Parity test for Ω− using polarized hydrogen target

Volume 18, number 3-

PARITY

P H Y S I C S LE T T E RS

TEST

FOR

~-USING

POLARIZED

1 September 1965

HYDROGEN

TARGET

S. M. BILENKY and R. M. RYNDIN

Joint Institute for Nuclear Research, Laborato~'y of Theoretical Physics, Dubna, USSR Received 6 August 1965

An e x i s t e n c e of t h e ~ - h y p e r o n with s t r a n g e n e s s S = -3, i s o t o p i c spin I = 0, s p i n and p a r i t y J P = ~+ and with m a s s of about 1680 MeV was p r e d i c t e d on the b a s i s of t h e SU(3) s y m m e t r y of s t r o n g i n t e r a c t i o n s [1-3]. The v e r y d i s c o v e r y [4] of the n e g a t i v e l y c h a r g e d b a r y o n with s t r a n g e n e s s -3 and with m a s s c l o s e to the p r e d i c t e d one was a b r i l l i a n t c o n f i r m a t i o n of t h e SU(3) i n v a r i a n c e . T h i s i s , at the s a m e t i m e , "indirect e v i d e n c e f o r the a b o v e - m e n t i o n e d v a l u e s of the s p i n and p a r i t y of the ~ " hyperon. H o w e v e r , a d i r e c t e ~ e r i m e n t a l d e t e r m i n a t i o n of t h e s e quantum n u m b e r s i s , no doubt, of g r e a t i n t e r e s t . The spin of the ~ - p a r t i c l e c a n b e d e t e r m i n e d by studying any of i t s n o n - l e p t o n i c d e c a y s , which a r e weak d e c a y s of t h e t y p e d ~ ½ + 0 (d, ~,1 0 a r e the p a r t i c l e spins). F o r t h i s p u r p o s e , a s is shown in r e f s . 5, 6 ( s e e a l s o [7]), it i s n e c e s s a r y to m e a s u r e t h e a n g u l a r d i s t r i b u t i o n and p o l a r i z a tion of the p a r t i c l e with spin ½ in t h e d e c a y of t h e polarized ~- hyperons. From these measurem e n t s one i s a b l e to d e t e r m i n e a s well t h e p a r a m e t e r s a , ~ and ~ c h a r a c t e r i z i n g the a b o v e d e c a y mode. In t h i s l e t t e r we will d i s c u s s a p o s s i b l e m e t h o d f o r d e t e r m i n i n g the ~ - - h y p e r o n p a r i t y . Since t h e d e c a y s of ~ - p a r t i c l e s a r e due to w e a k i n t e r a c t i o n s , the ~ - p a r i t y can only b e d e t e r m i n e d by i n v e s t i g a t i n g t h e s t r o n g and e l e c t r o m a g n e t i c processes for their production. Strangeness cons e r v a t i o n in s t r o n g and e l e c t r o m a g n e t i c i n t e r a c t i o n s and the l a r g e value of the ~ - s t r a n g e n e s s l e a d to t h e f a c t that t h e p r o c e s s e s of ~ - p r o d u c tion will involve, a s a r u l e , t h r e e and m o r e p a r t i c l e s in the final s t a t e . A d e t e r m i n a t i o n of the p a r i t y in t h e s e r e a c t i o n s can b e m a d e only by a n a l y s i n g t h o s e c a s e s in which t h e m o m e n t a of a l l p a r t i c l e s l i e in the s a m e p l a n e . H o w e v e r , the e x i s t e n c e of the b o s o n r e s o n a n c e (K K), having s t r a n g e n e s s 2, i s o t o p i c s p i n 1, z e r o spin and p o s i t i v e p a r i t y (its d i s c o v e r y by F e r r o - L u z z i et al. was r e p o r t e d by P r o f . S. G o l d h a b e r at the E r e v a n S u m m e r School [8]), a l l o w s u s to c o n s i d e r , 346

f o r ~ - p a r i t y d e t e r m i n a t i o n , a r e a c t i o n involving two p a r t i c l e s in the final s t a t e K- + p - ~ Q- + 0 ÷ ( K + K O) .

(I)

In ref. 8, for the processes of such a type (0 + ½ -~ J + O) there were obtained inequalities imposing restrictions on possible values of the spin and internal parity, allowing us to determine, in principle, their values. In order to determine the ~--hyperon parity u n a m b i g u o u s l y we p r o p o s e to u s e the r e l a t i o n s connecting the a s y m m e t r y in r e a c t i o n (1) on a p o l a r i z e d p r o t o n t a r g e t with the p o l a r i z a t i o n c h a r a c t e r i s t i c s of t h e ~ - when t h e p r o t o n s a r e u n p o l a r i z e d . T h i s method i s s i m i l a r to that p r o p o s e d f o r d e t e r m i n i n g t h e p a r i t y of A, ~ and ~. h y p e r o n s in r e a c t i o n s with a p o l a r i z e d p r o t o n t a r g e t [10, 11]. A s was shown by A. B o h r [12], i n v a r i a n c e u n d e r r e f l e c t i o n in the r e a c t i o n p l a n e p e r m i t s u s to f o r m u l a t e the g e n e r a l s e l e c t i o n r u l e which r e l a t e s the i n t e r n a l p a r i t i e s of p a r t i c l e s to the v a l u e s of the spin p r o j e c t i o n s on t h e n o r m a l to t h e r e a c t i o n plane. But in o r d e r to obtain the a b o v e m e n t i o n e d r e l a t i o n s b e t w e e n the o b s e r v a b l e q u a n t i t i e s it i s m o r e convenient to u s e the i n v a r i a n c e condition u n d e r r e f l e c t i o n s in the r e a c tion p l a n e in the m a t r i x f o r m [13]. In the c a s e u n d e r c o n s i d e r a t i o n we get

