Hyperon Polarization in Kaon Photoproduction From the Deuteron

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Had ron and Nucle ar Physics with Electromagnet ic ProbesK. Ma ruyama and H . Okuno (Ed i tors )2000 Elsevier Science B .V. A ll r ights reserved. 119

H y p e r o n p o l a r i z a t i o n i n K a o n p h o t o p r o d u c t i o n f r o m t h e d e u t e r o nH. Ya m am ura ~, K . M iyaga wa ~ , T . M ar t b , C . Benn ho ld c , H . Ha ber ze t t l CandW. G16ckle d~ D e p a r tm e n t o f A p p l i e d P h y s i c s, O k a y a m a U n iv e r s it y o f S c ie n ce ,1 - 1 R id a i - c h o , O k a y a m a 7 0 0 , J a p a nbJu rusan , F is ika , FMIPA, Un iver s i tas Indones ia , Depok 16424 , Indones iaC C e nter fo r N u c l e a r S tu d i e s , D e p a r tm e n t o f P h y s c s , T h e G e o r g e W a s h in g to n U n iv er s it y ,W a s h in g to n , D . C . 2 0 0 5 2d I n s t i t u t f ii r T h e o r e t i s c h e P h y s ik I I, R u h r - U n iv e r s i t s B o c h u m ,D - 4 4 7 8 0 B o c h u m , G e r m a n y

W e ana lyze the r e ac t ion 7 + d ~ K + + A(E) + N us ing the N i jmegen so f t core hype ron-n u c l e o n i n t e r a c t i o n s N S C 9 7 f a n d N S C 8 9 a n d a r e c e n t l y u p d a t e d p r o d u c t i o n o p e r a t o r f o rthe -7 + N ~ K + + A (E) processes . Signif icant ef fects of the Y N f ina l s ta te in te rac t iona r e f o u n d n e a r b o th t h e K + A N a n d K + E N t h r e s h o ld s .1 . I N T R O D U C T I O N

S in c e h y p e r o n - n u c l e o n s c a t t e r i n g e x p e r im e n t s a r e d i f f i c u l t t o p e r f o r m , h y p e r o n p r o d u c -t ion p rocesses such as ~ /+ d ~ K + + Y + N and e + d -- . e ' + K + + Y + N a p p e a r a sn a tu r a l c a n d id a t e s t h a t a l l o w e x p lo r in g t h e Y N i n t e r a c t io n . O n e c a n o b t a in t h e i n f or -m a t i o n o f t h e Y N i n t e r a c t i o n b y a n a ly z in g t h e c o r r e l a t e d Y N f inal s ta tes . An inc lus ived (e , e ' K + ) Y N e x p e r im e n t h a s a l r e a d y b e e n p e r f o r m e d in H a l l C a t T J N A F , w h i l e t h ed a t a f o r d (7 , K + Y ) N are be ing ana lyzed in Hal l B .

R e c e n t ly , w e f o u n d th a t v a r io u s m e s o n - th e o r e t i c a l Y N i n t e r a c t i o n s g e n e r a t e S - m a t r i xp o le s a r o u n d th e A N a n d E N th r e s h o ld s [ I ]. T h e p o l e n e a r t h e E N th r e s h o ld i s r e l a t e d t ot h e s t r e n g t h a n d t h e p r o p e r t y o f t h e A N - E N c o u p li n g a n d c au s es e n h a n c e m e n t s i n t h eA N e l a s ti c t o t a l c r os s se c t io n s . T h e h o p e i s t h a t t h e p o l e s t r u c tu r e o f t h e Y N t m a t r i xwi l l have v is ib le e f f ec ts in such p roduc t ion p rocesses men t ion above .

In th i s paper , we s tudy the inc lus ive d (7 , K + ) Y N and exc lus ive d (7 , K + Y ) N processesfor OK = 0 ~ and p red ic t var ious observab les inc lud ing po la r iza t ion observab les .2 . F O R M A L I S M

T h e r e a c t i o n p r o c e ss e s ~ /+ d ~ K + + A ( E ) + N a r e e x p r e s se d b y t h e o p e r a to r T / a sOTKJ

~ , j = A N , E N , ( 1 )


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F i g u r e 1. I n c l u si v e d ( 7 , K + ) c r o ss s e c t io n a s a f u n c t i o n o f l a b m o m e n t u m P K + fo r 0 K + , l a b - - "0 ~ a n d t h e p h o t o n l a b e n e r g y E ~ = 1 .3 G e V . T h e t w o t h r e s h o l d s K + A N a n d K + E N a rei n d i c a t e d b y t h e a r ro w s . T h e r e s u l t s a r o u n d t h e K + E N t h r e s h o l d a r e e n l a r g e d i n ( b ) .

