Parity violating non-leptonic decays of hyperons and of charmed baryons in SU (8)

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Pramftr~a, Vol. 8, No. t, 1977, pp. 56-67. ~) Printed in India.

Parity violating non-leptonic decays of hyperons and of charmed baryons in SU (8)

RAMESH C VERMA and M P K H A N N A

Department of Physics, Panjab University, Chandigarh 160014 MS received 21 June 1976; in revised form 13 August 1976

Abstract. The parity violatirg nol:-leptonic decays of hyperons and of charmed baryons are discussed in the framework of SU (8) symmetry. Several relations in addition to the ones obtained earlier by using SU (4) symmetry and 20"-dominance,

are obtained. The assumptien of 20"-dominance at the SU (4) level is no longer required for exrlaining the non-leptonic decays of 1/2 + baryons.

Keywords. Non-leptonic decays; SU (8) symmetry.

1. List of symbols:

Subscript A

B (.)

C

CP G

1 t , o n0(7~0)

,2,3,4 J a n d J + P (n) S

Subscript s

s u (n)

O p,n,~,p'

% and E=ap~

XUk and X(i,.) Superscript

Bar, * and + 56

antisymmetric

SU (3) baryon multiplet o f dimension n.

charm quantum number charge conjugation and parity weak coupling constant weak decay Hamiltonian

weak decay Hamiltonian ccrresponding to 720 representation

weak decay Hamiltonian corresponding to 1232 representation

G I M type weak hadronic currents SU (3) meson multiplet o f dimension n.

strangeness quantum number symmetric

n dimensional unitary symmetry group Cabibbo angle

four fundamental quarks (p type, n type, strange quark, charm quark, respectively)

Levi-Civita symbols

wave functions for spin 3/2 and 1/2 respectively conjugation.

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58 Ramesh C Verma and M P Khanna

enlargement of SU (3) to SU (6) is known to have given useful information about several properties of the uncharmed particles including their non-leptonic decays (Rosen and Pakvasa 1964; Babu 1965; Kawarabayashi 1965). Therefore, it is reasonable to expect that SU (8) symmetry considerations may give new insight into the properties of both charmed and uncharmed baryons. In this paper, We discuss the parity violating (pv)non-leptonic decays of the~e particles assum!ng SU (8) to be the symmetry group of strong interactions. For the weak Hamiltonian. we adopt the GIM scheme (Glashow et al 1970) (section 2).

We are able to obtain many new relations among the various decay amplitudes in addition to all the relations derived earlier by using SU (4) symmetry and 20"-dominance (Iwasaki I975; Gupta 1976). We also find that if we treat SU (4) as a subgroup of SU (8) we no longer have to assume 20*-dominance in order to explain the pv decays of charmed and uncharmed baryons (1/2+). This is because 84 representation of SU (4) subgroup of SU (8) does not contribute to these dacays.

For the S-wave decays of uncharmed baryons we obtain the following relations among the decay amplitudes:

AO_:Z'0+: S - = 1 : - - C 3 : 2 (1.1)

= 0. (1.2)

We also obtain the relations imposed by the /kl = ½ rule. Relation (1.1) is not new. It has been shown to be a consequence of SU (4) symmetry but with the assumption of 20"-dominance. Relation (1.2) cannot be obtained from SU(4) alone, however, it has been obtained by using SU (6) symmetry considerations. Relation (1.1) agrees with experiment within --, 40~. Relation (1.2) is a well known experimental result.

For /2- decays, we assume 20"-dominance at the SU (4) level. We find that the pv decays of the type 12- -+ S* + zr are forbidden, while 12--+ S + ~r and /2- ~ A + K- are allowed. In fact all pv decays of the type 3/2 + ~ 3/2 + + 0- are found to be forbidden. SU (4) symmetry together with 20"-dominance forbids the pv-decays 3/2 ÷ ~ 3/2 + + 0-. SU (4) symmetry used along with current algebra forbids t 2 - ~ ~+ + zr also (Khanna 1976). On the other hand in SU(6), the assumption of 35-dominance leads to the vanishing of t 2 - ~ A + K-. The uncharmed baryons (½+) decays and the ~2- decays are discussed in section (3.1).

