SOME SELECTION RULES BASED ON ISOSPIN AND CHARGE CONJUGATION

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SOME SELECTION RULES BASED ON ISOSPIN AND CHARGE CONJUGATION

K. Nishijima

To cite this version:

K. Nishijima. SOME SELECTION RULES BASED ON ISOSPIN AND CHARGE CONJUGATION.

Journal de Physique Colloques, 1982, 43 (C8), pp.C8-453-C8-455. �10.1051/jphyscol:1982831�. �jpa- 00222391�

JOURNAL DE PHYSIQUE

CoZZoque C8, suppZ6ment au no 12, Tome 43, ddcembre 1982 page C8-453

SOME SELECTION RULES BASED ON I S O S P I N AND CHARGE CONJUGATION

Department of Physics, University o f Tokyo, Hong 7-3-1 Bunkyo-ku, Tokyo 113, Japan

I would like to mention what was going on in Japan in some fields closely related to strange particles. To be more precise, I would like to discuss the selectionrules discovered by Fukuda and Miyamoto 1)2) in 1949 and later developmeuts.

The research on this subject started originally in connection with the question of gauge invariance in QED. On the basis of gaugeinvariance thephoton self-energyshould vanish identically3), but its calculation is very ambiguous and requires a careful treatment. Naive calculations lead to non-vanishing results. The decay of a neutral boson into two photons bears a similarity to the vacuum polarization in that both processes proceed through fermion closed loops with two out going photon lines. Thus Tomonaga suspected that something similar might happen in this process,too, andasked Fukuda and Miyamoto, then his collaborators in developing QED, to investigate this problem carefully4). Similar works were also carried out by Professor ~teinber~er5) and by Professor schwinger6).

In the decay of a neutral scalar meson into two photons (S + 2y) they haveagain found that gauge-variant terms are present. They had to use the Pauli-Villars regulator7) to eliminate them. They have also studied the relation between P -t 2y and A -t 2y and found a deviatipn from a result obtained by naively applying field equations and equal-time commutation relations. This kind of deviation is nnwknownasthe triangular anomaly, but at that time the difference between ambiguities and anomalies had not been recognized8).

After gaining some feeling about closed loops they proceeded to the study of the process T -t 3n 9) through which they tried to determine the spin and parity of the

T meson. This was essentially a problem of formulating selection rules. Since this research was a direct continuation of QED, however, selection rules were studied in perturbation theory. Whenever there is a closed loop the number of graphs is doubled by reversing the direction of the current in the loop. When their contributions are of the opposite signs, that process is forbidden at least in the lowest order perturbation theory. In this way they have found selection rules called after their namesl). Since I shall refer to them later in the modern terminology I shall not explicitely describe them here, but they were expressed in terms of the number of vertices involving vector and tensor couplings and that of the 'r3 coupling in isospin

$pace.

Within the framework of perturbation theory I have noticedin 1951 that theseselection rules are related to charge conjugationlo) 1 )and a rotation of T about the second axis in the isospin spacel 2). Unfortunately the research on this subject in Japanhad been limited to perturbation theory and formulation of invariance principles without reference to perturbation theory was not developed.

Meanwhile, in 1952, Pais and ~ost13)14) have formulated these selection rules without reference to perturbation theory. One of the selection rules by Fukuda and Miyamoto was derived on the basis of the charge conjugation (C) invariance of the theory. At the same time they have introduced an operation T which exchanges between proton and neutron on the basis of the approximative charge symmetry. They have defined T as a rotation of n about the first axis in the isospin space. This definition of T was sufficient to derive other selection rules by Fukuda and Miyamoto. They are based on

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982831

C8-454 JOURNAL DE PHYSIQUE

the approximate symmetries of the theory under T and CT.