w h e r e t h e o p e r a t o r d e s c ri b e s t h e e l e m e n t a r y p r o c es s e s ~ / + N + K + + A ( E ) a n d I ~d >~ ' ~ ' Kr e p r e s e n t s t h e d e u t e r o n s t a t e w h i c h is g e n e r a t e d b y th e N i j m e g e n 93 N N i n t e r a c t i o n[ 2] . T h e o p e r a t o r U q c o r r e s p o n d s t o t h e Y N f i n a l s t a t e i n t e r a c t i o n p r o c e s s e s , a n d i sr e p r e s e n t e d a s

= + j ) + E j ) +j ,= 5, j + j ,c J ' )uj ,j , (2 )j,

w h e r e Y / j is Y N i n t e r a c t io n i n c l ud i n g A N - E N c o u pl in g . W e ig n o re t h e K + m e s o ni n t e r a c t i o n w i t h t h e n u c l e o n a n d h y p e r o n i n t h e f in a l s t a t e s . F r o m E q s . ( 1 ) a n d ( 2) , o n ec a n d e d u c e t h e c o u p l e d s e t o f i n t e g r a l e q u a t i o n s f o r T i,

~ G(o '), l '~a >-O-~Kl'~d > + ~ V~j, Zj , l~a > . (3)j ,W e s o lv e t h i s s e t (3 ) a f t e r p a r ti a l - w a v e d e c o m p o s i t i o n in m o m e n t u m s p a c e . T h e t h r e ee l e m e n t a r y p r o c e s s ~ / + p ~ K + + A ( E ~ a n d ? + n ~ K + + E - a r e p r o p e r l y i n c o r p o r a t e di n t h e d r i v i n g t e r m i n E q . ( 3 ) . E q u a t i o n ( 3) is s o l ve d o n i s o sp i n b a s e s A N a n d E N , b u tt h e r e s u l t i n g a m p l i t u d e s a r e t r a n s f o r m e d i n t o t h o s e o n t h e p a r ti c l e ba s e s A n , E ~ a n dE - p b y w h i c h t h e i n c l u s i v e d ( ' ) , , K + ) , exclusive d ( ' ) ' , K + Y ) c r o s s s e c t i o n s a n d h y p e r o npo l a r i z a t io ns a re ca l cu la t ed . Fo r de t a i l s , w e re fe r t he r ea der to r ef .[3] .

3 . R E S U L T SA t p r e s e n t , w e c a l c u l a t e t h e o b s e r v a b l e s o n l y fo r t h e K + m e s o n s c a t t e r e d t o 0 d e g r e e

(OK+ = 0 ~ T h e N i j m e g e n s o f t- c o r e Y N i n t e rac t ions N SC97f [4 ] and N SC8915] and a


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r e c e n t l y u p d a t e d p r o d u c t i o n o p e r a t o r[ 6 ] f o r t h e 7 + N - + K + + A ( E ) + N p r o c e s s e s a r eu s e d .

F i g u r e l ( a ) s h o w s th e i n c lu s i v e c r o s s s e c t io n s w h i c h s u m u p t h e c o n t r i b u t i o n s o f t h eK + A n , K + E ~ a n d K + E - p f in a l s t a t e s . T h e s o li d a n d d a s h e d l i n es a re t h e p r e d i c t i o n s o ft h e N S C 9 7 f a n d N S C 8 9 Y N i n t e r a c t i o n s , r e s p e c t i v e l y . T h e d o t t e d l i n e s h o w s t h e r e s u l t so f t h e p l a n e w a v e i m p u l s e a p p r o x i m a t i o n ( P W I A ) . T h e a r r o w s i n d i c a te t h e t w o t h r e s h o l d sK + A N ( W = 9 77 .3 0 m e V h ) a n d K+P~N (pK = 869 .14 MeV /c) .

T h e t w o p r o n o u n c e d p e a k s a r o u n d PK = 9 4 5 a n d 8 0 9 M e V / c a r e d u e t o t h e q u a s i - f r e ep r o c e s s e s o f A a n d P~, w h e r e o n e o f t h e n u c l e o n i n t h e d e u t e r o n i s s p e c t a t o r a n d h a s z e r om o m e n t u m i n t h e l a b o r a t o r y s y s t e m . S i gn if ic a n t F S I e ff ec ts a re f o u n d a r o u n d t h e K + A Na n d K + E N t h r e s h o l d s . T h e c r o s s s e c t i o n is i n c r e a s e d u p t o 8 6 % b y F S I n e a r t h e K + A Nt h r e s h o l d . A r o u n d t h e K + E N t h r e s h o l d , a s s h o w n F i g . l ( b ) , t h e s t r e n g t h s a n d s h a p e s o ft h e e n h a n c e m e n t s b y t h e N S C 9 7 f a n d N S C 8 9 a r e q u i t e d i f f e r e n t .

