Spin Structure of the Nucleon Studied by HERMES

7/28/2019 Spin Structure of the Nucleon Studied by HERMES

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Hadron and N uclear Physics with Electromagnetic ProbesK. Maruyamaand H. Okuno (Editors)e 2000 Elsevier Science B.V. All rights reserved. 229

Spin s t ruc ture of the nuc leon s tudied by HER M ESY a s u h i ro S a k e m P *o n b e h a l f o f t h e H E R M E S c o l l a b o ra t i o n~ D e p a r tm e n t o f P h y s i c s, T o k y o I n s t i t u t e o f T e c h no log y ,2 - 1 2 - 1 0 o k a y a m a , M e g u r o - k u , T o k y o 1 5 2 - 8 5 5 1 , J a p a n

S p in a s y m m e t r i e s o f s e m i - in c lu siv e c r os s s e c t io n s f o r t h e p r o d u c t io n o f p o s i t i v e ly a n dn e g a t iv e ly c h a r g e d h a d r o n s h a v e b e e n m e a s u r e d i n d e e p - in e la s t i c s c a t t e r i n g o f p o l a r i z e dp o s i t r o n s o n p o l a r i z e d h y d r o g e n a n d a H e t a r g e t s i n t h e k in e m a t i c r a n g e 0 . 0 2 3 < x < 0 . 6a n d 1 G e V 2 < Q 2 < 1 0 G e V 2 . P o l a r i z e d q u a r k d i s t r i b u t io n s a r e e x t r a c t e d a s a f u n c t io no f x f or u p a n d d o w n q u a r k s . T h e u p q u a r k p o l a r i z a t i o n i s p o s i t iv e a n d t h e d o w n q u a r kp o la r i z a t i o n i s n e g a t iv e i n th e m e a s u r e d r a n g e . T h e p o l a r i z a t i o n o f t h e s e a is c o m p a t ib l ew i th z e ro . A m e a s u r e m e n t o f t h e s p in a s y m m e t r y in t h e p h o to p r o d u c t io n o f h ig h -p Thad ron pa i r s i s a l so p resen te d . Fo r h + h - pa irs wi th phi > 1.5 G eV /c an d phT2 > 1.0G e V / c , t h e m e a s u r e d a s y m m e t r y is n e g a ti v e, i n c o n t ra s t t o t h e p o s it i ve a s y m m e t r i e sty p i c a l l y m e a s u r e d i n d e e p i n e l a s t i c s c a t t e r i n g f r o m p r o to n s , a n d c a n b e i n t e r p r e t e d t oar i se f rom a pos i t ive g luon po la r iza t ion .1 . I N T R O D U C T I O N

T h e H E R M E S e x p e r im e n t s t u d i e s t h e s p in s t r u c tu r e o f t h e n u c l e o n u s in g s e m i - in c lu siv ep o la r i z e d d e e p in e l a s ti c s c a t t e r i n g ( D I S ) . In t h e Q u a r k - P a r to n M o d e l ( Q P M ) , t h e s p in o ft h e n u c l e o n m a y b e d e c o m p o s e d a s :

N 1 1 A E + L q + A G + L z (1 )w h e r e A E , A G , Lz q, a n d L z a a r e t h e c o n t r i b u t io n s f r o m q u a r k a n d g lu o n s p in a n d q u a r ka n d g l u o n o rb i t a l a n g u l a r m o m e n t u m . A E c a n be f u rt h e r d i v id e d a m o n g t h e q u a r k f la v or s,a n d b e tw e e n v a l e n c e a n d s e a c o n t r i b u t io n s :A E = A U v + A d v + A u s + A g + A d s + A d + A s + A g . ( 2 )P r e v io u s i n c lu s iv e e x p e r im e n t s p r e c i s e ly m e a s u r e d t h e p o l a r i z e d s t r u c tu r e f u n c t io n g l ( x ) ,w h ic h c a n b e i n t e r p r e t e d i n t h e Q P M a s th e s u m o v e r al l t h e f l a vo r s o f p o l a r i z e d p a r to nd i s t r i b u t i o n f u n c ti o n s (P D F s ) A q - ( q + ( x ) - q - ( x ) ) "