In section (3.2) we discuss the pv-non-leptonic decays of the charmed baryons.

These are three channels of charm changing ( ~ C = ~ I) non-leptonic decays of charmed particles (Altarelli et al 1975 a) corresponding to the different modes of change in strangeness, viz., /k S -- 0, + 1, - - 1. The predominant decay mode is the A C = / k S = - - 1 decay mode, the amplitude of this mode being larger than that of the /kC ---- 0 decay mode by a factc~r of cot 0 (0 is the Cabibbo angle).

Hence it is expected that the charmed particles will decay faster than the uncharmed ones. SU (8) symmetry forbids many o f the charm-changing decays.

We derive relations among these decay amplitudes at both the SU (4) and SU (8) level. These are recorded in section (3.2).

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.

Hyperons and charmed baryons in SU(8)

Tensors corresponding to representations o f symmetry groups;

57

B,~ec =- 120 representation of SU (8) /~A~c =__ 120" do.

Ms a ~- 63 do.

Tt~,e] ~c,o] :: 720 do.

T{*.s ~- (c,o): 1232 do.

A, B, C, D as indices run from l t o 8 .

D a ~ ~ 20 representation of SU (4) N~,. ~ =--- 20' do.

P~ ~- 15 do.

-- 15 ® 1 do. (

T t-~'gj t " / . # ] ::--2 20" do.

7~,y,~) ~ 84 do.

a, fl, 7, ~ run from 1 to 4.

3. Symbols for the decay modes of hyperons.

A ° = ) A ° ~ P + r r - A ° = ) AO -+ N + ~r °

~w_- = ) 3----> A + ~

~oo =) So__> A +,~o

2:o + =)Z'+ --> p + ,~o E+ + = ) Z + ~ N - b r r + Z'- = ) Z - --~ N + rr-

I. Introduction

Recently, there have been indications that strong interactions may be invariant under the group SU(4) that accommodates charmed particles in addition to t~e usual uncharmed ones. Non-leptonic decays of both charmed and uncharmed baryons have been discussed in literature using the SU (4) symmetry framework (Iwasaki 1975 ; Altarelli et al 1975 (a and b); Kingsley et al 1975). In these papel s, in addition to SU (4) symmetry, 20"-dominance of the weak interaction Hamil- tonian is assumed. This assumption is the SU (4) equivalent of the well-laxown octet-dominance phenomenon at the SU (3) level. Application of the spin-unitary symmetry independence hypothesis (Giirsey and Radicatti 1964) now, should

|e~d to the enlargement of the symmetry group SU (4) to SU (8). Similar

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Hyperons and charmed baryons in SU(8) 59 2. The I-Iamiltonian

In describing weak non-leptonic decays we make the following assumptions:

(a) the symmetry group of the strong interactions is SU (8), (b) weak interaction Hamiltonian H~ conserves CP, (e) H,~ has the current x currcnt form and is symmetric, i.e., H,~ can be written as:

ar = a/(2v'2)(]J+ + ]+ ])

(2.1)

where J and J+ are the GIM type weak hadronic currents, which transform as the adjoint representation of the symmetry group of the hadrons.

