Baryonium annihilation into meson+vector meson

I

8.B

I I

Nuclear Physics 42 (1963) 638---641; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

BARYONIUM ANNIHILATION INTO MESON + VECTOR MESON H. GOLDBERG and Y. NE'EMAN Israel Atomic Energy Commission Laboratories, Rehovot, Israel Received 9 November 1962 Abstract: Assuming that the decay of baryonium into meson+vector meson proceeds through an intermediate virtual vector meson, some selection rules and branching ratios of this decay are derived from the octet version of unitary symmetry.

I. Introduction M o r r i s o n 1) recently r e p o r t e d 369 events in which the p r o d u c t s o f p p a n n i h i l a t i o n were 2 mesons, either n + n - , K ÷ K - or K ° K 6. T h e b r a n c h i n g ratios o f these annihilations were interpreted 2) by the use o f the octet version o f unitary s y m m e t r y 3.4), a s s u m i n g t h a t the m a i n c o n t r i b u t i o n to the process includes a final interaction m e d i a t e d by a vector meson o r a system with similar t r a n s f o r m a t i o n properties u n d e r SU(3), i.e. an octet representation o f S U ( 3 ) 3 . 4 ) (i.e. a s u p e r p o s i t i o n o f pO. a n d ~o°-like states) t.

/'

tTI

vm

\ Fig. 1. However, this intermediate state m a y well decay into a p s e u d o s c a l a r and a vector meson. In fact, events in which the p r o t o n i u m decayed into p + n were r e p o r t e d Recent information submitted during the last Rochester Conference necessitates some numerical corrections in this interpretation. 638

BARYONIUM ANNIHILATION

639

during the last Rochester Conference ( C E R N , 1962). T o get firm results, we do have to assume here that the main contribution to the process p + p --* m e s o n + v e c t o r meson

(1)

proceeds through a virtual vector meson. This is because such an assumption, in the frame of unitary symmetry, is sufficient to pick out a set of selection rules and branching ratios for these annihilations out of the large a m o u n t of freedom given by the model in general.

2. Branching Ratios and Selection Rules The baryons, antibaryons, mesons and vector mesons are all octets, transforming similarly under SU(3). Let them be denoted as

(I//i I//2 Ip3 I//,11p5 ,I//6 I//7 ~8) = (p, n, £ + , A , - r°, S - , _=o, . - - )

(G G G G G G ~ ; T G ) = (z-, ~z, z-, ;i, ~ , ~v ~, ~) (q~, q~2 q~3 q~, q~5 *6 q~7 q~s) = ( K + , K°, n+, ~/0, no, re-, ~0, K - ) /a (B~"" ~" BoIt n~la Bs) - (K *+", K *°", p+", ~,", .o., V-", ¢*% K*-") a-'2 ~~" 3 ~~" 4 x"5 - -

The interactions Lt(ff, ip, ~), L t Off, ~k, B ~) and Ll(~, B,, B ~) are trilinear forms t, invariant under SU(3). There are two possibilities to form an invariant trilinear out of three octets 3): the coefficients of one form are totally symmetric (coupling of type D), and the coefficients o f the other one are totally antisymmetric (coupling of type F). There are no a-priori reasons for a choice of an appropriate linear combination of the D- and F-couplings for Li(ff, ~,, q~) and L~(~, ~b, B ~) tt The ambiguity does not exist in the case of Lt(~, B,, B"), if this be responsible for the final decay of the baryonium. This is because this vertex part is quadratic in the B" field operators. I f we write (2)

L, = } i G A k ° " O k B u t a ~ ,

then A kz'' = A k''~. Hence only the D-part appears, and we have A kz'' = d ~a'', where the coefficients d ktm are totally symmetric and defined as follows tit.

d"S=-½, d1~=},/3, d ' ~ = ~ / ~ , d 257 =

--}43,

d~=~/~, d~'~=-½, d 346--~ l,

d 455 =

l,

d 444=

-1.

(3)

The coefficient d k~mvanishes when ( k l m ) is not a permutation of one of the triplets o f indices appearing in the above list. t Note that these do not have to be Lagrangians; they represent the vertex part contribution. The Ll(¢, Bu, Bu) may proceed through a baryon triangular loop. tt However, the large binding energy of A in hypernuclei implies an appreciable D contribution in Ll(tp, W, ¢) for low energies. ttt These coefficients differ from the d defined in ref. s), table II. However, they appear in table 1Ii multiplied by 4/~,/3.