1 2 ( q + ( x ) q - ( x ) ) = 1gP (x) -- --2 E eq -- -'2 E e ~ Aq (x ).q q

(3 )*E-mail address: sakemi@ nucl.phys.titech.ac.jp


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T h e f u n c t i o n , q + ( - ) , r e p r e s e n t s t h e d i s t r i b u t i o n o f q u a r k s o f f l a v o r q w i t h s p i n p a r a l l e l( a n t i - p a r a l l e l ) t o t h e n u c l e o n s p i n , a n d e q i s t h e q u a r k c h a r g e i n u n i t s o f t h e e l e m e n t a r yc h a r g e . H e r e , x i s t h e B j o r k e n s c a l i n g v a r i a b l e x - Q 2 / 2 M ~ w h i c h i s d e t e r m i n e d b y t h es c a t t e r e d l e p t o n ' s k i n e m a t i c s , w h e r e Q 2 a n d ~ a r e t h e n e g a t i v e s q u a r e d f o u r - m o m e n t u ma n d e n e r g y o f t h e e x c h a n g e d v i r t u a l p h o t o n , a n d M i s t h e n u c l e o n m a s s . B y m e a s u r i n g9 1 ( x ) f r o m v a r i o u s t a r g e t s a n d i n t e g r a t i n g o v e r x , i t h a s b e e n f o u n d t h a t A E i s o n l y a b o u ta t h i r d o f t h e n u c l e o n s p i n , a n d t h a t t h e s t r a n g e s e a s e e m s n e g a t i v e l y p o l a r i z e d .

I n t h e s e m i - i n c l u s i v e m e a s u r e m e n t s , h a d r o n s a r e m e a s u r e d i n c o i n c i d e n c e w i t h t h es c a t t e r e d l e p t o n . H a d r o n p r o d u c t i o n s i n D I S a r e d e s c r i b e d w i t h t h e a b s o r p t i o n o f av i r t u a l p h o t o n b y a p o i n t - l i k e q u a r k a n d t h e s u b s e q u e n t f r a g m e n t a t i o n i n t o a h a d r o n i cf i n a l s t a t e . M e a s u r i n g a s y m m e t r i e s i n s e m i - i n c l u s i v e r e a c t i o n s y i e l d s f u r t h e r i n s i g h t s i n t ot h e i n d i v i d u a l c o n t r i b u t i o n s o f t h e q u a r k f l a v o r s t o A E . I n t h e s e r e a c t i o n s , o n e a l s od e t e c t s t h e p r o p e r t i e s o f t h e f r a g m e n t s o f t h e n u c l e o n b r e a k u p a f t e r t h e i n i t i a l s c a t t e r i n g ,w h i c h a r e c o r r e l a t e d t o t h e f l a v o r o f t h e s t r u c k q u a r k i n t h e r e a c t i o n .

O n e w a y t o m e a s u r e A G ( x ) i s b y i s o l a t i o n o f t h e l e a d i n g o r d e r Q C D p h o t o n g l u o nf u s i o n d i a g r a m . I n d e e p i n e l a s t i c s c a t t e r i n g , o n e c a n d o t h i s v i a c h a r m p r o d u c t i o n o rd i j e t p r o d u c t i o n . J e t s e p a r a t i o n i s n o t p o s s i b l e a t m o s t f i x e d t a r g e t e x p e r i m e n t s d u e t ot h e c e n t e r o f m a s s e n e r g y n o t b e i n g h i g h e n o u g h . H o w e v e r i t i s p o s s i b l e t o u s e h i g h -P T h a d r o n s i n s t e a d o f j e t s . A f e w p h e n o m e n o l o g i c a l s t u d i e s o f t h e s e n s i t i v i t y o f s p i n -d e p e n d e n t h i g h - p T h a d r o n p h o t o p r o d u c t i o n a n d l o w - Q 2 e l e c t r o p r o d u c t i o n t o t h e p o l a r i z e dgluon dis tr ibut ion AG have been conducted [1][2113] .T h i s pa pe r r e po r t s on the e x t r a c t ion o f po l a ri z ed qua r k d i s t r i bu t ion f rom d a t a t a ke n bythe H ER M ES exper im ent us ing the 27 .5 GeV beam of longi tud ina l ly po la r ized pos i tronsin the HERA s torage r ing a t DESY, and on the po la r ized g luon d is t r ibu t ion ex t rac tedf rom the spin a s ym m etry of h igh-pT hadrons .

2 . T H E H E R M E S E X P E R I M E N TThe HERMES exper iment was des igned to opt imize semi- inc lus ive DIS measurements

[4] . The exper iment i s loca ted a t the DESY labora tory in Hamburg , Germany, where a27 .5 GeV pos i t ron (or e lec tron) beam is c i r cu la ted in the HER A r ing . Th e po s i t ron beamis na tura l ly po la r ized t r ansve rse to the beam d i rec t ion due to an a symmetry in the emis-s ion of synch ro t ron rad ia t ion , an d longi tud ina l po la r iza t ion a t the H ER M ES in te rac t ionpoin t is provided by a pa i r o f m a tched spin ro ta tor s . The ave raged beam pola r iza t iondur ing the ru n i s 55 % wi th a r e la tive sys tem at ic unce r ta in ty in the m easure me nt of 4 .0% ( 3 . 4 % ) f o r t h e 3 H e ( H ) d a t a .