In SU (4), the currents can be written as:

J = ~n cos 0 +pA sin 0 - - p ' n sin 0 + p'h cos 0 (2.2 a) J+ = hpcos 0 + gp sin0 - - ~ p ' sin0 + ]p' cos 0 (2.2 b) (The Dirac matrices in the definitions of J a n d J+ have beert omitted). And the effective hamiltonian for various non-leptonie decay modes may be written as:

H ~ cz*'zxs=-I = sin0 cos 0 (pbip--p'Ahp' + b.c.) (2.3 a)

HZXC,,zxn,.-1 = cos ~ 0 (pnXp' + h.c.) (2.3 b)

HZXC=-zxs=-I = _ sin 2 0 (pAhp' + h.c.) (2.3 c) H~c=-~. As=0 = sin 0 cos 0 (pa~ p' --pn~p' + h.c.). (2.3 d) If the symmetry group of strong interactions is SU (8), the GIM hadronic currents should transform like 63 representation of SU (8) (assumption c). Then, the weak Hamiltonian transforms as:

63 ~ 63 = 1 G 63__. + _63~ G 720 @ 945 Q 945* • 1232. (2.4) Because of the symmetric nature of H, 0, only symmetric representations in the direct product (2.4) contribute; i.e.,

H, ,~ 1 • 63, Q 72__0 • 1232. (2.5)

It is a highly specific property of the weak interactions in the GIM model that the bilinear in currents do not contain any adjoint representation, so 63, must be absent. The singlet cannot contribute to strangeness changing and/or charm changing decays. So the H, transforms as:

720 ® 1232.

Equivalently, in case of SU (4), H~ transforms as:

(2.6)

H. 20" ® 84. (2.7)

The obvious generalization of 2_0"-dominance at SU (4) level to SU (8), is 720- dominance. That implies n~glecting 1232 part of the weak interaction Hamil-

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60 Ramesh C Verme and h4

P

K h c y y ~ a

tonian. However, if 1232 part of

- I-&

is neglected, CP-invariarso@: a l l pv- non-leptonic decays of charmed and uncharmed baryons zero. Therefore we adopt

the

viewpoint that in SU (8) framework both 726 and 1232

-

representations contribute to the weak; interaction Hamiltonian and a t h e SU (4) level 20'domi-

-

nance may be assumed if needed.

In

classifying the particles in SU (8) multiplets, we put 1 1 2 and 3/2+ baryons

in

the (20f, 2) and (20, - 4) components of the totallr symmetric representation

-

120 of

% (8)

(Kobayashi et a1 1972), generated in the direct product:

-

g@8@8=56@120$158@168. - - -

- - -

(2.8)

Pseudoscalar mesons are placed in (15, - 1)

-

componant of the adjoint representation 63

- of

SU (8). generated in

- the d i m

product:

ParWe umteat~ of the different SU(4) rndtiplets are the felloaving:

0 0 0

20:

- ^10, ^{( A -}

^2.-

^$-

^Q-)

when the subscripts W t e the charm of the

SU

(3) multiglets,

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Hyperons and charmed baryons & SU(8) 61 3. Parity violating non-leptonic decays

Consider the direct product B @ B (~ M, i.e.,

!_2_0" ~ 12__0 @ 63 -= ! ~ 4 (63) Q 720 • 2 (945)

Q 2(945*) Q 4(1232) Q 3 (.13104) G 2(17920 )

~) 2 (17__920") O 24255 G 94500

(~ 174636 Q 174636* G 318500. (3. t) In general we must take (20", 1) ccmpot, ent of every representation appearing in this airect product. But as discussed in section 2, in the GIM model, weak Hamiltonian transforms like 720 and 1232 representations only.

The various pieces of the nonleptonic weak Hamiltonian transforming as 720 and 1232 can be written as:

H(7~.o~ BA~C'BAB ₀ ₌ c M~' ~tc,o] 3 t [ C ' , D ' ]

H(x 1'a21 BABC' B , s c Mg' ,r(c,=) l (C,,D,I T.tG,D)

H (~2"~'~)~ ⁼ Bac'°'BABz Mr~ • ~ c , , ~ , )

H t~:;~) ₃ : B "~c' Baco Mff" T, (c.o) _(C',D')

HC~'-,:~.~) /~A'C'D' BacD _-, ₌ M~. r (c,o) ' (o'.~,) (3" 2) where ,4, B, C are SU (8) indices running from 1 to 8.