1 0

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F i g u r e 2 . ( a ) E x c l u s i v e d ( 'y , K + A ) c r o s s s e c t i o n a n d ( b ) A r e c o il p o l a r i z a t i o n w i t h i n c o m -i n g p o l a r i z e d p h o t o n a s a f u n c t i o n o f t h e A s c a t t e r i n g a n g l e i n t h e A n c . m . s y s t e m . T h ep h o t o n l a b e n e r g y is E ~ = 1 .3 G e V . T h e o u t g o i n g k ao n la b m o m e n t u m a n d a n g l e a rePK+ = 8 7 0 M e V / c a n d OK+ = 0 ~ respec t ively .

F i g u r e 2 ( a ) i l l u s t r a t e s t h e e x c lu s i ve d ( 7 , K + A ) c r o ss s e c t i o n s j u s t b e l o w t h e K + E Nt h r e s h o l d (PK = 8 7 0 M e V / c ) . T h e F S I e f fe c ts a r e s ee n b o t h a t v e r y f o r w a r d a n d a t l a r g ea n g l es . T h e P W I A c r o s s s e c t i o n s a r e b a s i c a l l y z e r o a t b a c k w a r d a n g l e s, w h i le t h e F S Ic a l c u l a t i o n s s t i ll s h o w s o m e s t r e n g t h . F i g u r e 2 ( b ) d e m o n s t r a t e s t h e A r e c o il p o l a r i z a t i o n sw i t h i n c o m i n g p o l a r i z e d p h o t o n . T h e A r ec o il p o l a r i z a ti o n s i n P W I A a r e a l m o s t on e .T h i s i s b e c a u s e t h e i n c o m i n g p h o t o n is p o l a r i z e d a l o n g t h e z ax i s, b u t t h e t a r g e t d e u t e r o nis u n p o l a r i z e d a n d t h e o u t g o i n g K + m e s o n c a r ri e s n o s p i n a n d a n g u l a r m o m e n t u m i n t h i scase (OK = 0 ~ H o w e v e r , t h e f in a l s t a t e i n t e r a c t i o n s c a u s e t h e l a rg e d e v i a t i o n s f r o m o ne ,a n d t h e p r e d i c t i o n b y N S C 9 7 f is q u i t e d i f fe r e n t fr o m t h a t o f N S C 8 9 .


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O z - p [ d e g ]

F i g u r e 3 . ( a) E x c l u s i v e d (7 , K + E - ) c r o ss se c t io n a n d ( b) E - r e co i l p o l a r i z a t i o n w i t hi n c o m i n g p o l a r i z e d p h o t o n a s a f u n c t i o n o f t h e E - s c a t t e r i n g a n g l e i n t h e E - p c .m .s y s t e m . T h e p h o t o n l a b e n e rg y is E ~ = 1 .3 G e V . T h e o u t g o i n g k a o n l a b m o m e n t u m a n da n g l e a r e PK+ = 8 65 M e V / c a n d OK+= 0 ~ respe c t ive ly .

,,! !

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~ 3 0 - , ' , K + -- ~ = , , ' ' A N=~ ~ 2 0 - , "

1 0D07 0 0 8 0 0 9 0 0 1 0 0 0

P K [MeV/c]

F i g u r e 4 . I n c l u s i v e d (~ /, K + ) c r os s s e c ti o n i n t h e P W I A a s a f u n c t i o n o f l a b m o m e n t u mP K + f o r OK+ = 0 ~ a n d p h o t o n l a b e n e r g y E ~ = 1 .3 G e V . T h e s o l i d c u r v e s h o w s t h ep r e d i c t i o n b y t h e p r e s e n t v e r s io n [6 ] o f t h e p r o d u c t i o n o p e r a t o r f or 7 + N ~ K + + A ( E ) ,w h i l e t h e d a s h e d l i n e c o r r e s p o n d s t o t h e p r e d i c t i o n b y a n o l d v e r s i o n [ 7 ] .


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Hyperon Polarization in Kaon Photoproduction From the Deuteron