them in terms of a universal Fermi interaction (UFI) framed in terms of DS The recent revived success of U F I in explaining weak interaction of non-strange particles makes the suggestion of its extension to strangeness violating interactions attractive 4) There is a degree of arbitrariness in doing so, b u t tins is reduced in DS b y its symmetrical treatment of baryons In particular a scheme will be constructed that has universal features and which m a y provide an understanding of the unexpected weakness of hyperon leptonIc decays 5) and simulate some of the more successful predlchons of the AI ~ ½ rule for non-leptonlc decays It m a y be objected that a picture so approximate as DS should not be expected to be used to understand weak interactions The philosophy of tins approach is the same as that of the AI = ½ rule or other more detailed t T h r o u g h o u t t h e paper we use t h e n o t a t i o n of ref 1) 599

600

J

C, P O L K I N G H O R N E

assumptions 6) about the isobaric nature of weak interaction currents. These latter approaches have utility and meaning even though the much stronger electromagnetic interactions violate isobaric spin conservation. Of course the violations of DS are more violent and important than those of the conventional isobaric scheme and so the predictions of the theory are fraught with greater ambiguity. However, if K + and K ° do have opposite parity, conventional isobaric spin assignments are no longer possible and we are only left with the modified/'-spin defined by DSt. This paper indicates a successor to the zJI ---- ½ rule in that case. The most significant violations of DS arise from the actual triplet-singlet particle nature of the supposed pair of doublets Na and N 8. The ultimate understanding of this seems far off. Some phenomenological account can be taken of it, however. Pals 8) has pointed out that a mixing parameter could appear in the distribution of T o and A ° between the neutral members, Nm° and Ns °, of the doublets. It would be nice to get some idea of this parameter from associated production data, but since the DS forbidden process

~++p ~ I + + K +

(1)

has a cross-section comparable with the DS allowed modes near threshold this does not seem to be possible. We shall see that the data on hyperon leptonic decays might indicate something about this parameter. The strength of the interaction (1) is a warning against supposing that DS allowed interactions will always predominate over those not allowed. The precise circumstances in which this might happen cannot be formulated without solving the strong interaction problem but we shall see that some coherence can be brought into the pattern of weak decays through a UFI framed in terms of DS by supposing that there at least the rule gives a rough indication of strength. This supposition rather resembles those in which the medium strong K-meson interactions are taken not to alter too greatly conclusions reached about the form of weak decays in their absence 8). Indeed, it should be better because global symmetry 9) supposes DS to be exact for pion-baryon interactions and DS also takes into account what may be the major factors in the K-meson-baryon interaction. 2. U n i v e r s a l F e r m i Interaction

The doublets divide into two groups: N 1 and Na with positive and neutral members; N 8 and N 4 with neutral and negative members. If the UFI is thought of as arising from the combinations of two currents (Lorentz space factors are omitted m what follows) it is natural to generalize the nucleon E-decay current into a contribution ~1 ~ N 1 ~1~'2 ~ + N ~ I r+N8 (2) t A different approach to thin problem has been made b y Takeda and Kato ~).

PAlS DOUBLETS AND THE UNIVERSAL FERMI INTERACTION

601

from the first group and to add to this the corresponding combination N3~+N3+N4~+N4+Naz+N 4

(3)

from the second group. Combination of the last members of (2) and (3) with the other baryon currents or with the lepton currents will give strangeness-vlolatlng weak decays and the form of these cross term currents has been chosen to give the rule

AS1

--=

+1

(4)

Tins prevents the couphng with leptons giving the decay X+ -+ N ° + e + + v

(5)

A ° --+ P + e - + ~

(6)

but does permit the decay with a partial lifetime larger b y a factor 10 than the current experimental hmlt 5) This xs calculated on the basis of a universal couphng constant and the assumption that N~O (1/~/2)(AO--2o) (7) =

The strange story of pion fl-decay makes one hesitant to assume the final existence of a contradiction If, however, the results on hyperon leptomc decays remain unchanged, it is possible to reconcile them wlth U F I b y abandoning the (certainly not accurate) equation (7) The weakness of the fl-decay is then to be interpreted in terms of the mixing parameter as showmg that the N2° state is prlnclpaUy X °, and so the Na ° state must be principally A ° The fl-decay of the X ° would, of course, form an unobservable fraction ( ~ 10-1~) of the fast X ° decays The extension of U F I so far considered is certamly not adequate to describe all weak interactions, for It does not cause any S~-non-conservlng decays. Since these decays have strengths comparable to the S~-nonconserving decays, it is contrary to our philosophy to suppose that they arise solely from the failure of DS One must therefore add to the currents a cross-term between the two doublet groups such as N,Na+N~N 4