BAs c and M~ are tensors corresponding to the 120 and 63 representations of SU (8) respectively.

The SU (4) × SU (2)substructure of BAsc and MB a is given by [The Greek letters a,/~, ~,, etc. indicate SU (4) indicate; and the Roman letters i, j, k, etc. indicate SU (2) indiccs]

1 N~,O~ N~aj

-+ ek~Xi %,pa N~ p~] ] (3.3 a)

and

a • . i 1 , ~

where the following definitions have been used:

(1) x, ll = ~,z~, x11~ = 0 / ¢ 3 ) ~1/a, x l n = ( l / s / 3 ) 4,-1/~, x2~ = ¢'-,n where ~m are the normed wave-functions for S--- 3/2, S, = a.

(2) xl's are no~med spin-l/2 wave fimetions.

(3.3 b)

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62 Ramesh C Verma and M P Khanna

(3) DaB~, N t~'¢J , P~ and V~ are tensors (Kobayashi et al 1972) representing 20, 20', 15, 15 • 1_ representations of SU (4) group respectively.

(4) % and %¢pn are the Levi-Civita symbols for SU (2) and SU (4) respectively.

3.1. Decays o f the hyperons

From CP invariance, only CP = - - 1 combination (/4"o. (m2~ - - H3 (v'3*)) can contri- bute to the parity violating decays. No contributions arise from H0 (720), H~ (12s~)

H4¢1232) , the CP = + 1 pieces. On taking (H ts.t'°'11,3 -- ,rst2"*J~ts, 411 projection of the Hamiltonian, a straightforward calculation yields the following relations among decay amplitudes.

V ' 3 1 2 S - = x"3 ~o__ .~ o \ / 6 - ,'1_ - . . . o \ / - ~ A o = o - - x '~- 2 + = X - _

and

(3.4 a)

23+ + = O. (3.4 b)

Clearly these decays satisfy A I = ½ rule and the relation (1. I) and (1.2).

So far we have not assumed 20"-dominance. On making that assumption, we also get

a - + Z* + ,0 = 0. (3.5)

In fact we see that allpr decays of the type 3/2 '~ -+ 3/2 + + 0-are forbidden. The SU (4) symmetry together with 20"-dominance also gives this result. It is not necessary to use SU (8) to get it.

3.2. Decays of charmed baryons

We take the weak Hamiltonian transforming like (20", 1) and (84, 1) components of both 720 and 1232 representations. For L C # 0 decays, it transforms like 6 Q 6* under SU(3) symmetry group (Altarelli etal 1975 a and b). In the considerations of mass spectrum of the charmed baryons it is found (Kobayashi

• + ~, 61 A~ + / ~ etal1972; Gupta 1976) that decays like Z,a--->Alrr,~IK; --->,~r, 91--> 8'1 K will be strong decays. While strong decays of other charmed baryons [B (3) and B (3*)] will depend upon the masses of charmed mesons. There are large number of probable weak decay modes of these charmed baryons [B (3) and B (3*)]. These are given in tables 1 and 2 respectively. We have calculated the decay amplitudes for pv decays, first, using SU(4) symmetry. Later, additional relation are obtained in SU (8) symmetry framework.

Using SU (4) symmetry and 2_0"-dominance we get the following relations:

0 ~ C 1 ~ C 2 ~--- C 7 ~ C 1 0 ~ - C l l ~ C20 ~ C~3 ~--- C29

= b~ = b l ~ ~ bla = bxs = bj~ = b i t = bx8 = bx9 = b~3 = b~s = ba9

= a 5 ~-~ a s = a 8 : a 9 ~ a l e =,aal : a 1 4 ~--- a 1 9 : a ~ l = a 2 2 (3.6)

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Hyperons and charmed baryon,v in SU (8)