(340

H. GOLDBERG AND Y. NE'EMAN

The baryon-antibaryon wave may be described as a combination of waves of definite SU(3) character. There is some ambiguity in such a description, arising from the fact that the representation [1 0 - 1 ] appears twice 5) in [2 1 0 ] ® ® [0 - 1 - 2 ] , and it is not clear which octet is chosen by the annihilation. The ambiguity is irrelevant as long as the baryonium does not correspond to the weight (0 0 0); because once an octet is chosen, the coefficients d k~mfix the form of the outgoing wave, and hence also fix the branching ratios o f the outgoing mesons. However, the ambiguity is indeed relevant when the baryonium wave corresponds to the weight (0 0 0). For the projection of [bb) on different octets will generally contain different mixtures of T = 0 wave and T = 1 wave (both corresponding to the weight (0 0 0)); and changes in this mixture affect the branching ratios. The above cited experimental results 1) for the reaction + p ~ 2 mesons

(4)

showed the pp-wave to be orthogonal to the T = 0 wave of the octet chosen by the intermediate vector meson 2). Yet it follows from the existence of pn events that an appreciable amount of the T = 0 component must be present in the wave responsible for the decay into meson + vector meson, as no prt may emerge out of the T = 1 wave. TABLE 1 B r a n c h i n g ratios p

a ( K * + K ° ) : e ( K * * K + ) : a(p+~/°): e ( t o n +) = 1.63 : 1.63 : 1 : 1.14

,4p

o(K*+r/°) : o ( t o K +) : o ( K * + ~ e) : tr(o°K +) : a(K*Ozr +) : o ( p + K °) = 1 : 1.1 : 3.44 : 3.36 : 6.87 : 6.71

~*p

The same as in the ,,lp annihilation

Z '+ p

a(KS+z~ -) : o ( p - K ÷) : tr(K*°r/o) : tr(o~K °) : o'(K*O~) : o'(pOK°) = 6.77 : 6.64 : 1 : 1.09 : 3.38 : 3.32

n

a(K*OK - ) : a ( K * - K o) : a((o~z-) : a ( p - ~ °) = 1.63 : 1.63 : 1.14 : 1

,/In

T h e s a m e as in the ~'~p a n n i h i l a t i o n

~.o n

T h e s a m e as in the -P~p a n n i h i l a t i o n

-P-~- n

T h e s a m e as in the A-p a n n i h i l a t i o n

p

fin

0"(~3~ "°) : o'(pOr/°) = 1.14 : i o~+,"t - ) : a ~ - n +) : a ( p ° n °) : o(~orl°) = 1.2 : 1.2 : 1.2 : I

T h e s a m e relations as in the ~ p a n n i h i l a t i o n

Using the Born approximation the above interpretation implies the branching ratios given in table 1 for the corresponding annihilations. The branching ratios for pp and nn may be predicted in spite of the fact that one does not know the form of the mixture of the T = 0 and T = 1 parts in the wave responsible for the annihilation into vector meson + meson. In addition we have

BARYONIUM ANNIHILATION

6,41

cr(pp -) K * + K - ) = o ( p p ~ K * - K +) = a ( n n --. K * ° K-6) = o(nn --. K * ° K ° ) , a ( p p ~ K * ° K-6) = c r o p -) K * ° K °) = a ( n n -~ K * + K - ) = a ( n n --. K * - K + ) . The annihilations cited in table 1 are the only ones in which the antibaryon with p or n m a y go through an octet channel, as none o f the baryoniums Z - p , SOp, ~ - p , Z + n, SOn and ~ - n m a y f o r m a virtual vector meson belonging to an octet. Therefore, on the assumptions made above, one should expect the cross sections for the annihilations o f these baryoniums into meson + vector-meson to be small c o m p a r e d with those listed in the table. We would like to thank S. Nussinow for a helpful discussion.

References 1) 2) 3) 4) 5)

D. R. O. Morrison, London Conference on High Energy Physics, 1962 (Imperial College) Y. Dothan, H. Goldberg, H. Harari and Y. Ne'eman, Phys. Lett. 1 (1962) 308 M. Geli-Mann, Report CTSL-20, California Institute of Technology Y. Ne'eman, Nuclear Physics 26 (1962) 222 H. Goldberg and Y. Ne'eman, Israel Atomic Energy Commission Report IA 725