Protonium two-mesons annihilation

V~Zz~,e I, nmnber 8

PH~.~ICS

in r e f s . 3) and 4). H o w e v e r , a f~w s i m p l e p r e d i c Imve been m a d e f o r the Sakata m o d e l , u s i n g s y m m e t r i e s 3). S i m i l a r p r e d i c t i o n s a r e p o s e t b l e f o r oue v e r s i o n of the octet m o d e l ; n a m e l y the one asmaning i n v a r t a n c e under the R - t r a n s f o r mation 2,4). T h e s e p r e d i c t i o n s a r e a s follows:

t5 July 1962

channel h a s the o c t e t (1,1) s w n m e t r y , one m i g h t think t h a t the dominant contribution g o e s through an i n t e r m e d i a t e s t a t e having t h e s e quantum n u m b e r s , such a s the ( K * , p , u) octet. T h i s p o s s i b i l i t y h a s been s u g g e s t e d by G o l d b e r g and N e ' e m a n 6), Although t h e s e annihilation p r o c e s s e s m a y e n a -

+ p " K + + K - ) = ~ ( ~ + n - - ~+ + ~ - ) = ~C~ + n - KO + g o )

$ a ~ d ~ model:

~

~

c~i~ + p -- ~+ + ~ ' ) = ~(P'+ p -- K° + E°) = ~(~K+ n -" f + + ~ ' ) = ~('lf + n - K+ + K ' )

model:

+ p "" ~ + 1t") = ~

LETTERS

Recent e x p e r i m e n t a l r e s u l t s on p r o t o n - p r o t o n :mnthiktflon at r e s t s e e m to be in d i s a g r e e m e n t with both predictions. The charged pion p a i r p r o dm:flon is e~weral t i m e s L~rger than both the c h a r g e d s a d the n e u t r a l kaon p a i r production. T h e s e d a t a a r e t h e r e f o r e inconsistent with both the Sakata mode~ a n d with the octet m o d e l a s s u m i n g R - i n v a rlm~w. R-invaxtance is aband~ned in the octet m o d e l , the above predtcUrms no longer bold and a g r e e m e n t with ex3~rlment ca~ be obtained. Tiffs a g r e e m e n t is not a signfficar~ t e s t of the m o d e l , since t h e r e a r e numy contrflmting channels whose a m p l i t u d e s ean always be ad~ueted to fit the data. H o w e v e r , it i s i n t e r e s t i n g t~ note that all channel ampLttudes e~eept one s f i d s a t i s f y the s~mple p r e d i c t i o n abnve * . . ' b obtain a g r e e m e n t wi~h e x p e r i m e n t it i s tiros n e c e s s a r y to a s s u m e that the dominant c o n ~ c o m e s f r o ~ the one channel whose a m p l l ~ e s not s a t i s f y t h e s e p r e d i c t i o n s . A s t t d s *~ result can be obtained from table 1 of ref. 4) for melkm-baryon reactions, since baryons, antiharyons md r,~8ons all transform according to the same (1, 1) representation of SU3.

PROTONIUM

ble conclusive t e s t s of the Sakata m o d e l and o~ the octet model including/s-inv~xiance, there s e e m s to be little hope of getting a c o n c l u s i v e t e s t of the g e n e r a l octet m e d e L In o r d e r to obtain m o r e i n dependent data t h a n the a v a i l a b l e n u m b e r ct a d j u s t a b l e p a r a m e t e r s I~ is n e c e s s a r y to inclur',e m e s o n p a i r p r o d u c t i o n in antihy~ ~ -on annihilation. Such e x p e r i m e n t s s e e m hardly f e a s i b l e at p r e s o n t .

Rsfel'er~ce8 1) S. Sakata, Progr. Theor. Phys. 16 (1956) 686. M. Ik~da, S. Ogawa and Y ~ , Progr. Theor. Phys. 22 (1059) 715; 23 (1960) 1073. S. Sawada and M. Yonezawa, Progr. Theor. Phys. 23 (1960) 662. 2) Y. Nete.~lan, Nuclear =~Jhysics 86 (1961) 222. .Salav-~ and J.C. Ward, Nuovo Cimento 20 (1961) 419. M. C-eli-Mann, Cal. Te ~.hn. Reports CTSL-20.