Table 1

63

Oecayi,,~ AC - - A S - - ! AC:4, AS =O ~C= AS- -~

partlde

o) B(3)~B(~) ÷ P(9~

g"L~ 01 = ~0 "~" K 4" 01 = ~LOI Jl" K W' a2 = ~ + K ° ~2 = ? - ° + rr*

o 3 = z ~ + ~ r * % = - = 1 + = "

a 5 = E ; + e e 5 = E C + 17"

=ZT + n " ~6 : Z * , + R"

o 7 = Z : + ~ r - ~7 = Z ~ ' + K- -"~ % = Z? + x"

% . Z*, + ~(°

o ~ . Z ; ' + I~ °

tD B(3) ~ B ( 3 ¶ + P{9)

eM= ~,'~+-F 1/~

als= A'* -I-

~ . ~ : K , ' + X °

- ' " a~8= K,* + K "

= 2

c ) ' B ( 3 ) ~ B ( 6 ) + p(3 t )

~ a~9= E ° + F "

a ~ o = A + F * a2~= fl +C~

a22. p +CP

b 8 = ..E: + K"

b9 : EC+ K"

b10 - E°,'F ?r+

b15 : E,* + ~{ *

% = Z; + rr"

~L9 : Z?'+ rr

~20 : ~ e~l" T/*

b22 = E~*'I" T/

b24. K,* ~t" K i

~2s= -=~'+ K"

o26, ~;'+ K ° b27= &'~*Jr V"

o28. K: + b.~9. ^7+ ~"

b30= ~'~*'PI" K "t b31 = A;*'I ~ W e

b32= ~ 1 + F+

b33= ~e~. C)4.

b34= A "4- D 4' b35= £ ÷ + D"

t)36= EeJr F * W37- ^ + ¢"

b3B= N 4" D*

b39. p 4" D •

b40= £ ' + ^{F +} b4~ = ^P+ O"

c., = a ~ + I t * c 2 = = , + ~ "

c 3 = .'3.~, 4" K * c 4 = ?.,~ + f r * c 5 = E,~ + 1to c 6 = E * , + c7 =~-,* + n~

c 8 : Z; + K~

c 9 = Z , ' + K ~ c10 = =, 4" '#'+ _+

c., = Z T * + ~ °

q 4 = E'~ + Tr"

c15. ;:+ +

q 7 = +',* + ~ "

q 8 • ~ 7 + = *

c 1 9 . ~ o + O*

<20= ~ o 4" F + c 2 1 = Z ° 4" D + , : 2 2 = A + I:)*

c23= ~'+ 4" D"

c24. Z~' 4" D"

P - - 9

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6 4 R a m e s h C V e r m a a n d M Tnhle 2

P Khannq

B(3*) ~ B { 8 ) + P(9) Decoy,ng

particle AC= - A S = - I AC=-I~ AS=O A C = & S ~ -1

'ILl* 025= N"I"K ÷ b42= N " F ~ * c 2 5 . P + R °

(126 = p + K o b43 = p + f i e C26 . T.+T/.o

b44= P'J" 11 c27 - T~++r/

b45 = P-I" f]" c28 = ~-*'t'fl"

b4,6. ~tl- K o c29= A.Fg"

b47. A Jr K + C30= T-.°~-'ff"

b48 = ,~.0~ K * C31 . L~'-K ""

="1" 027" Nar~" b4g" P + K ° c32 "~÷q'tT°

0 2 5 . p .~,o b.50" ~'~..l.,/7 o C33.~.1T~

029 = P "~T~ b51 = ~+'Jr f~

a30= P-1"~1' b52= .T-.~r1'~"

(131 = ~.*"~- K o b53 - A-.I,-/'/÷

c32. A"~'K + b54= ~-~r# +

o ~ . zo+K ÷ %~. Z*+K*

- I 034. p + T r - %6= P + K - c34. Z*4- ~ -

0 3 5 . N ' ~ ' ~ ° b57 = N'IL~ 0 C35=/~-f-I~0

036= N "1" f~ DSE5 = $'~L T/- C36= T'°.H~, o 037. N -)1L 7"/' b59 = ~.~L ~o c37 = ~gf.~o e 3 5 . A "]'K ° b60= /~.Jr~/ c 3 8 . . ~ 1 ~

a40 - ~-"~K4" D62 : ~'~¢ ?'r° c4 O- ~-~t'~*

% 4 - Z% ^n'