T h e H E R A b e a m p a s s e s t h r o u g h t h e c e n t e r o f a 4 0 c m l o n g c y l i n d r i c a l s t o r a g e c e l lc o n t a i n i n g p o l a r i z e d 3 H e o r 1 H . I n 1 9 9 5 , t h e 3 H e t a r g e t a t o m s b e c a m e p o l a r i z e d t h r o u g hm e t a s t a b i l i t y - e x c h a n g e o p t i c a l p u m p i n g [ 5 ] . P o l a r i z a t i o n i s 4 6 % w i t h a f r a c t i o n a l u n -c e r t a i n t y o f 5 ~ 0 . I n 1 9 9 6 a n d 1 9 9 7 , a n A t o m i c B e a m S o u r c e ( A B S ) u s e d p e r m a n e n ts e x t u p o l e m a g n e t s a n d r a d i o - f r e q u e n c y u n i t s t o s e l e c t d e s i r e d h y p e r f i n e s t a t e s o f I . AB r e i t - R a b i p o l a r i m e t e r ( B R P ) m o n i t o r s t h e p r o t o n p o l a r i z a t i o n , w h i c h i s 8 6 % d u r i n g t h er u n .

T h e H E R M E S d e t e c t o r i s a n o p e n - g e o m e t r y f o r w a r d s p e c t r o m e t e r . A s e r i e s o f t r a c k -i n g c h a m b e r s p l a c e d b e f o r e a n d a f t e r a d i p o l e m a g n e t d e t e r m i n e m o m e n t a a n d d i r e c t i o n s


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o f t h o s e p a r ti c l e s . A th r e s h o ld C e r e n k o v d e t e c to r , a T r a n s i t i o n R a d ia t i o n D e te c to r , aP r e s h o w e r C o u n te r , a n d a n E le c t r o m a g n e t i c C a lo r im e te r a l lo w s e p a r a t i o n o f e l e c t ro n sf r o m h a d r o n s . T h e C e r e n k o v f u r th e r p r o v id e s id e n t i fi c a t io n o f p io n s a b o ve p a r t i c l e m o -m en ta o f 5 .6 and 3 .8 Ge V /c in 1995 and 1996-7. The da ta f rom the po la r ize d 3He andp o l a r i z e d 1H t a r g e t s i s u s e d t o e x t r a c t q u a r k p o l a r i z a t i o n s , a n d t h e p o l a r i z e d I t a r g e td a t a i s u s e d t o s t u d y t h e g l u o n p o l a r i z a t i o n , r e s p e c t i v e l y .

3 . F L A V O R D E C O M P O S I T I O N O F T H E P O L A R I Z E D Q U A R K D I S T R I -B U T I O N S

3 .1 . S p i n a s y m m e t r i e s o f s e m i - i n c l u s i v e c r o s s s e c t io n sI n p o l a r i z e d d e e p - in e l a s t i c s c a t t e r i n g , o n e c a n c o n s t r u c t a c r o s s - s e c t i o n a s y m m e t r y A l l

o f p a r a l le l a n d a n t i - p a r a l l e l o r i e n t a t i o n s o f t h e n u c l e o n s p in t o t h e l e p to n b e a m s p in :o-T~ -- crT~

All - crT~ + crT~" (4)U n d e r t h e a s s u m p t io n t h a t g 2 (x ) is z e ro , t h e m e a s u r e d d o u b le - s p in a s y m m e t r y A ll isd i r e c t l y r e l a t e d t o t h e a s y m m e t r y o f t h e v i r t u a l p h o to a b s o r p t io n i n n u c le o n , A l ( x ) , a n dto t h e s t r u c tu r e f u n c t io n r a t i o , gl(X)/Fl(X):

g lA~ = Fh = D( 1 + 7) ' (5)w h e r e D , ~ , a n d ~ a re k in e m a t i c f a c to rs . F o r t h i s d is c u s sio n , t h e i n d e x h o f t h e a s y m m e t r ya n d s t r u c tu r e f u n c t io n i n c lu d e s b o th i n c lu s iv e p o s i t r o n d a t a a n d c o in c id e n t p o s i t i v e a n dn e g a t iv e h a d r o n s a n d i d e n ti f ie d p io n s ( h + , h - , 7r+ , and 7r - ) .

