Volume 101 B, number 6 PHYSICS LETTERS 28 May 1981

PARITY VIOLATING RADIATIVE WEAK DECAYS AND THE QUARK MODEL

M.B. GAVELA Laboratoire de Physique des Particules, 74019 Annecy-le- Vicux, France

A. Le YAOUANC, L. OLIVER, O. PENE and J.C. RAYNAL

Laboratoire de Physique Th~orique et Hautes Energies l, Universit~ de Pari~-Sud, 91405 Orsay C~dex, France

and

T.N. PHAM Centre de Physique Th~orique de l'Ecole Polytechnique 2, 91128 Palaiseau, France

Received 18 December 1980

we propose a model for radiative weak decays of hyperons with baryon exchanges in the s- and u-channels as described by the quark model: the I/2 ÷ (56, 0 +) for parity con~rving, and the first excited 1/2- (70, [-) for parity violating ampli- tudes. Special attention is drawn on the problem of gauge invariance. We get a large Z+--* P3' asymmetry of the right sign. The parity violating amplitude although SU (3)-suppressed, is of the order 6rn/w (6m, SU (3)-breaking parameter; w, baryon level spacing), which is not small. In the quark model the parity conserving amplitude is also SU(3)-suppressed contrarily to the usual belief.

We have emphasized elsewhere [ 1 ] the role of the low-lying negative pari ty baryons (70, 1 - ) as interme- diate states in the calculation of parity-violating am- pli tudes (S-waves) in pionic hyperon non leptonic de- cays. Their con t r ibu t ion to S-waves, playing the same role as the ground state pole cont r ibut ion to P-waves

in the q u M ~ term, gives a large correction to the commuta to r and removes the discrepancy of a factor

2 with exper iment . This interpretat ion is very natural and one wonders about the cont r ibu t ion of these in- termediate slates to parity-violating weak radiative

transit ions such as Z + ~ PT, A ~ nT, etc. In particular, it is interesting to ask if one can unders tand the ob- served large Z + ~ P7 asymmetry * ' wi thout invoking exotic currents [3] , jus t from the usual Cabibbo cur- r e n t - c u r r e n t interact ion. We know from a theorem due to Hara [4] *2 that the parity-violating ampli tude

i Laboratoire associ~e au Centre National de la Recherche Scientifique.

2 Groupe de recherches associ~ au Centre National de la Recherche Scientffique.

, l Manz et al. [21 is the most recent result. ,2 See also Vasanti [ 3 ].

0 0 3 1 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / S 02.50 © North- l tol land Publishing Company

D ( Z + ~ PT) must vanish in the exact SU(3) limit. But since the intermediate states are the (70, 1 - ) ba- ryons, we can hope - and it is indeed the case - that this ampli tude will be of order6 m/6o [Sm is the SU(3) breaking parameter, w the baryon level spacing]. Since 8 m / w is not small (of the order ~ 1/2), we natural ly expect a rather large SU(3)-breaking effect for the

parity violating ampli tude, hence a large asymmetry for Z ÷ ~ P7 in spite of Hara's theorem ~ 3

In what lbllows we will consider a very simple model: lowest lying baryon intermediate states in the s- and u-channels; positive parity (56, 0 +) for pari ty conserving, and negative parity (70, 1 - ) for parity violating ampli tudes (fig. 1). Positive (negative) parity

*3 Calculations of parity violating amplitudes in the quark model have been carried out in different approaches re- cently by Riazuddin and Fayyazuddin [5 l-, and by Close and Rubinstein [6], on which we will comment later. Picek [7] has considered also the 1/2- intermediate states in the bag model in a method roughly similar to ours. A calcula- tion along the same lines is being carried out by Rauh (Heidelberg).