% 5 - Z:f- ~r * b 6 6 . ~-I"K °

- - 27++ c o t 0 = c3 ---- V ' 2 c4 --- 2 c 5 = 2 / V ' ] c6 = - - V ' ] c8 = co = Clo

= - - V ~ c21 --- V ? ' c , = c2, = - - V ? ' c31 = - - V ? ) c~, ( 3 . 7 )

~ - ~ = b l = bo_ = 263 = ~ V ] b , = - - ~ / ~ b ~ = b , = - - v ' ~ b ~ = v ' ~ b ~ - - bxo " = - - b . = ~ b14 = b3e = ~ X/T//2 b34 = ~ ~ / 2 b 3 ~ --- ~/()b37 = b38 = b , o = b41 = 2 b a t = - - V 6 b ~ 6 = VE}b58 ( 3 . 8 ) Z ' + t a n 0 = - - V ~ a l = V ~ a , . = - - a 3 = - - a 4 = ~ a 7 = ~ V 3 / 2 a 2 o

= a2z = a e , = ~ / f ) a27 = V ' i 2 a _ ~ = ~ / ( ) a ~ , = ~ V ' ] ~ a z ~ ( 3 . 9 ) A ° c o t 0 = ~ 1 / 2 eL. = ~ 1 / 2 c1.~ = - - c,:,~ = 1 / V ' ~ co6 = - - 1/X/~-c3o

= V 2 7 3 c~o = - v ' ~ c ~ = ~ C~o ( 3 . 1 0 )

A ° - = 1 / V ' 2 b . = - - 1 / 2 b 3 o = 1 / 2 b3~ = b 4 2 = -v/~ b4~ = - - b 5 5

= 1 / 2 b~7 = b65 = - - 1 / 2 b6~ = b6~ ( 3 . 1 I)

A - ° t a n 0 = - - 1 / 2 a17 = - - 1 / 2 a 1 8 = a31 = ~ / 2 ~ a3~ = %/~a33

= ~ / ~ 3 a ~ = - V : a~, = a , o ( 3 . 1 2 )

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Hyperons and charmed baryons in SU(8) 65 (Z A °_ -k I ~ / V 6 ) c o t 0 --- cla = - - e17 --- - - V'6 car

( 2 V ~ A _ ° + Z + / 2 V ~ ) cotO = c14 = - - ~ c1~

(2A~/v/6 --I~_/3) c o t 0 = - - c27 = V/2f/3 caz = - - V/:2/-3 e,a A o ^-

(2 - / V ' 3 q- 4 1 + / 3 V / 2 ) c o t 0 = C'~s == c39

(~V/~ A°-- -- Z++/Z~cz3) c o t 0 = ca,

(4A°__/V'] q- 4Z+/3 ~ / ] c o t 0 --- ct6 ( 3 . 1 3 )

( 2 n o + S + / V ( ) ) = V'f) b2z = - - b , 6 = - - V ] b,s = ba.

2A°/Vf) - I~+/3 = (1/2) V 2 b~a = bzs = (1/2) V'~ b.,.9 --- - - 2 / V ' ] b , ,

-- 2/~/3 bs~

( - + X + / V ' 6 ) = - - V ( ) bs~ V ~ 3 b53 - - 2 / V ' ] bs. - - 2 b,o

= 2b~z ---- 2 / ~ / ] b6a

( 2A°-/ V'f) - - 2 Z + /3) = 2b44 = 1/ V'2 b,~ ---- - - l l v ' ] ba~. = - - 1/v/] b a = b, ( 2 ~ °- - z++/V~,~ = b,o = V 2 b~.~ = b ~