H E R M E S h a s m e a s u r e d a s y m m e t r i e s f o r i n clu siv e a n d s e m i - in c lu siv e h + a n d h - r e-ac t ions f rom 1995 , 1996 , and 1997 runn in g . These a sym m etr ie s a re shown in F igu re 1 .Inc lus ive DIS da ta a r e se lec ted f rom ev en ts wi th cu ts on Q2 > 1 GeV 2, y = L,/E < 0.85,and the f ina l had ron i c s ta t e mass , W 2 > 4 GeV 2 . T he s izes o f the inc lusive even t sam plessat is fy ing the se re qu irem en ts w ere 2 .2 x 106 an d 2 .3 x 106 for 3He an d 1H respect ively .T h e a n a ly z e d s e m i - in c lu s iv e e v e n t s f o r m a s u b s a m p le h a v in g a d e t e c t e d c h a r g e d h a d r o na n d W 2 > 1 0 G e V 2. A c u t o n t h e h a & o n e n e r g y f ra c t i o n , z > 0 .2 , a n d t h e F e y n m a n v a r i-able , x f > 0 .1 , a l so se lec ts nuc leon f r agmen ts f rom the cu r ren t r eg ion . The uncer ta in t iesi n b e a m a n d t a r g e t p o l a r i z a t i o n m e a s u r e m e n t u n c e r t a in t i es , u n c e r t a in t i e s i n R(x , Q2),e x p e r im e n ta l y i e ld f l u c tu a t i o n i n 1 9 9 5 a r e t h e d o m in a n t c o n t r i b u t io n s t o t h e s y s t e m a t i cu n c e r t a i n t y o f t h e m e a s u r e d a s y m m e t r i e s .3 .2 . I n t e r p r e t a t i o n o f t h e a s y m m e t r i e s

I n t h e Q P M a n d u n d e r t h e a s s u m p t io n o f f a c to r iz a t i o n , o n e s ee s t h a t t h e p h o to a b s o r p -t i o n a s y m m e t r y p r o b e s t h e h e l ic i t y d i ff er e nc e o f t h e p a r to n d i s t r i b u t io n s A q ( x ) :

h(z,QAq(x Q,2)Dq ) ( 1 + R ( x ))A~(x, z) - E q % , (6)1 +T h e a s y m m e t r i e s a r e a s s u m e d to b e Q 2 in d e p e n d e n t a s t h e e x p e r im e n ta l v a lu e s s h o w n os ig n if i ca n t Q 2 d e p e n d e n c e . T h e f r a g m e n ta t i o n f u n c t io n s D qh (z ) a re s p in i n d e p e n d e n t a n dr e p r e s e n t t h e p r o b a b i l i t y t h a t a s t r u c k q u a r k q f r a g m e n t s i n to a h a d r o n t y p e h .


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F ig u r e 1 . R e s u l t s fo r t h e v i r t u a l p h o to n a s y m m e t r i e s f r o m H E R M E S 1 9 95 ,1 9 96 , a n d1 9 97 d a t a . T h e t o p r o w s ho w s th e a s y m m e t r i e s o n t h e 1 H t a r g e t ; t h e b o t to m r o w s h o w sthe 3He ta rg e t . The co lum ns a re the inc lus ive , semi- inc lusive h + , and sem i- inc lus ive h -a s y m m e t r i e s f r o m l e f t t o r i g h t . T h e i n c lu s iv e a s y m m e t r i e s a r e c o m p a r e d w i th t h e S L A CE143 [6] and E154 [7] m easu rem en ts . Fo r the semi- inc lus ive asym m etr ie s wi th 1H ta rge t ,a compar ison wi th the SMC [8 ] r esu l t s a r e shown .


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pqh rep resen t s the p robabi l i ty tha t a de tec ted hadron h i s o r ig ina ted f rom a s t ruck qua rkof f lavor q in the nucleon.

Using these pur i t i e s , t he a symmet r i e s in equa t ion 6 may be rewr i t t en a sA ~ ( ~ ) : ~ P ~ ( x ) zx q ( ~ ) 1 + Rq q(x) 1 + 3 2. (8)

T h e a sy m m e t r i e s , p u r i t i e s , a n d q u a r k p o l a r i z a t i o n s m a y b e g r o u p e d i n t o m a t r i c e s , a n dthese equa t ions can be so lved us ing ma t r ix a lgebra ,~ ( ~ ) = P . 0 ( ~ ) . ( 9 )The qua rk po la r i za t ions a re ob ta ined by l eas t squa re min imiza t ion t echn iques .

T h e q u a r k p u r i t i e s r e l e v a n t fo r t h e H E R M E S e x p e r i m e n t h a v e b e e n e s t i m a t e d w i t h aMo nte Car lo s im ula t ion of unpo la r i zed DIS. The s imula t ion m ode l is based on LU NDst r ing f ragm enta t ion [9 ], CT EQ low Q2 unpola r i zed p a r to n d i s t r ibu t ion s [10]. Af te r nu-c lea r cor rec t ions aHe asymmet r i e s a re re l a t ed to qua rk d i s t r ibu t ions in the p ro ton .