417

Volume 101B, number 6 PHYSICS LETTERS 28 May 1981

[ " it p' N e * / P

r" Z*. r,,* p

I'~" - P, N* * /P

z ' Z ~ n~ - p

. ' ,QP~, I ¢ r ",,d# p

~a)

$ u

(d)

(b)

• , f ~ , d i

, ( e )

(c)

Fig. 1. (a) s- and u-channel 1/2 + and 1/2- exchanges computed in the text. (b) Penguin contribution and (c) t-channel K* and Q exchanges not computed in the text. (d) W exchange within the baryon (----x--) and (e) penguin interaction within the baryon ( • ).

states can also in principle contribute to parity violat- ing (parity conserving) amplitudes, but these vanish in the exact SU(3) limit. We will neglect these contribu- tions and consider for the moment the exact SU(3) limit for the weak and electromagnetic vertices, but allow SU(3) breaking f o r the bound state masses ap- pearing in the energy denominators , jus t as we proceed for the pionic decays in ref. [1]. SU(3) breaking in the weak and electromagnetic vertices (due to distor- sion of the space and spin wave functions from the m s - m mass difference) could be potentially impor- tant for SU(3)-suppressed amplitudes as D(~ + -~ p'y) and will be considered in detail elsewhere. Moreover, to be consistent with our low-lying intermediate state approximation one should also consider meson t- channel exchanges (vector K* and axial-vector Q, respectively for parity conserving and parity violating amplitudes) (fig. 1). However, such contributions are much smaller than the baryon exchanges,just as addi- tive pion emission (one quark emission of a pion) is small relative to the two-quark interactions within the baryon and subsequent pion emission [1,8].

In what follows we will pay special attention to the basic problem of gauge invariance. In a process like 2 + ~ PT, the most general matrix element for a real photon is

Consider first the 1/2 + intermediate state. We need the two vertices, the weak

(PlHw(0) I ]~ +) = Up(a:c÷p + b:c+p75)u:c+ , (2)

and the electromagnetic (for a real photon)

~ ( p , ) [ F l ( O ) 7 u + F2(O)iouv( p, ,_ p)V] u(p) . eu ' (3)

llermiticity and CP invariance require air = aft, bif = -b f i , and similarly Cif = Cfi , Dif = --Dfi , for any i, f. Moreover, the photon being a U-scalar, one gets, in the exact SU(3) limit, for transitions between partners of U-spin doublets,D~+p = D= _ ~ _ = 0 (Hara theorem).

Considering both s- and u-channel 1/2 + contribu- tions we get

Cx+p = [a:c+p/(M,: - Mp)] [FP(0) - F~+(0)], - (4 )

D~c+p . . . . [bz+p/(M,: +Mp)] 1I~(0) + F~:+(0)].

The Hara theorem is satisfied in this approximation since bif = 0 in the limit of SU(3). In this approxima- tion only the parity conserving amplitudes survive. For a typical neutral transition we get:

C:co:co = [azoro/(M~: - M:c)l [F~° (0 ) - - / ;2o (0 ) ]

+ [a-oa/(M= - m A )]F½ '~ :co (0) , (5)

and similar expressions for the other decays which can be found in ref. [9].

Since if we only retain the lowest lying positive parity baryons only the parity conserving amplitudes survive, we need to consider the states of the next level (70, 1 - ) of spin-parity 1 /2- . Consider as an ex- ample a particular transition 1~ + -+ P"t and a particular intermediate state 1 /2- , octet of SU(3). We will have s-channel N *+ and u-channel g *+ exchanges. The weak vertex parametrizes in the form

fiy,+(ap~,+ + bpz,+3, 5)up , (6)

and the electromagnetic one - - t . i v , ~ S * + ' r ' +

u z ( p )Oouv(p - p ) 75)/;2 ( O ) u z . ( p ) . e u , (7)

the 75 is present due to the negative intrinsic parity of 2 *+ (similarly for N *+ --* PT). Note that the hermi- ticity of Jura requires/; 'f* 2:(0)= -F~Z*(0 ) . We get from s- and u-channel exchanges:

• t

~ ( p ' ) I l o u v ( p - p ) V ( C + D 7 5 ) l u ( p ) ' e ~ ' . (1)

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Volume 101 B, number 6 PHYSICS LETTERS 28 May 1981

D~ +p = F ~ + :~ *+(0) a z , + p / ( M p -- M z , )

- FPN*+(O)az+ N . + / ( i : : - M N . ) , (8)

CE+p = - F ~ +:~ *+(O)b~.+p/ (Mp + M ~ . )

- qN*+(0)bE+ N,+/(M s + MN, ) .