3) C, A. Levinson, H.J. L ~ n and S. Mea/~kov, Nuovo Clmento 23 (1962) 236. 4) C.A. L~vinson, H.J. Lipkin and S. Meshkov, Physics Letters 1 (1962) 44. 5) Preliminary results of CERN and Coll~ge de France groups, eommunicsted at the symposium held st Imperial College, London, March 1962, by D.R.O.Morrison. 6) Y.Dothsn, H.Goldberg, H.Harari and Y.Ne'eman, Physics Letters 1 (1962) 308.

TWO-MESONS

ANNIHILATION

Y. DOTHAN, H. GOLD~tERG, H. HARARI and Y. N E ' E M A N Israel Atomic Energy Commission Laboratories, Rehoveth Received 18 June 1962 M o r r i s e n h a s r e c e n t l y r e p o r t e d * 369 o b s e r v e d events in which the p r o d u c t s of ~ p annihilation w e r e 2 m e s o n s . Of t h e s e , 56 e v e n t s w e r e K + K ", 63 events w e r e K ° K ° and 250 events w e r e ~ + ~ ' ; ~.~o • Preliminary results of CERN and Coll~ge de France gromm, communtea~ed at the symposium held at Imperial College, London, March 1962 by D.R.O.Morrt~m. Ti~ns reBults w,.~e discussed from the point of vf the Sakats mode; by Levinson et al. 1). 308

~o #o wa~ o b s e r v e d . A s the e n e r g y a v a i l a b l e f o r the two m e s o n s is about 2 GeV, c o n s i d e r a t i o n s of p h a s e s p a c e alone cannot explain such ~ d i f f e r e n c e b e tween ~KK m d ~ , We wou~d like to show that u ~ l t a r y s y m m e t r y 2) in i t s ' b c t e ¢ ~ v e r s i o n 3,4) can explain the a b o v e r e s u l t s . The a n a l y s i s i s b a s e d on the a s s u m p t i o n that the m a i n contribution to the p r o c e s s includes a f i n a l i n t e r a c t i o n m e d i a t e d ~,y a "~ector-

Volume I, number 8

PHYSICS LETTERS

15 July 1962

for LI(~, V, ¢) and

L~(~,~, s~} ~.

This ambiguity does not exiBl ~ the case of L I ( ¢ , ~ # ¢ , B~) wb. :h is r e s p o n s i b l e f o r the final r e a ~ i o n in the decay of ~p. A s ~ p is odd under c h a r g e conjugation, so m u s t be the c u r r e n t which ~ppears in L i ( ¢ , ~ u ¢ , B#) and c r e a t e s the two m e sons. It follows float only the F - c o u p l i n g a p p e a r s a p a r t of D-coupling would imp ty a F a C i a l c u r r e n t which is even under c h a r g e eonlugatlon. Hence m e s o n *; and that this v e c t o r - m e s o n belongs to a b a s i s of an o c t e t - r e p r e s e n t a t i o n of SU(3) ,~,4) (i.e. it is a superpo~itinn of the s t a t e s ~o and ~}. The usual selection r u l e s situate the protonlum at r e s t in the 3S 1 state; a l s o , this s~ate is odd u n der c h a r g e conjugation. A c c o r d i n g l y we have ~" + p -~ 1~- + ~ + ~+p-K-+K

+

gO+KO

(r=l)

L~¢,8#¢, B/O and the ~.oeHielents defined a s f~tlows: f148=½

,

/2s8:j~,

states).