R - 1 M ( p f , P i ) i o . , -- rM(pf, Pi) •

(2)

H e r e M{pf,pi ) i s t h e r e a c t i o n m a t r i x , pi(pf) is t h e i n i t i a l (final) m o m e n t u m in the c . m . s . , n = = Pi × P f / t P i ×Pf ] i s t h e n o r m a l to the r e a c t i o n p l a n e , R = exp (iTrs. n) and ia.n a r e the o p e r a t o r s of the spin r o t a t i o n of the ~ - p a r t i c l e and of the p r o t o n at an a n g l e ~ a r o u n d the n o r m a l , while ? = ?f/l i i s the r e l a t i v e p a r i t y (Ii, If a r e the i n t e r n a l p a r i t i e s of the i n i t i a l and final s t a t e s ) . T h e o p e r a t o r R can be e a s i l y expanded [13] in t e r m s of the t o t a l s y s t e m of spin t e n s o r s T lm :

Volume 18, number 3

2J R =l

~=0

PHYSICS LETTERS

l m=-l

m ,

4

~ff

1

where

al : (_1)J2/(2/+1) ~ F (2J-l)! 7½ (J--~l)! L(2J+/+I):(2J+I)J (4) f o r odd l and a l = 0 f o r even l ( J ] s h a l f - i n t e g e r ) . We c o n s i d e r p r o c e s s (1) in t h e c a s e when the p r o t o n t a r g e t i s p o l a r i s e d . The a s y m m e t r y is a s follows

~i~ - a_p e - ~P + (~_~ ( P ' n )

Sp( M q . n M +) Sp(MM+ )

,

(5)

w h e r e P i s t h e t a r g e t p o l a r i z a t i o n , while ap i s the d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e p r o c e s s on the t a r g e t with the p o l a r i z a t i o n P. Using (2), (3) and (5) we find _1

e = fP.n

~

lodd

( - i ) a l ~ 0 Y~rn(n)(~+l) e" (6) m

H e r e ^ Sp(TlmMM+)/Sp(MM +) i s t h e m e a n v a l u e of t h e ~ o p e r a t o r T l m , in r e a c t i o n (1) on the u n p o l a r i z e d t a r g e t . D i r e c t i n g t h e z - a x i s along n and s u p p o s i n g t h a t the t a r g e t p o l a r i z a t i o n i s orthogonal to t h e r e a c t i o n p l a n e (P = Pn), we g e t =

e = I P ~ (-i)a/
1 September 1965

s y m m e t r y a r e d e t e r m i n e d by t h e d y n a m i c s . E v i dently, f o r the p a r i t y d e t e r m i n a t i o n i t i s n e c e s s a r y to c h o o s e s u c h e n e r g i e s and a n g l e s f o r which t h e s e v a l u e s a r e not s m a l l . If in t h e a v a i l a b l e i n t e r v a l s of a n g l e s and e n e r g i e s the v a l u e s e n t e r i n g (6) t u r n out to be s m a l l , then f o r t h e p a r i t y d e t e r m i n a t i o n one can u s e o t h e r r e l a t i o n s following f r o m (2). We give h e r e one of t h e m lodd

(~p

+ff_p

-

= ?p .

(8)

H e r e p = (1/ap).Sp(TlOM½(l+a.P)M~is the m e a n v a l u e of T lO in the c a s e when the t a r g e t i s polarized. In c o n c l u s i o n we note that t h e method s t a t e d a b o v e c a n a l s o be a p p l i e d to t h e r e a c t i o n K-+p~K

++K °+~-.

(9)

One should, h o w e v e r , c h o o s e only such c a s e s when the m o m e n t a of a l l p a r t i c l e s l i e in t h e s a m e p l a n e , a s was m e n t i o n e d above. The a u t h o r s a r e g r a t e f u l to L. I. L a p i d u s and Ja. A. S m o r o d i n s k y f o r the d i s c u s s i o n of t h e s e problems.

(7)

Thus, in o r d e r to d e t e r m i n e the p a r i t y of the ~ h y p e r o n it i s n e c e s s a r y to c o m p a r e the r e s u l t s of two e x p e r i m e n t s . The f i r s t one c o n s i s t s in m e a s u r i n g t h e a s y m m e t r y of r e a c t i o n (1) on a p o l a r i z e d t a r g e t . In the s e c o n d e x p e r i m e n t we m u s t d e t e r m i n e t h e m e a n v a l u e s of T lO in the r e a c t i o n with an u n p o l a r i z e d t a r g e t . If t h e p a r a m e t e r a i s l a r g e , t h e m e a n v a l u e s 0 f o r t h e odd l can be d e t e r m i n e d , a c c o r d i n g to B y e r s and F e n s t e r [5], by m e a s u r i n g the a n g u l a r d i s t r i b u tion of h y p e r o n s in n o n - l e p t o n i c d e c a y s of t h e ~ - . H a i s s m a l l , then 0 with odd l can b e d e t e r m i n e d [5] f r o m the m e a s u r e m e n t s of t h e l o n gitudinal p o l a r i z a t i o n of h y p e r o n s . At p r e s e n t p o l a r i z e d t a r g e t s with the p r o t o n p o l a r i z a t i o n of about 70% have b e e n c o n s t r u c t e d . T h e m e a n v a l u e s 0 and the v a l u e of the a -

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