Quite independently of Pais and Jost, Kroll and Foldy15) have also introduced the T operation in nuclear physics and discussed selection rules resulting from the approximate invariance. They have also defined T as a rotation of T about the %

axis isospin space. As long as one employs the Pauli matrices for the isospin, the transformation CT defined by Pais and Jost does not commute with the isospin. The right choice was to define T as the rotation of T about the second axisintheisospin space.

In this sense I had the right choice of the axis but stayed in the framework of perturbation theory. Pais and Jost, and Kroll and Foldy succeeded to formulate in- variance principles without reference to perturbation theory but had a wr

of the axis. The right combination was found by Professor Michel in 1953

1gJl; goice

defining T as the rotation of n about the second axis. The product CT, called U by Professor Michel, then commutes with the three components of the isospin and can be employed as a genuine quantum number for a self-charge-conjugate isospin multiplet.

In 1956 Professors Yang and ~eel7) introduced the now familiar name of G conjugation and applied the G invariance to the nucleon-antinucleon annihilation.

REFERENCES

(1) H. Fukuda and Y. Miyamoto, Prog. Theor. Phys. A(1949) 389. This was a generalization of the work of Furry.

(2) W.H. Furry, Phys. Rev. z(1937) 125.

(3) J. Schwinger, report of the session on QED.

( 4 ) H. Fukuda and Y. Miyamoto, Prog. Theor. Phys. A(1949) 347, 394.

(5) J. Steinberger, Phys. Rev. 76(1949) 1180. -

( 6 ) J. Schwinger, Phys. Rev. g(1951) 664.

(7) W. Pauli and E. Villars, Rev. Mod. Phys. g(1949) 433.

( 8 ) H. Fukuda, Y. Miyamoto, T. Miyazima, S. Tomononaga, S. Oneda,

S. Ozaki and S. Sazaki, Prog. Theor. Phys. A(1949) 477.

H. Fukuda and Y. Miyamoto, Prog. Theor. Phys. 4(1949) 392. SeealsoH.Fukuda, S. Hayakawa and Y. Miyamoto, Prog. Theor. ~hys: z(1950) 283, 353.