SU(3) selection r~l~s The b a r y o n s , a n t i b a r y o n s , m e s o n s and v e c t o r mesons" a r e ~ ! o c t e t s , t r a n s f o r m i n g ~imilarly under SU(3). Let them be denoted

fkh~ a r e

a n t i s y m m e t r t c and

f158=½j~,

F~7_~ i356

( r = 0.1)

(where the neutral kaons m u s t be mixed K~I, K~2

i

f167=~

,

;

F~7 ~_ ~ j ; ,

:~.

fklm vanishes

when (/Hm) is not a permutation of one of the t r i p l e s of indices appearing in the above 1~et +t. The ~ p wave may be described as a combination of waves of definite U(3) character: IPP) : . , / - r ~ ¢ ([20-2]; mixed T)

- ½ J~ ¢ ([2-1-1]; r = 1) = ( p , n , T , + , A , ~ O , ~ ' , ~ o , ~ -) ,

= (~-,~°,~-,X,~o,~+,~,~),

(¢I ¢2 ¢3

¢~.

¢5 ¢6

~7

@8)

= (K+ K o ~+ ~ 0 ~ ~-' Ko K - ) ,

= (K' +~', K*°", p~", ~ , pO~, ~,-~,, g,ot~, X*'~'), The interact ~ n s L I ( ~ , ~ , @), L I ( ~ , @, E~, m~d LI(@, ~#¢, B ~) axe t r i l i n e a r f o r m s , i n v a r i a a t under SU(3). Ther~ ~re two possibilities to f o r m an inv a r i a n t trfl~near out of t h r e e o ~ e t s 3): the c o e f f i cients of one ~,orm a r e totally s y m m e t r i c (coupling of type D), : ~d the coefficients of the o r d e r one a r e totally anti~ ' ~ m e t ~c (coupling of type F). T h e r e a r e no a p r : o c i r e a s o n s f o r a choice ~ an a p p r o p r i a t e linear combination of the D - and F - c o u p l i n g s

* It is not esm ,n~ial ,o assume that the vector mesons are element,~ry particles and not many mesons bound state..tIowe~ er, for the use of the Bor~ approximation we shall ~ s ~ w e th ~.vector-mesons to be elemantary particles. T~m meums no change in the dynamical consequences: ~ee NishiJtma 5).

' ~¢

([11-2] T

i)

+ ~,, -~-~/r~¢ (rlo lj, mixed T) + i J~ ~ ([000] ; r : 0). (The ¢ ' s a r e n o r m a l i m ~ wave ~ m c t i o n s ) Note that t h e r e a r e two p a ~ s ~ ~ p -- orthogonal to each o t h e r - which belong to d'~ierent b a s e s of [ 1 0 - J ] . We choose combinations which a r e c h a r a c t e r i z e d by T ( r a t h e r than by ~ and D) t i t . A s the r e a c t l s n goes through an octet channel, only ¢ ([10-1] ; t However, the strength of the ~EA i~eractton (as follows from the large binding energy of A in h_~ernuclei) implies an apprectabie D part in LI(Y, Y, ~) (see ref. 3)). If B~ emerge from the demand of local gauge invarlance, LI(~, ¥ , ~ ) and LI(i, ~ , B ¢) must be of the F-type (see ref. 6)). t t The fkl~ as defined hele are different from these defined ".n ref. 3) table H, because of different choice of bases for ~ and #. Howe~~r, they ~Dpear In table IV (multiplied by 4J3). t i t As there are two representations |10-1| in the decomposttieu of [10-1] x [10-1] one may choose the two octets which constitute bases for [10-1] In many ways. Here we choose one basis in such a way that tts vector corresponding to the weight (000) and having T= 0 is orthogonal to the ]~p wave, the seccmd octet is then uniquely determined by the orthogonallty condition.

309

. mzmber 8

VolL,~

PHYSICS

m l x e d T~ and • ([10-1] ; r = 1) contribute. I n ' o r d e r to get a fit with the e x p e r i m e n t , the annihilation is a s s u m e d to be due to the ~ ([10-1] ; T = I) part. Momentum space c o n s i d e r a t i o n s , using the Born approximation, will favor ~ p -- ~" ~r~ over ~ p .. ~o Ko or ~ p - K" K + by the ratio 1.56 " i. T-a~ng into account the coefficients of the F - c o u p llng In L I ( @ , ? ~ , B/2) one gets

2)

" C~K~K - " c~:)~o = 6.25 " 1 " 1 " 0 .