(8)

This satisfies the rule

AS~

-

+i

(9)

and may be combined with the other baryon currents to glve all the observed decays Rules (4) and (9) together ensure that the cascade cannot decay directly to a nucleon. However, the absence of hyperon leptonye decays means that (8) cannot be coupled to the lepton currents This introduces an

60.0

j c VOLKXSGHORN~

asymmetry into the couplings The currents would be supposed to fall into three classes (1) leptons, (ll) within baryon groups, (hi) cross terms between baryon groups, with couphngs between 0) and (n), and (n) and (hi) only This scheme is mlmmal to the idea that the exchange of a heavy boson is the medium of U F I An alternative scheme which is in accord with this latter idea is to take the cross terms as N1N,+N2N 3

(10)

These change both $1 and S 2 and couphng wlth the Sl-vlolatmg currents gives Sz-vlolatmg decays into strongly interacting particles Such decays into leptons are, however, forbidden and so a completely ~ymmetncal coupling scheme can be constructed A consequence of this scheme would, however, be that the cascade could decay directly into a nucleon It would be interesting to know more about the properties of 8 It m a y be that the very small number of known 8 ' s 10) is due to failure to recognize them when they do not have a cascading decay. Certainly this second scheme seems an otherwise more attractive w a y of systematlzlng the weak decays

3. D e c a y R u l e s

The A I ---- ½ rule provided some insight into features of the weak decays into strongly-interacting particles If Pais' suggestion about opposite K + - - K ° parity is correct, conventional isobaric spin has no meaning but DS defines a different/'-spln, conserved b y strong interactions, wh,ch is ½ for each baryon doublet, 1 for the plons, and 0 for the K-mesons Some features of the old A I = ½ rule are simulated b y the present formulation of U F I In particular we can explain the long lifetime of K + Its decay takes place through S2-vlolatmg interactions containing such terms as Nlz+Nz • N 4 N 1 (11) The total effect is to produce a change of/'-spin"

IAI'I _~ 1,

(12)

a result which is independent of the choice of cross-group couplings However, the state of two plons into winch a charged spmless meson can decay has I'-spm 2 and so (12) forbids thls decay of K + in the DS approximation (We note that the K + leptomc decays also appear to be unexpectedly weak 11), as one would expect in terms of the picture presented in tins paper ) In a similar manner the rule (12) produces the same consequences for K+~ decay as those which follow from the conventional A1----½ rule

PAIS DOUBLETS

AND THE

UNIVERSAL

FERMI

INTERACTION

603

The decay of K ° takes place through terms such as NI~+N ] • N2~-N I

(13)

winch glves

IAI'[

=< 2

(14)

In tlus theory there is no simple connection between K+ and K° decays and so no problem arises about httlng the KI° decay brancinng ratlo i~) The other most successfulprechctaonof the AI = ½rule was the brancinng ratio of A decay. Tins as a more difficult matter to chscuss an terms ff tins theory However, Okubo, Marshak and Sudarshan is) have pointed out that another type of mteractaon can simulate the AI = ½result and thelr arguments can be adopted m s]mllar form an the present theory ff the flrst of the two a]ternatave schemes as chosen

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

A Paxs, Phys Rev 110 (1958) 574 A Pals, Phys Rev 112 (1958) 624 A Pals, Phys R e v , to be pubhshed R P Feynman and M GelI-Mann, Phys Rev 109 (1958)193 Eisler, Plano, Prodell, Samaos, Schwartz, Stelnberger, Conversl, Franzlm, Manelh. Santangelo and Sflvestrlnl, Phys Rev 112 (1958) 979 S Okubo, R E Marshak, E C G Sudarshan, W B Teutsch and S Welnberg, Phys Rev 112 (1958) 665 G Takeda and M Kato, Progr Theor P h y s , to be publLshed B D'Espagnat, J Prenttm and A Salam, Nuclear Phymcs 5 (1957) 447 M Gell-Mann, Phys Rev 10b (1957) 1296, J Schwlnger, Ann of Phys 2 (1957) 407 cf J R Oppenheimer, Proceedings of CERN Conference on High Energy Nuclear Ph)slCS (1958) 288 S Oneda, Nuclear Physics q (1959) 426 M Gell-Mann, Nuovo Clmento 5 (1957) 758 S Okubo, R E Marshak and E C G Sudarshan, to be published