We see from these expressions that in the limit of exact su(3)

Mp - M ~ , = M~ - MN, = -co ,

a~:,+p = a:~:+N, + , F ~ +z*+ = F~2N* ,

so that D:~+p = 0, the Hara theorem is satisfied by the cancellation of both terms* a. Since Mp - M,..:, = -co - 5 m , M ~ : - M N , = - -60 + 5m, 6m = M ~ - Mp, we expect a parity violating amplitude of order

2 ~ +2:*+ D2:+ p ~ ( 2 8 m / c o ) a x , + p F 2 (0 ) . (9)

We will not consider the contribution of t / 2 - inter- mediate states to the parity conserving amplitudes, since b p x , + vanishes in the SU(3) l imit , just as bp~:÷.

In general, considering all 1 /2- intermediate states belonging to the (70, 1 - ) we will have two octets 28, 48, one decuplet 210, and one singlet 21, where 2S+1(a) denotes the SU(3) multiplet a and the total quark spin S which combined with L = l will g iveJ P

= 1 / 2 - . For example, the to ta lDz+p amplitude will be given by

F~+Y'*+ (O)a).: .+p/(Mp - M y . , ) D2;+ p = 28,48,210

pN *÷ - F 2 (O)a~+N*+/(Mrc, - M N , ) , (1o)

and for a neutral transition like A ~ nT,

F ) \Y*° ( O ) a y . o n / ( M n - M y , ) DAn = 210,28,48,21

F~ N*° ( O ) a A N , o / ( M A - M N . ) , (1 l ) 2848,2 t0

,4 This is not the case for models taking intO account only nearby states, the N*, neglecting the excited hyperon ex- changes [6,9]. Crucial cancellations between N*'s appearing in rr decays of hyperons, require also the consideration of u-channel resonances!

where y , 0 can be A* (I = 0) or Z * ° ( 1 = 1), and N *0 can h a v e / = 1/2 o r / = 3/2.

Now we need to compute the weak couplings air, a i f , and the radiative El couplings (70, 1 - ) -~ (56, 0 +) + 7- The weak couplings have been already considered in previous work [1,8]. The nonrelativistic limit gives the following parity conserving and parity violating in- teractions in momentum space

H pc'pv = ( G I r l 2 ) sin 0 C cos 0 C W

r(-)v(+) X ~ . i ] _ _

i . 1 [ l + ( p i - p / ) 2 / M 2 w ] OPC'pv ' (12)

where r ( - ) u = d, v(+)s = u, and the propagator factor will give a contact interaction in the limit (1 fm) -2

(Pi - p / ) 2 . ~ M 2 _+ oo. The operators Oi/ are given by *s

o ~ c = (1 -o ; . ° / ) , (13)

OPV = ( 2 m ) - I

x ~ - ( ° i - ° j ) " I(t't - v / ) + (v~ - p})]

+ i [ ( p i - p / ) - ( p ~ - p ~ ) ] "(oiXoi)} . (14)

It can be seen from the spin-space structure of the (56, 0 +) and (70, 1 - ) wave functions that these opera- tors automatically ensure the octet dominance [11]: only the antisymmetric flavor pieces in the indices i , j of the baryon wave functions survive, ensuring the A1 = 1/2 rule for hyperon pionic decays. This second quan- tization argument can be verified explicitly on these

non-relativistic operators, as we have shown in ref. [ 1 ]. Hence, decuplets having a symmetric flavor wave func- tion give a vanishing contribution. Weak matrix ele-