:,~.,-~-" ~ - - o

This is not f a r L-ore the e x p e r i m e n t 2 / r e s u l t s which a r e approximately 4.45 - I. 125 • I - 0 *.

Pisc,~ssio~

References 1) C.A. Levinson, H.J. Lipkin, S. Meshkov, A. Salam and R. Munir, Physics Letters 1 (1962) 125. 2) E.g.: M.Ikada, S.Ogawa and Y.Ohnttki, Progr. Theor. Phys. 22 (1958) 715; 23 (1960) 1073. T.hese papers deal with the Sakata model. 3) M.Geil-Msnn, The elghtf~Id way, Report CTSL-20, California Institute of Technology, Pasadena. 4) Y. Ne'eman, Nuclear Physics 26 ~1961) 222. 5) K. NishiJima, Phys. Rev. 111 (1958) 995. 6) R. Utiyama, Phys. Rev. 101 (1956) 1597.

+ meson

~ the antibaryon is either ~'--=.~,-'--U o r -------I; and the same holds f o r the reactions &ut~bzryon ~ neutron -" meson + m e s o n "

when the antibaryon i s e i t h e r ~-4: ~ o r ~L -~. That i s because these r e a c t i o n s cannot o c c u r through a v i r t u a l vector m e s o n ,belonging to an octet. The branching r a t i o s in table 1 are a s s o c i a t e d with the corresponding annihilations. Momentum space considerations in the Born approximation have been always taken into account, f i s the m o m e n t u m space f a c t o r , which i s a f u n c t i o n of the m a s s of ~oo. If we a s s u m e tb~t ~ = (550 M e V , J = 0"), t h e n f = 0.74. ( C r o s s s e c tions which do not a p p e a r in this table v a n i s h , e.g. c;(~ n -" ~oo ~oo) = 0.)

We should like to thank Y. Eisenberg. D. K e s s l e r , C . A . Levinson, H . J . Lipkin, S.Meshkov, S . N u s s i nov and G.A. Snow for h e l p ~ l discussions.

The a t , ~ e interpretation implies a few p r e "icti~s. I~ Compared ~rith the aforementioned c r o s s s e c tions, one should expect an a p p r e c i a b l e d e c r e a s e L: t~.e cross sections for ~.tii~rs"o.n ~ proton - m e s o n

15 July 1962

LETTERS

.\n ~ d i ~ i o ~ of a s ~ a ] ~ pa~-t of the ~ ( [ 1 0 - 1 ] : m i x e d T) ~ v e w'~.l! g~ve s o m e w h a t b e t l e r r e s u l t s .

Table 1

~n - 3.12

1

cr(~° ~-)

"o'(K

°

"

K ' ) = 3.12

•

1

K')v.,,,,

~p

0~(No ,..~} • ~(!< -~ - o ) • ~(K" , o o ) = 2 " I ' 3 /

AT,

:,~-~p i c(K o .~) . cr(K+ .-o) . e(K + ~oo) = 2 " 1 : 3 f I ~ ~i-----= ~

•

•

e ( K + ~ ' ) " o'(K ° 'tr° ) : o'(K"O 'rr° ° ) = 2 • 1 • 3 /

(;(K+ ~') : (r(K° ~o) • ~ ( K o ~oo) = 2 : 1 " 3 f

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i~ ~----~p ,! o'(K" r ' )

" c ( K ° ~ o ) . (~(Ko ,rroo) = 2 " I . a f i ~-=n

cr(K° = + ) " o'(K + ~r°) • o'(K + 'rr° ° ) = 2 : I : 3 f .

3tO

•

.

.

.

.

.

.

0