In so lv ing equ a t ion 9 , one would l ike to sepa ra te the sp in con t r ibu t ions o f s ix qu a rkflavors" u , d , s , g , d and ~. In fac t , s ta t i s t ics and l imi ted sensi t ivi ty to th e s ea qua rk f lavorsrequ i re a se l ec t ion of the mo de l on ave rage sea po la r i za t ion . A s imple a ssum pt ion of f lavorindependent sea po la r i za t ion i s used he re"Aq~ Ad~ Au~ Ad A~2 Ag As

- . . . . . . . . ( 1 o )qs ds us d ~ g s3 .3 . E x t r a c t e d p o l a r i z e d q u a r k d i s t r i b u t io n s

Using the s ix expe r im enta l a sym me t r i e s Ap e, Ap h+ , Ap h- , AaHee, AaHeh+ , A aHeh- shownin Figure 1 , t h ree qua rk po la r i za t ions have been ex t rac ted : ( A u + A g ) / ( u + f z )( x ) , t h et o t a l u p f la v o r p o l a r iz a t io n ; ( A d + A d ) / ( d + d ) ( x ) , t he to t a l down f l avor po la r i za t ion ; and( A % / q s ) ( x ) , t he ave rage po la r i za t ion of the sea qua rks . Af te r mul t ip ly ing by x and th eu n p o l a r i z e d PD F p a r a m e t e r i z a t i o n , F i g u r e 2 sh o w s t h e r e su lt s f ro m t h is e x p e r i m e n t i nn i n e xB j b in s . T h e e x t r a c t i o n h a s b e e n r e p e a t e d w i t h G R V p a r t o n d i s t r ib u t i o n s [ 11 ], w i t ht h e i n d e p e n d e n t f r a g m e n t a t i o n m o d e l , a n d w i t h d i f f e r e n t p a r a m e t e r i z a t i o n fo r t h e f i t o fthe LUND s t r ing mode l to HERMES mul t ip l i c i t i e s ; a sys t ema t i c unce r t a in ty i s a ss ignedf rom the va r i a t ion of the re su l t ing qu a rk po la r i za t ions . For x > 0 .3 , i t is a ssu me d tha tsea po la r i za t ion does no t con t r ibu te s ign i f i can t ly to the measured a symmet r i e s ; t he seapola r i za t ion , ZXq---~(x) i s se t t o ze ro wi th a sma l l sys t ema t i c unce r t a in ty .q s

I n F i g u r e 2 , t h e p a r a m e t e r i z a t i o n s o f D e F l o r i a n e t a l . (0.1 < AG < 0.8, L O ) [12]Ge hrm an n a nd St i r l ing (G luon A , LO) [14], and Gl i i ck e t a l . ( S t a n d a r d , L O ) [ 1 3 ] a rep r o v i d e d for c o m p a r iso n . A c o r re c t io n o f ( I + R ) t o th e D e F l o r i a n a n d G l ii ck p a r a m e t e r -i za t ions is necessa ry fo r cons is t ency . These pa ra me te r i za t ion s agree wi th the HE RM ESresu l ts . F igure 3 com pares the ex t ra c ted va lence qua rk po la r i za t ion wi th the s imi l a r


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e x t r a c t i o n b y t h e S M C e x p e r i m e n t . N o t e t h a t t h e H E R M E S d e f i n it i o n o f t h e fl av o r i n-d e p e n d e n c e o f s e a p o l a r i z a t i o n d i f fe r s sl i g h tl y fr o m t h e m o d e l c h o s e n b y S M C ; i t h a sbeen ve r i f i ed tha t the re su l t s a re insens i t ive to the s l igh t d i f f e rences be tween the mode ls .W i t h i n s t a t i st i c a l a n d s y s t e m a t i c u n c e r t a in t i e s, t h e r e su l t s of b o t h e x p e r i m e n t s a g re e ,t h o u g h h i g h p r e c i si o n H E R M E S p r o t o n d a t a i s m o r e s e n s i ti v e to A u v a n d A~2 [1 5].

M o m e n t s o f t h e q u a r k d i s t r ib u t i o n s i n t h e m e a s u r e d x r a n g e a r e d e t e r m i n e d f ro m t h ea r e a u n d e r t h e m e a s u r e d p o i n ts . F o r c o m p a r i s o n t o p r e v i o u s m e a s u r e m e n t s , t h e d i s t ri -b u t i o n s a r e e x t r a p o l a t e d t o lo w x b y c o n s t a n t f i ts t o t h e d a t a ; t h e l ow x e x t r a p o l a t i o n i sq u o t e d b u t n o v a l u e i s q u o t e d f o r t h e u n c e r t a i n t y d u e t o t h e o r e t i c a l a m b i g u i t i e s . T h e r e -s u l t i n g i n t e g r a l s i n t h e m e a s u r e d r e g i o n a r e l i s t e d i n T a b l e 1 . T h e i n t e g r a l s a r e c o m p a r e dt o p r e d i c t i o n s f r o m Re f e r e n c e 1 6 , w h i c h a r e c o r r e c t e d t o f o u r t h o r d e r i n Q C D ; t h e s e p r e -d i c t i o n s h a v e b e e n e x t r a c t e d f r o m in c l us i ve d a t a a s s u m i n g S U ( 3 ) fl av o r s y m m e t r y . T h eH E R M E S v a l u e s a r e s l i g h t l y s m a l l e r i n m a g n i t u d e t h a n t h e s e p r e d i c t i o n s .