#s In connection with the expression for o~.Vr~ we comment on two recent papers. Riazuddin and Fayyazuddin [5 ] make simply a minimal substitution in this expression, Pi ~ Pi - eQiAi, obtaining an effective HwPV for 3' emission. They get D o: l /ko ' ko being the photon energy. This seems contrary to the small k o behaviour allowed for D from general prin- ciples [ 10]. In fact, making this minimal substitution in all terms in (14) we get zero, since (Pi - 17/) + (P~" - P)) "* (Qi - Q]) + (Qi - 1) - (Q] + 1) = 2 (Q i - {2]) - 2 = 0, and the second term gives the operator 2i(~i X¢]) (antisymme- tric in spin, symmetric in flavor) which has zero matrix elements in the ground state. Close and Rubinstein [6] seem to consider only the first term in (14). Note that both are necessary; the Al = 1/2 rule is ensured by the relative weight and sign of both terms, which are of the same order of magnitude [ 1 ].

419

V o l u m e 1 0 l B, n u m b e r 6 P H Y S I C S L E T T E R S 28 May 1981

ments between ground state baryons are proport ional to the matrix element.

(~kSlg(rl - r2)l~S) ,

irrespectively of the potential assumed between quarks. The results are the following:

a22 +p :a An : a~on :axoa :a-.o22o :ax-22-

= 1: I / x / - 6 : - - l l x / 2 : - x / 2 1 ~ - : o : o , (15)

with

422,p = - 3x/2G sin OCcosOc (~lSlS(rl - r2)l~kS). (16)

For the weak transitions 1 /2 - ~ 1/2 + we need a con- crete potential , and we will adopt the harmonic oscilla- tor. Details are given in refs. [ 1,8]. These matrix elements are given in table 1 in terms of the quanti ty

S . . . . 6G sin0 C cosOc(ddSlS(rl - r 2 ) l ~ s ) ( m R ) -1 , (17)

where now the mean value o f S ( r 1 - r2) is understood in the harmonic oscillator potential , and (mR) - l comes from the mean value of quark velocities (p /m) present in t t pv.

As for the radiative couplings we will follow the old Copley et al. model [12] in the harmonic oscillator potential as well. The electromagnetic interaction matrix element, given by the operator (q = Pi -- Pi')

; . . . . 2 , n . . . . . .

X exp( - - - i q ' r i ) , (18)

T a b l e 1

Weak m a t r i x e l e m e n t s ( ( 5 6 , 0*)I/-/~, v; (70 , 1 - ) ) in t e r m s o f the

q u a n t i t y S = - 6 ( 3 s i n 0 c cos 0c (~SlS( r I - r 2 ) l ~ s) (l/mR).

T r a n s i t i o n ( f iHI i>

Z*+(28) ~ p N*+(28) "-" Z + • S/2 x*÷(48) ~ p N*+(48) ~ Z* - S y * + ( 2 1 0 ) - , p A*+(210) ~ X+ 0 22*0(28) " n N * 0 ( 2 8 ) - ' X ° S/2,ur2 22*0(48) --> n N * o ( 4 8 ) ~ 220 S/x,I~ 2 2 " 0 ( 2 1 0 ) -~ n A*0(2 10) "', X 0 0

A * 0 ( 2 8 ) -" n N * 0 ( 2 8 ) --+ A -S/2xfO A * 0 ( 4 8 ) ~ n N * 0 ( 4 8 ) ~ A -S/x/6 A * 0 ( 2 1 ) ~ n A * o ( 2 I ) -.. ~o -S/x~6 ._-.o , - ( 2 8 ) _~ y o , - 2 2 . o , - ( 2 8 ) ~ - o , - 0

- * o , - ( 4 8 ) --+ .X ° , - X * o , - ( 4 8 ) -* Xo, - 0

- * 0 , - ( 2 10) -+ 22 0 , - 22"0 , - (2 1 0) -+ . x o , - 0

_=*0(28) ~ A A*O(28) --, xo S1,,/6 X * 0 ( 4 8 ) ~ A A*0(48) ~ -o 2S/x/6

between 1 / 2 - , 1/2 + states composite of quarks, has to be compared with the phenomenological coupling F2(0) defined above f o r an on-shell resonance N* or Y,* de- caying via an E1 transition into the ground state. The non-relativistic calculation by the quark model has to be identified with the non-relativistic limit o f (7) . Due to the 2" 5 in this expression, we get

F~.+~ ' * (0 ) 1 [×?(a" t )× i ]" ~"r' (19)

where ~ 7 is the pho ton energy which f o r an on-shell resonance is equal to co, the mean baryon level spacing.