K. Nishijima, Prog. Theor. Phys. g(1951) 614. For a similar observation, see also :

C. B. Van Wyk, Phys. Rev. E(1950) 487.

K. Nishijima, Prog. Theor. Phys. g(1951) 1027.

In this paper the T operationwas defined by - 1

T T~ T = - ? (- : transposition) i

A. Pais and R. Jost, Phys. Rev. x(1952) 871. For a similar approach, see also

L. Wolfenstein and D. G. Ravenhall, Phys. Rev. - 88(1952) 279.

N. Kroll and I. Foldy, Phys. Rev. s(1952) 1177.

L. Michel, Nuovo Cim. x(1953) 319.

C. N. Yang and T. D. Lee, Nuovo Cim. ?(I9561 749.

DISCUSSION

L. M1CHEL.- I t h i n k t h a t t h e Fukuda - Miyamoto r u l e s were w e l l known, may be n o t t o P r o f e s s e u r S t e i b e r g e r because he made a s i n a g a i n s t them i n 1951. P r o f e s s e u r Yangand me were tough t o him about t h i s . I had t h e n t h e o p p o r t u n i t y t o make a l o n g review a r t i c l e i n t h e f i r s t volume of P r o g r e s s i n Cosmic Rays P h y s i c s , and t h e n I e x p l a i n e d t h e s e r u l e s . I e x t e n d e d them t o c u r r e n t s ; I i n t r o d u c e d two k i n d s of c u r r e n t s ; and P a i s and J o s t quoted my review paper. There was a l o o p h o l e i n my paper a t t h a t time t h a t I wanted t o c o r r e c t . The argument I used was v e r y simple. I knew from C a r t a n ( n o t from Wigner y e t !) t h a t i f you have t h e r o t a t i o n groupand i f y o u a d d a n o p e r a t i o n t h e s q u a r e of which i s one i n o r d e r t o form a group which i s t w i c e l a r g e r , youalways f i n d t h e r o t a t i o n s and r e f l e c t i o n s . So, t h e p o i n t was t o f i n d when you add c h a r g e c o n j u g a t i o n t o i s o s p i n , what i s t h e o p e r a t o r o r r e f l e c t i o n and I c a l l e d i t U. I s a i d e x a c t l y i n t h e a b s t r a c t of t h i s paper [N. C i m . lO(1953) 1 9 4 4 what I had done. I intcoduced a new quantum number and I c a l l e d i t i s o t o p i c p a r i t y . I was v e r y c a r e f u l i n t h e i n t r o d u c t i o n t o g i v e t h e main r e s u l t : s i n c e t h e r e was t h i s n e w q u a n t u m n u m b e ~ ; i s o t o p i c p a r i t y , were n mesons p o l a r v e c t o r s o r a x i a l v e c t o r s ? I s a i d t h e y w e r e - p o l a r v e c t o r s , a l l of t h e same p a r i t y ( n e g a t i v e p a r i t y ) and I a p p l i e d i t t o N-N a n n i h i l a t i o n , t o some meson decays ( a t t h a t time t h e r e was t h e 5 meson) b u t Fukudaand Miamoto had done i t b e f o r e me. I must s a y t h a t I d i d n ' t know P r o f e s s o r N i s h i j i m a ' s work, b u t I knew of c o u r s e t h a t P a i s and J o s t had n o t used t h e r i g h t t r a n s f o r m a t i o n a s h e s a i d ; I must say t h a t s e v e r a l p e o p l e d i d t h e same t h i n g and extended i n a f t e r . Every y e a r a p a p e r appeared on t h e s u b j e c t Bethe and Hamilton, Amati and V i t a l e , and P r o f e s s o r s Lee and Sang extended it t o s t r a n g e p a r t i c l e . But P r o f e s s o r N i s h i j i m a asked a q u e s t i o n : why d i d n ' t you l i k e t h e word i s o t o p i c p a r i t y , what d i d G-parity mean ?

C.N. YANG.- The name G was a r b i t r a r i l y chosen because we had t o have a name. It had no r e l a t i o n s h i p w i t h t h e l e t t e r s C and T. Now I d i d n ' t want to go i n t o t h i s s u b j e c t , b u t s i n c e it came up

...

And i n t h e p r o c e s s , we were informed by v a r i o u s f r i e n d s t h a t t h e r e h a d b e e n d i s c u s s i o n of t h e s e s e l e c t i o n r u l e s i n t h e p a p e r s which were a l r e a d y p u b l i s h e d . So we looked i n p a r t i c u l a r i n P a i s and J o s t , and Michel. We were n o t aware of t h e Japanese p a p e r s . The name G was a l r e a d y i n o u r work, and we d i d n o t f i n d t h a t t h e s e l e c t i o n r u l e due t o G s t a t e d i n c l e a r terms was t h e r e i n any of t h e p r e v i o u s p a p e r s . So we went ahead and p u b l i s h e d i t t h e way t h a t we s t a t e d i t . The main p o i n t was t h a t we made a c l e a r c u t e x p e r i m e n t a l l y c o r r e l a t e d s t a t e m e n t w h i l e p r e v i o u s p a p e r s had t o o much group t h e o r y i n them.

L. M1CHEL.- I a g r e e t h a t i t was a n e g l i g e a b l e c o n t r i b u t i o n . The t r u e c o n t r i b u t i o n w a s n o t t o d i s c o v e r quantum numbers f o r known r u l e s , i s o s p i n and c h a r g e c o n j u g a t i o n , t h e t r u e c o n t r i b u t i o n was t o go o u t of t h e c l a s s i c a l frame of i s o t o p i c s p i n and f i n d new quantum numbers l i k e s t r a n g e n e s s , a s Gell-Mann and N i s h i j i m a d i d .