m e a s u r e d r e g i o n l o w -xA u + A t 0 .51 -t- 0 .02 4- 0 .03 0 .04A d + A d -0 .22 4 - 0 .06 4 - 0 .05 -0 .03A s + A g -0 .01 4 - 0 .03 4 - 0 .04 0 .00

t o t a l i n t e g r a l p r e d i c t i o n s0.57 4. 0.02 + 0.03

-0.25 + 0.06 4- 0.05-0.01 4- 0.03 4- 0.04

0.66 4. 0.03-0.35 4. 0.03-0.08 4. 0.02

T a b l e . l : T h e fi r st m o m e n t s o f t h e e x t r a c t e d p o l a r i z e d p a r t o n d i s t r i b u t i o n s .

4 . S P I N A S Y M M E T R Y I N T H E P H O T O P R O D U C T I O N O F H A D R O N P A I R S4 . 1 . A n a l y s i s

T h e c r o s s s e c t i o n a s y m m e t r y All i s g iven byN - L + _ N + L -All = N _ L + + N + L p (11)

w h e r e N + ( N - ) is t h e n u m b e r o f h a d r o n p a i r s o b s e r v e d w h e n t h e t a r g e t s p i n is p a r a l l e l( a n t i - p a r a l l e l ) t o t h e b e a m s p i n d i r e c t i o n . T h e l u m i n o s i t i e s f o r e a c h t a r g e t s p i n s t a t e a r eL + a n d L p t h e l a t t e r b e i n g w e i g h t e d b y t h e p r o d u c t o f t h e b e a m a n d t a r g e t p o l a r i z a t i o nva lues fo r each sp in s t a te .

T o i d e n t i fy t h e h a d r o n p a i r s o f i n t e r e s t, i t w a s r e q u i r e d t h a t a t l e a s t o n e p o s it i v e h a d r o nh + a n d a t l e a s t o n e n e g a t i v e h a d r o n h - b e o b s e r v e d in t h e s p e c t r o m e t e r . E a c h o f t h e s et w o h a d r o n s w e r e r e q u i r e d t o h a v e a m o m e n t u m g r e a t e r t h a n 4 . 5 G e V / c a n d t r a n s v e r s em o m e n t u m P T g r e a t e r t h a n 0 .5 G e V / c . H e r e , P T is d e f in e d w i t h r e s p e c t t o t h e p o s i t r o nb e a m a x i s. I t w a s r e q u i r e d t h a t t h e i n v a r i a n t m a s s o f t h e tw o h a d r o n s y s t e m ( a s s u m i n g t h eh a d r o n s t o b e p i o n s) b e g r e a t e r t h a n 1 .0 G e V / c 2. T h i s e ff ec t iv e ly r e d u c e d t h e b a c k g r o u n dar i s ing f rom d i f f rac tive p roces ses , spec if i cal ly the dec ays o f vec to r m esons . In o rde r toi n c l u d e s t a t i s t i c s f r o m l e p t o p r o d u c t i o n a t Q 2 ~ 0 , i t w a s n o t r e q u i r e d t h a t t h e s c a t t e r e dp o s i t r o n n e c e s s a r i l y b e o b s e r v e d i n t h e s p e c t r o m e t e r .

T h e m e a s u r e d All i s s h o w n i n F i g u r e . 4 . A n e g a t i v e a s y m m e t r y i s o b s e r v e d a t h i g ht r a n s v e r s e m o m e n t a o f t h e n e g a t i v e h a d ro n s . I t sh o u l d b e n o t e d t h a t s m a l l a n d p o s it iv e