The apparently parity-violating form of (19) for the electromagnetic interaction comes from the minus intrinsic parity of the initial baryon. Once ~ is factor- ized from the quark model results, we get the couplings F2(0 ). Note that now, in computing the second order perturbation expression we can use F2(0) which we can extrapolate safely using the relativistic coupling - i o u . q V e U 7 5 F 2 , (7). Now qU is the true four-momen- ttUn in the X + -~ P7 decay for example, and not any longer the photon four-momentum in the decay of an on-shell N* resonance N* -~ N% In this way we ensure gauge invariance in our second order process. We give in table 2 our results for F2(0 ). In these expressions we bare used the harmonic oscillator relation R 2 = (moa)- l ,6

, 6 T h e a r g u m e n t in t h e e x p o n e n t i a l - R 2 w 2 / 6 fo l l ows f r o m

the f ac t t h a t in the f o r m f a c t o r e x p (-R2k2/6) we have to

t a k e k = ~o- t ~ w the m e a n level spac ing s ince we COhlpuie

F 2 ( 0 ) fo r a t rue d e c a y i n g s ta te N* ~ NT.

T a b l e 2

Rad ia t i ve c o u p l i n g s (70 , 1 - ) -+ (56 , lY-) + 7 in t e r m s o f the q u a n t i t y X = mR exp ( - R 2 w 2 / 6 ) (e/2m).

Transition F2(0)

N*+(28) -~ p 2 2 ~ ( 2 8 ) ~ ~+ -(2+R2to2)X/3x/2 N*+(48) --, p X*'+(48) -+ 22+ 0 N * 0 ( 2 8 ) -~ n .~*o(28) --, - o (2+R2oa2/3)X/3x/-2 N*°(48) -+ n -*0(48) ~ .-o R2to2X/9xI~ • , ' * - ( 2 8 ) -+ ~ - __*-(28) ~ - - X/2-R2~2X/9 ~ * - ( 4 8 ) ~ Z - " - * - ( 4 8 ) ~ " - - -R2w2X/9x~2 X * o ( 2 8 ) --+ Z 0 -- (2 + R2w2/3)Xl6x/-f Z * 0 ( 4 8 ) ~ Z0 _R2~ZX/18x/~_ 22"0 (28 ) --* A A * ( 2 8 ) --* Z 0 -(2+R2w213)XI2x/-(~ ~ ' * 0 ( 4 8 ) ~ A A * ( 4 8 ) "-* Z 0 -R2w2X/6x/'O A*( 2 l ) --* 220 (2 +R2w2)X/2x/-f~ A * ( 2 8 ) ~ A (2 +R2w2/3)X/6x/2" A * ( 4 8 ) -* A R2co2X/18x/2 A*( 2 l ) - ' A (2 +R2~2)X/6~/2-

I

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Volume 101 B, number 6 PttYSICS LETTERS 28 May 1981

From the sum of all intermediate state contributions [28 ,48 , 210 (vanishing), 2 1 ] using tables 1 and 2 we

get:

Dr+p = x/-'2~(Sm/co)K, D:~o n = K ,

DAn = (K/x/-3-)(I - 25m/co) ,

D~o A = -(KIx¢/3) (1 - ~m/co),

D_.-o~:o = - K ( I + 6re~co), D.-_~:_ = 0 , (20)

with

K = (2 + R2co2)G sin 0C cos 0 c

X [(~si6 (r 1 - r2)l~s)/co] exp ( -R2co2 /6 ) " / ap t.

These expressions satisfy the relations

D~+p = O(6m), x/~DAn - D~o n = O(Sm) ,

x/~D~oA - D.-o :~o = O ( 6 m ) .