(4A °- - - X+/x/6) -= - - b~ = - - b~ ( 3 . 1 4 )

(A°__ + X++/a/?~) t a n 0 = a25 = a2, ( 2 A ° - - - l~_/v'?O t a n 0 = a12 = - - a,8

(2A°__tv/3 - - 41+13~/2) t a n 0 = - - an0 = - - aa,

(4A°_/~/] - - 4 X + / 3 x / 2 ) t a n 0 = a~,

(4A°__/v/f) -4- 27+/6) t a n 0 - - - - a2~ ---- - - a3,

(SA°-/~f) --27+/3) tat, 0 = axs. ( 3 . 1 5 )

S U (8) s y m m e t r y c o r t s i d e r a t i o n s ( w i t h o u t 2 0 " - d o m i n a n c e ) give f o l l o w i n g r e l a t i o n s i n a d d i t i o n t o a b o v e r e s u l t s "

( I ) T h c d e c a y a m p l i t u d e s i n ( 3 . 7 ) , ( 3 . 8 ) a n d ( 3 . 9 ) v a n i s h . (2) A _ ° c o t 0 = ( I / 2 ) V 2 c~, = V ~ / 4 e ~ = - - 1 / 2 e , , = - - ~ Y / / 2 c~.,

= V'3//2 % = 1 / V ' ~ ca,

(3) A °_ = V 3 / - 2 b2z --- 1/2 b~5 = - - 1/4 b~ = V'3/2 b~s = V?) b,, = - - V 6 ba

(4) A.* t a n O = - - I / 2 aaa = V ' 3 / 3 2 aza = V ~ / 4 aa~ ---- az~ = ~ V ' ~ / 8 a u

= -

V~/2aao. (3. ~6)

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66 R a m e s h C Verma and M P Khanna

It is interesting to note that SU (8) symmetry forbids all charm changing non- leptonic decays of the following types:

B (3) --~ B (6) -t- P (9) - + ~ (s) + p (3.).

That so many decay amplitudes vanish is a specific result of SU (8) symmetry.

It may be pointed out that all charm changing decays are now expressed in terms of only two parameters: the F_ ° decay anaplitllde and the Cabibbo angle 0.

4. Conclusion

Comidering SU (8) to be the symmetry group of strong interactions, we are able to reproduce all the relations among pv non-leptonic decay amplitudes that l~ave been derived earlier by using SU (4) symmetry together with the assumption of 20"-dominance. We do not have to make this latter assumption for the non- leptonic decays of baryons (1/2+). Irt addition we get the experimentally well satisfied result X + ---- 0 ; and new relations among the charm changing non-leptonic decay amplitudes. Even though in our calculations we have throughout assumed the GIM scheme, we wish to point out that tile result X + = 0 and the vanishing of decay amplitudes in relations (3.7), (3.8) and (3.9) are the explicit consequences of SU(8) symmetry alone. We also note that SU (8) symmetry considerations, naturally account for the contributions coming from 84 representation of the sub.

group SU (4), as far as pv decays of 1/2 + baryons (charmed and uncharmed) are concerned. But if 20"-dominance is also assumed, SU (8) symmetry further forbids the decays of the type ~Q--+S*q-zr. in fact we regain the result olvtained from SU (4) symmetry and assumption of 20"-dominance, viz., all decays of the type 3/2 +-+ 3/2+ q- 0- are forbidden.

Because SU (8) symmetry is valid only in the static limit, we have not consi- dered the parity conserving decays of baryons. For describing these decays SU (8~ symmetry has to be used. Tile discussions of the parity conserving decays will be taken up elsewhere.

Acknowledgements

We are thankful to J K Bajaj for interesting discussions and for reading the manu- script. RCV gratefully acknowledges the financial support given by CSIR, New

Delhi.

References

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Olashow S L, IUoupoulos I and Maiani L 1970 Phys. Rev. D 2 1285

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Parity violating non-leptonic decays of hyperons and of charmed baryons in SU (8)