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,'5"~+ 0.3: 3


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w h e r e D i s t h e v i r t u a l p h o t o n d e p o l a r i z a t i o n f a c t o r a n d A i a n d f i a r e , r e s p e c t i v e l y , t h ea s y m m e t r y a n d f r a c t i o n o f e v e n t s a r i s i n g f r o m p r o c e s s i . U n d e r t h e a s s u m p t i o n o f a z e r os p i n a s y m m e t r y f o r V M D p r o c e s s e s , t h e f i r s t t e r m v a n i s h e s . F o r t h e s m a l l r e g i o n o f t h ep h a s e s e l e c t e d b y t h e p r e s e n t a n a l y s i s , t h e a s y m m e t r i e s f o r Q C D C a n d P G F a r e g i v e nb y :A p G r , ~ < apGF > A G / G (13)AQCDC ~ < (~QCDC > A q / q (14)The subprocess asymmet r ies 5 ' s a re d i rec t ly ca lcu lab le in LO QCD. They a re &PaR = --1(exact ly , for real photons and massless part ic ipants) , and 5QCD C ~ 0.5 (for the averagek inem at ics o f th i s ana lysi s ) . The po la r ized quark d i s t r ibu t ions Aq(x) a re re la t ive ly wellknown f rom inc lus ive and semi- inc lus ive po la r ized DIS measuremen ts . The con t r ibu t ionsof the var ious p rocesses were de te rm ined us ing the P Y TH IA M onte Car lo genera to r [17 ].Th e P Y TH IA p a ra m e t e r s we re c h os e n a c c o rd i n g t o Ref. [ 1 8] wh i le th e J E TS E T f ra g -men ta t ion parameters were tuned to semi- inc lus ive deep- ine las t i c sca t t e r ing da ta f romH E R M E S .

In the region of in teres t ( phi > 1 .5 GeV /c a nd p~2 > 0 .8 Ge V /c ) , the m odel was foundto descr ibe the shape o f var ious d i s t r ibu t ions re la tive ly wel l, though the norm al iza t ionof the cross sect ion was found to be under es t im ated . In th is model , the cross sect ionat h igh P T i s domina ted by the pho ton g luon fus ion , so th i s da ta was used to ex t rac tA G / G . The Monte Carlo showed no leading part ic le ef fects (as the background f romQCDC was smal l ) , desp i te the f ac t tha t the da ta show a t endency to more nega t ive Al lfor ph - > 1 .5 Ge V /c , a s opposed to l a rge phT+. The mea sured asy m m et ry (now averagedover the two p lo t s f rom Figure .4 ) i s com pared w i th p red ic tions f rom the M onte Car lo w i thdif ferent assumptions for A G / G in Figure.5 . The bes t f i t value for A G / G in th i s modelis A G / G = 0.41 + O.16(stat .) + O.04(syst.) at an average xa of 0 .17 [19] .5 . C O N C L U S I O N S A N D O U T L O O K

T h e f i r s t t h r e e y e a r s o f H E R M E S d a t a t a k i n g h a v e y i e l d e d h i g h s t a t i s t i c s p o l a r i z e dd e e p - i n e l a s t i c s c a t t e r i n g d a t a o n 3 H e a n d I t a r g e t s . T h e p o l a r i z e d m e a s u r e m e n t s y i e l di n c l u s i v e a n d s e m i - i n c l u s i v e c h a r g e d h a d r o n a s y m m e t r i e s , w h i c h h a v e b e e n p r e s e n t e d a s af u n c t i o n o f x . I n t h e f r a m e w o r k o f t h e Q u a r k - P a t t o n M o d e l t h e s e a s y m m e t r i e s a r e s i m u l -t a n e o u s l y f i t t e d t o o b t a i n h e l i c i t y d i s t r i b u t i o n s f o r u p , d o w n , a n d s e a q u a r k s . A m e a s u r e -m e n t o f t h e s p i n a s y m m e t r y A t 1 i n q u a s i - r e a l p h o t o p r o d u c t i o n o f h i g h P T h a d r o n p a i r si s a l s o p r e s e n t e d . W h e n i n t e r p r e t e d i n a L O Q C D m o d e l i m p l e m e n t e d i n t h e P Y T H I AM o n t e C a r l o g e n e r a t o r , a v a l u e o f t h e g l u o n p o l a r i z a t i o n i n t h e n u c l e o n A G / G i s e x -t r a c t e d .

F u r t h e r s e n s i t i v i t y t o s e a p o l a r i z a t i o n s i s g a i n e d b y i d e n t i f i c a t i o n o f t h e d i f f e r e n t c o -i n c i d e n t h a d r o n m e a s u r e m e n t s . I d e n t i f i c a t i o n o f p i o n s f r o m h a d r o n s b y t h e H E R M E St h r e s h o l d ( ~ e r e n k o v c o u n t e r , m a y p r o v i d e b e t t e r s e n s i t i v i t y t o A s i n t h e q u a r k p o l a r i z a -t i o n e x t r a c t i o n [ 2 0 ] . A t p r e s e n t H E R M E S i s t a k i n g a n e w d a t a s e t w i t h h i g h s t a t i s t i c so n t h e d e u t e r i u m t a r g e t , w h i c h w i l l s i g n i f i c a n t l y i m p r o v e t h e p r e c i s i o n o n t h e d - q u a r kh e l i c i t y d i s t r i b u t i o n . I n 1 9 9 8 , t h e T h r e s h o l d ( ~ e r e n k o v c o u n t e r w a s r e p l a c e d w i t h a R i n g