The first relation is just Hara's theorem. The second and third come from the fact that the interaction transforms like the x-component of U-spin and x/3A _ ~0 belongs to the U-spin triplet.

One has also %/3CAn - CEo n = 0 (and similarly for E0) at order ( 6 m ) - 1 due to cancellation of s and u ground state pole contributions [the only allowed at order (6m) -1 ] from equality of magnetic moments

in the U-spin triplet. In this calculation we have made the assumption

of neglecting spin-dependent qua rk -qua rk forces which split and mix the states belonging to (70, 1 - ) , the calculation would be too dififcult to handle other- wise.

Let us now compute the rates and the asymmetries:

1P = (e2/rr) [(M 2 - m2)/2M]3(ICI 2 + ID]2),

a = 2 Re (C*D)/(ICI 2 + IDI 2) ,

where M (m) denote the initial (final) mass. To compute C we adopt the values of the total mag-

netic moments [13] (in nuclear magnetons l /2Mn):

/ ap=2 .79 , pn = - 1 . 9 1 , /aA . . . . 0.61,

/at°t = 2.33 _+ 0 .13 , /a~_ = --1.48 -+ 0.37,

/a_.-o = --1.237 -+0.016, /a,--- = --0.75 -+0.06,

and we use the SU(6) relations/azOA =/ap/X/r~,/aZo = /ap/3.

Remember that we must subtract from these expres- sions the normal magnetic moment since only F2(0 ) enters in our relations. As for the magnitude of the weak matrix elements we adopt , from non-leptonic hyperon 7r decay, (P-waves):

(~SltS(rl - r 2 ) l ~ s) = 1.1 X 10 -2 GeV 3 .

The value of D is rather sensitive to the level spacing co. The 1/2- states are widely spread out, from A*(1405) to N*(1700) and we will adopt a value co -.~ 500 MeV, though we must keep in mind that spin-dependent

splittings have been neglected in the calculations. In all the expressions we adopt R 2 = (mco) -1 with m = 400 MeV. This gives table 3 compared to the relative scarce experimental situation. Since the Z + -* P7 asymmetry and the rate are very sensitive to the dif- ferences/az+ - / a p , we have taken into account the ex- perimental errors for/az+ in table 3. For the other tran- sitions we have taken the central values of the magne- tic moments. F o r D we adopt 6m = 200 MeV.

We get a large asymmetry for Z+ -* PT. There are two reasons for this: one is that 6re~co is not small,

Table 3 Predictions for asymmetries, rates and branching ratios (BR).

Transition Absolute rate BR Asymmetry: (107 s- l ) (10 -3 )

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

+0 30 ^_+0.26 +0 32 -0.80 ' )2+ ~ P7 1.15_0119 0.92_0.14 -0.19 ~o ~ nv 7.0 10 -1° -0.98 A ~ n7 0.24 0.62 -0.49 ---0 ~ A7 1.0 3.0 -0.78 -o --, ).:o.~ 2.5 7.2 -0.96

Experimental Experimental BR a

+0.31 (1.15 +0.13) X 10 -3 -0.70_0.27

0 . 5 + 0 . 5 %

<7%

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Volume 101B, number 6 PHYSICS LETTERS 28 May 1981

the parity violating amplitude is large. The other is z+ the small difference F 2 (0) - FP(0).

Note that we obtain the right sign for the asymme- try due to the fact that F~ ÷ - F ~ < 0, the empirical SU(3) breaking of the magnetic moments goes in the right direction * 7. We must emphasize, however, that

if the SU(3) breaking was the one suggested by the quark model:

/ap - / l :c+ = (1 -- m d / m s ) / 6 M p ,

we would get an effect o f s econd order in the SU(3)-

breaking of the w r o n g sign:

F~+(0) - /~2(0)

= (2Mp) -1 [ - ~ ( 1 - m d / m s ) + (1 - M p / M r ) ]

.~ (~Srn )Z /M3p .

