PC violation and weak pion production

Volume 14, number 1

PHYSICS LETTERS

r e q u i r e s f u r t h e r study. It f o ll o w s f r o m the s t r u c t u r e of eq. (13), h o w e v e r , that if T 3 and Y a r e chosen to be o b s e r v a b l e s , and both t h e i r e i g e n v a l u e s a r e not z e r o , at m o s t two of the p ( R ) p S w i l l be c o m m u t i n g o b s e r v a b l e s . In c o n c l u s i o n , we m a y o b s e r v e that our r e s u l t s a r e not in c o n t r a d i c t i o n to t h e o r e m s r e c e n t l y p r o v e d by McGlinn and by M a y e r et al. [9]. T h e i r t h e o r e m s d e m o n s t r a t e the i m p o s s i b i l i t y of having g r o u p s the g e n e r a t o r s of which c o n s i s t only of t h o s e of the i n h o m o g e n e o u s L o r e n t z group and an i n t e r n a l s y m m e t r y group. Since the group p r o p o s e d by us h as a n u m b e r of g e n e r a t o r s in addition to both of t h e s e s e t s , the a b o v e - m e n tioned t h e o r e m s do not apply. A m o r e d e t a i l e d and e x t e n s i v e r e p o r t on t h i s w o r k w i l l be m a d e l a t e r .

h o s p i t a l i t y of the Institute f o r T h e o r e t i c a l P h y s i c s to him. References

1. F. Gffrsey and L.A.Radieati, Phys. Rev. Letters 13 (1964) 173. 2. A.Pais, Phys. Rev. Letters 13 (1964) 175. 3. F.Gffrsey, A.Pais and L.A. Radicati, Phys. Rev. Letters 13 (1964) 299. 4. M.A. Baqi B~g and V. Singh, Phys. Rev. Letters 13 (1964) 418. 5. M.A.Baqi B~g, B.W. Lee and A.Pais, Phys. Rev. Letters 13 (1964) 514. 6. For a short discussion of LH, see M.Hamermesh, Group Theory (Addison Wesley Co., Mass., 1962). 7. E.M.Corson, Introduction to tensors, spinors and relativistic wave equations (Blackie and Son Ltd., 1953), Ch.H. 8. H.Weyl, The theory of groups and quantum mechanics (Dover Publications, Inc.). 9. W.D.McGlinn, Phys. Rev. Letters 12 (1964) 467; M. E. Mayer, H.J.Sehnitzer and E. C. G. Sudarshan, Concerning space-time and symmetry groups (in press).

We would like to thank P r o f . W. T h i r r i n g f o r helpful d i s c u s s i o n s . One of us ( T . F . ) would a l s o like to thank P r o L T h i r r i n g f o r extending the

PC

VIOLATION

AND

1 January 196.5

WEAK

PION

PRODUCTION

E. GIUSTI Scuola di Perfezionarnento in Fisica, Florence University and

G. K A R P M A N Laboratoire de Physique Nuclbaire, Facult~ des Sciences, B . P . no 1, Orsay (Seine et Oise)

Received 7 December 1964

T h e c r o s s s e c t i o n of the pion p r o d u c t i o n r e a c t i o n : (fig. 1) Ul + N ~

l+N'

+~

h a s been computed by D o m b e y [1], D e n n e r y [2], B e r m a n and V e l t m a n [3] and o t h e r s s t a r t i n g f r o m the following hypothe se s: a) CVC t h e o r y is valid. b) the f i n a l state is d o m i n a t e d by the N~3 r e s o n a n c e . c) weak i n t e r a c t i o n s c o n s e r v e P C . A r e c e n t e x p e r i m e n t has r a i s e d s e r i o u s doubts as to the v a l i d i t y of the l a s t a s s u m p t i o n c) [4]. But, even if t h i s e x p e r i m e n t can be i n t e r p r e t e d without the v i o l a t i o n of P C , one can st i l l find r o o m f o r such a h y p o t h e s i s in high e n e r g y p h e n o m e n a [5]. In any of t h e s e c a s e s , one of the p o s s i b i l i t i e s opened to t h e o r i s t s i s to i n t r o d u c e new i n t e r a c t i o n t e r m s in the n u c l e o n i c c u r r e n t [5]. With t h i s point of v i ew , one can go back to s o m e of the p r e v i o u s c o m p u t a t i o n s , taking into account P C violation. We adopt the f o r m a l i s m of D o m b e y , which i s in f a c t a t r a n s p o s i t i o n of a method a l r e a d y used in the study of pion photoproduction [6,7]. To i n t r o d u c e P C v i o l a t i o n , we m e r e l y add two t e r m s to the r e g u l a r o n e s a l r e a d y u s ed : i k ~ ( k 2) and i ~ u k V ~ s E ( k 2 ) . As is w e l l known, by using the c o n s e r v a t i o n of the e l e c 60

Volume 14, number 1

PHYSICS L E T T E R S

1January1965 )J

N' Fig. 1 tric charge, w e find that ~o = 0. Therefore, the vectorial part of the interaction is not modified b y P C violation. R is useful, in the calculatiorl, to introduce the W meson, whose influence can be eliminated in any case if w e let M W ~ oo. One is thus led to a four particle problem (N N W ~). The scattering amplitude of the reaction: W + N ~ ~ + N' is written as a s u m of relativistic inva o riants: T = g f m ~ u i where: m ~ = A m A ~ + BmBp. +..., ~ f m A ~ ui... are the vectors and pseudo-vectors that can be constructed with the help of the 7 matrices and the m o m e n t u m of the particles. One then admits that A, B... are solutions of integral equations of the type: 1 I