9/10

I

A G / G = - I

_

A G /G =O -_[ ' 2 2 2 2 2

_

A G / G = + I

' ~ 0 " 60 . 4 p _ > h + . 5 ' G e V / c ' ' ~ .... ' 1

. . . . . . . . t io +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-0.2-0.4- 0 . 6- 0 . 8- 1 0 . 5 0 . 7 5 1 1 . 2 5 1 . 5 1 . 7 5 2h - ( G e V / c )P T

' ~ 0 : 6 I p h - > l '. 5 G e W c ' ' ' 1: i I +. . . . . . . . . . . . + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . 1, . , + + ' 1" - 1 , , , - t0 . 5 0 . 7 5 1 1 . 2 5 1 . 5 1 . 7 5 2h , ( G e V / c )P T

~ " ~ I I I 1h l0 . 6 P T > 1 . 5 G e V / c / ~ -

~ - 0 . 40 . 2

- 0 . 2- 0 . 4- 0 . 6 - - - G S A ( < A G / G > ~ 0 . 4 )- 0 . 8 . . . . G S B ( < A G IG > ~ 0 . 3 )

. . . . . . G S C (< A G / G > ~ - 0 .1 )5 I I I. 1 0 . 5 o . 1 1 . 2 5 1 . 5

237

1 . J 75 2h 2 ( G e V / c )P T

Fi g u r e 4 . T h e m e a su r e d a sy m m e t r y : t h e t o pplot is All as a function of p T h - fo r phT+ > 1.5GeV/c and the bo t tom p lo t i s A l l a s a func -t ion of pT h+ for p~- > 1.5 GeV /c . Th e r ight -mo st poin t in each p lot is ident ica l . On ly thes t a t i s t i ca l e r ro r i s shown.

Figure 5 . Al l compared wi th di fferent pos-sibi l i t ies for AG/G. Upper to lower sol idb la c k c u rv e s a r e f or A G / G = - 1 , 0 , a n d1, respect ive ly. Dash ed, dot te d, a nd dot -dashed curves are for LO fi t s of Ref . [14]

Imaging (~e renkov counte r (RICH) . Thi s new de tec tor w i l l i den t i fy 7 r , K , and p pa r t i c l e so v e r n e a r l y a ll m o m e n t a a c c e p t e d b y t h e sp e c t r o m e t e r . A s k a o n a sy m m e t r i e s p r o v id e d i-rec t sens i t iv i ty to s t rang e qua rk po la r i za t ion in the nuc leon , a de te rm ina t io n of sea qu a rkpola r i za t ion w i th much h ighe r p rec is ion i s expec ted a f t e r the new run .

R E F E R E N C E So

2.3.4.5.6.7.8~9.10 .11 .12 .13 .

M. Fontannaz , D. Schiff , and B. Pi re , Z. Phys. C 8(1981) 349A. Bravar , D. von Harrach, and A. Kotz inian, Phys. Let t . B421 (1998) 349A. Afanasev , C .E . Car l son , and C. Wahlqu i s t , Phys . Rev . D58 (1998) 054007K. Ackers t a f f e t a l , Nucl . Ins t rum. Methods A 417(1998) 230D . D e Sc h e p p e r e t a l , Nucl . Ins t rum. Methods A 419(1998) 16K. Abe e t a l , Phys. Rev. D58 (1998) 112003K. Abe e t a l , Phys. Rev. Let t . 79 (1997) 26B. Adeva e t a l , Phys. Rev. Lett . D58 (1998) 112001B . A n d e r so n e t a l , Phys. Rept . 97(1983) 33H.L. Lai e t a l , Phys. Rev. D126 (1997) 1280M. Gliick e t a l , Z. Phys. C67(1995) 433D . d e F l o r i a n e t a l , Phys. Rev. D57 (1998) 5803M. Gliick e t a l , Phys. Rev. D53 (1996) 4775


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14. T. Gehrmann and W.J. S t ir l ing, Phys. Rev. D53 (1996) 610015. K. Ackerstaff e t a l , Phys. Lett. B464 (1999) 12316. J . E l l is and M. Kar l iner , Inv i ted Lectures a t th e Intern at ion al School of Nucleon Spin

S t ruc ture , Er ice , Augus t 1995 , hep-ph/9601280.17. T. S jSstrand, Comp. Phys. Comm. 82 (1994) 74. The Monte Car lo resul ts were ob-

ta ined us ing PYTHIA ve rs ion 5 .724 and JETSET ve rs ion 7 .410 .18. G.A. Schuler and T. SjSstrand, Nucl. Phys. B407 (1993) 53919. A. Airapet ian e t a l , Phys. Rev. Let t . ( in press) , hep-ex/990702020. L.L. Frankfur t e t a l , Phys. Lett. B230 (1989) 141

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Spin Structure of the Nucleon Studied by HERMES