In this case, both C and D will be suppressed in the SU(3) limit, the asymmetry would be large, of order (Sin) 0, but of the wrong sign. The fact that F~+(0)

- F~2(0) is practically small implies that it will be very sensitive to other model dependent perturbative correc- tions. On the other hand, the pv amplitudes can also

receive other SU(3)-suppressed contributions besides the one coming from the energy denominators in the perturbation expression. These effects can affect both the weak and the electromagnetic couplings.

A remark concerning the transition "#- ~ Y--7. We

get zero since ax - ~ - = a_- ,z . _ = 0 in the approxima-

• 7 it is important to note that the sign of the asymmetry is unambiguously predicted once one makes the consistent definitions (1), (2), (3), (6), (7) and uses the non-relativistic

- - t + s . + . t reduction of~(p')Tuu(p) = u(p )[(Pta P~a ) l°lav(P - p)Ulu(p) /2m in (18) (the minus sign in front is due to the metric). The normal magnetic moment at the quark level iotav( p' - p)v has the right ordering of momenta, con- sistent with the form of the electromagnetic vertex at the bound state level (1) and (3). The iotav( p' - p)V~, s coupling is also consistently defined in (1) and (7) removing a phase ambiguity in the definition of 3's- The relative phase of II~v c and H~ v matrix elements is fixed by the current current interaction. The (70, 1 -) wave functions are tab- ulated in ref. I l l .

• 8 Therefore, the excited positive parity baryons (Roper mul- tiplet) may give relatively large contributions.

tion of neglecting additive or penguin diagrams, since we do not have combination su in the - - - . Penguin

diagrams and additive 7-emission via K* or Q domi- nance can give a contribution. We can guess that the asymmetry for "-- ~ ~ - 7 will also be large, although the rate can be expected to be smaller than for ~÷ -~P3'.

In conclusion, we have shown the importance of considering the negative parity baryons observed and predicted by the quark model as intermediate states in the calculation of parity violating amplitudes in hyper- on weak radiative decays. We have shown that a large

asymmetry for ~+ ~ P7 has nothing of a mystery, be- cause the parity violating amplitude is of order 8re~to which is not small, and because of the strong cancella- tion between the proton and Z + anomalous magnetic moments * 8

R e f e r e n c e s

[ 11 A. Le Yaouanc, L. Oliver, O. P~ne and J.C. Raynal, Nucl. Phys. B149 (1979) 321.

[2] A. Manz et al., Phys. l.ett. 96B (1980) 217. [3] H. Fritzsch and P. Minkowski, Phys. Left. 61B (1976)

275; N. Vasanti, Phys. Rev. DI3 (1976) 1889.

[4] Y. Hara, Phys. Rev. Lett. 12 (1964) 378. [51 Riazuddin and Fayyazuddin, Trieste preprint (1979). [61 F. Close and H. Rubinstein, Rutherford preprint (1980)

Nucl. Phys., to be published. [7] I. Picek, Phys. Rev. D21 (1980) 3169. [8] A. Le Yaouanc, L. Oliver, O. P~ne and J.C. Raynal, Phys.

Lett. 72B (1977) 53; C. Schmid, Phys. Lett. 66B (1977) 353.

[9] G. Farrar, Phys. Rev. D4 (1971) 212, see also R.E. Marshak, Riazuddin and C.P. Ryan, Theory of weak interactions in particle physics (Wiley-Inter- science, New York, 1969).

[ 10] M.K. Gaillard, in: Weak interactions, School of Elemen- tary particle physics (Basko Polje, 1977).

[11] J. KSrner, Nucl. Phys. B25 (1970) 282; J. Patiand C. Woo, Phys. Rev. D3 (1971) 2920; K. Miura and T. Minamikawa, Prog. Theor. Phys. 38 (1967) 954.

[12] L. Copley,G. Karl and E. Obryk, Nucl. Phys. BI3 (1969) 303.

[ 13] See: L. Montanet, review talk Intern. Conf. on High energy physics (Madison, Wl, USA, 1980).

422