±

1

+lf.oA~(v,, VB, X2)

1

±

A±c and A~:R are computed from the Born approximation and:

+kN,)kW ( =

'

UB -

2M '

u=

2MN

(the ± sign comes from crossing symmetry properties). To solve these integral equations, one uses experimental information (hypothese b)): more than 50% of the observed ~ - N have an invariant mass close to that of the N;3 [8]. For these events, it is admitted that the phase of the ~ - N state is precisely 633 , the phase of the resonance. It has been shown [9] that, in these conditions, one could write, for A for instance: A=

a

I - (X/Xr) -iF

Here a is the projection on the state (33) of the Born term A BA, Xr and r being the position and width of N~3. If w e project the B.A, term responsible of P C violation on the state / = -~, 3~ w e get: 2

- fE(2iTkP# + iykq#) UB+U 4eq/x. Let us n o w project on the J = ~ state; w e obtain:

FT2 =A~ {½(W+M~ r

-

(¢o/kq) (EI+M) (E2 +M)cY}

' : - A a (El + E2+ q0)

F4

E3cosO(~-

F~l =Aa =,4

(El +

qk(W+M) ~)

(E 1 + M)(E2 + M)

3 cos o (gl+E2+qo)

qk

(W+M)~'+w'~)

61

Volume 14, number 1

PHYSICS LETTERS

1 January1965

The notations a r e i d e n t i c a l to those used by Dombey [1]. The F} a r e the p r o j e c t i o n s of F i on the ~ , ½ state. To obtain a s i m p l e e x p r e s s i o n , we go to the static l i m i t and c o n s i d e r the case where the lepton is an electron. We come thus to a f o r m u l a which g e n e r a l i z e s the total c r o s s section e x p r e s s i o n obtained by Dombey: 4

da dfktT 2

gN M T2

1

128u5 T1 ( ~ 2 + M 2 ) 2

q [ 16q 2 k 2M~(2 2 t 1 sin2 ~ + ;~2) + 8q2M2_(4tl+3X2 4 t l k c o s ~ p ) + × 4~ W--

+ 64q2ktlM+M_(k- k 0 cos ~) + 32q2n2k2(2t~ - 2kot I + ½;~2) sin 2 5331 and n = - 4~e(h 2) (1/fq3). E(~2) i s the f o r m factor of the PC violating t e r m . More detailed r e s u l t s conc e r n i n g the ~ m e s o n will be published l a t e r . We wish to thank P r o f . E. A r n o u s , R. Gatto and R. Natal for t h e i r kind i n t e r e s t throughout this work.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

N.Dombey, Phys. Rev. 127 (1962) 653. Ph.Dennery, Phys.Rev. 127 (1962) 664. S.M. Berman and M.Veltman, Cern preprint. 9276/Th.455 (1964). J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Phys.Rev. Letters 13 (1964) 38. N.Cabibbo, Cern preprint. 9368/Th. 464 (1964). S.Fubini, Y:Nambu and V.Wataghin, Phys.Rev. 111 (1958) 329. R. Blankenbecler, S.Gartenhaus, R.Huff and Y.Nambu, Nuovo Cimento 17 (1960) 775. M.M. Block et al., Physics Letters 12 (1964) 281. R.Blankenbecler and S.Gartenhaus, Phys.Rev. 116 (1959) 1297. * * $ * *

POSSIBLE DETECTION OF INTERMEDIATE BOSONS THROUGH ANTIPROTON ANNIHILATION A . W E I S and P . K A B I R *

Institute for Theoretical Physics, University of Copenhagen, Denmark Received 20 November 1964

It i s a f a i r l y w i d e s p r e a d belief [ 1] that weak i n t e r a c t i o n s a r e t r a n s m i t t e d through an i n t e r m e d i a r y field whose quanta have come to be called " i n t e r m e d i a t e bosons". The p a u c i t y of events c h a r a c t e r i s t i c of such p a r t i c l e s in the CERN n e u t r i n o e x p e r i m e n t [2], and the consequent lower l i m i t s of 1.3 - 1.8 GeV for t h e i r m a s s , m a k e s it d e s i r a b l e to find a l t e r n a t i v e methods of s e a r c h i n g for i n t e r m e d i a t e b o s o n s of higher m a s s . In this note, we o b s e r v e that such i n t e r m e d i a t e b o s o n s W m a y just p o s s i b l y be detected through the resonant reactions ~+n~

W-~

l- + P~,

(1)

where l s t a n d s for a muon or an e l e c t r o n , if the leptonic channels comprise a major decay mode (i.e.

with a branching ratio of ten procent or more) of W -decay. The g e n e r a l f o r m of the m a t r i x e l e m e n t for a p r o c e s s of the type (1) can be w r i t t e n as

V2 * Present address: CERN, Geneva 62

A2qot)Un][8q~-q(~q~IVq2-M2+i-m]-l[~l~(l+~5)uu],(2)