The Proton and the Photon Who is Probing Whom in Electroproduction

7/28/2019 The Proton and the Photon Who is Probing Whom in Electroproduction

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Hadron and Nuclear Physics w ith Electromagnetic ProbesK. Mamyamaand H. Okuno (Editors)2000 Elsevier Science B.V. All rights reserved. 201

The pro ton and the photon , who i s prob ing whom in e lec t roproduct ion?A h a r o n L e v y *S c h o o l o f P h y s i c s a n d A s t r o n o m yR a y m o n d a n d B e v e r l y S a ck l er F a c u l t y o f E x a c t S c ie n ce sT el A v iv U n iver s i ty , T e l A v iv , I s r ae l

T h e l a t e s t r e s u l ts o n t h e s t r u c t u r e o f t h e p r o t o n a n d t h e p h o t o n a s s ee n a t H E R A a r er e v i e w e d w h i l e d i s c u s s i n g t h e q u e s t i o n p o s e d i n t h e t i t l e o f t h e t a l k .

1 . I N T R O D U C T I O NT h e H E R A c o l l i d e r , w h e r e 2 7 . 5 G e V e l e c t r o n s c o l l i d e w i t h 9 2 0 G e V p r o t o n s , i s c o n s i d -

e r e d a n a t u r a l e x t e n s i o n o f R u t h e r f o r d ' s e x p e r i m e n t a n d t h e p r o c e ss o f d e e p i n e la s ti c eps c a t t e r i n g ( D I S ) i s i n t e r p r e t e d a s a r e a c t i o n i n w h i c h a v i r t u a l p h o t o n , r a d i a t e d b y t h ei n c o m i n g e l e c t r o n , p r o b e s t h e s t r u c t u r e o f t h e p r o t o n . I n th i s t a l k I w o u l d li ke to d i s c u s st h i s i n t e r p r e t a t i o n a n d a s k t h e q u e s t i o n o f w h o i s p r o b i n g w h o m [1].T h e s t r u c t u r e o f t h e t a l k w i ll b e t h e f ol lo w in g : i t w il l s t a r t w i t h p o s i n g t h e p r o b l e m ,a f t e r w h i c h o u r k n o w l e d g e a b o u t t h e s t r u c t u r e o f t h e p r o t o n a s s e e n a t H E R A [2] w i ll b ep r e s e n t e d f o ll ow e d b y a d e s c r i p t io n o f o u r p r e s e n t u n d e r s t a n d i n g o f t h e s t r u c t u r e o f t h ep h o t o n a s s e e n a t H E R A a n d a t L E P [ 3 , 4 ] . N e x t , a n a n s w e r t o t h e q u e s t i o n p o s e d i n t h et i t l e w i l l b e s u g g e s t e d a n d t h e t a l k w i l l b e c o n c l u d e d b y s o m e r e m a r k s a b o u t t h e n a t u r eo f t h e i n t e r a c t i o n b e t w e e n t h e v i r t u a l p h o t o n a n d t h e p r o t o n [5].

2 . T H E Q U E S T I O N - W H O IS P R O B I N G W H O M ?2 .1 . T h e p r o c e s s o f D I S

T h e p r o c e s s o f D I S i s u s u a l l y r e p r e s e n t e d b y t h e d i a g r a m s h o w n i n f ig u r e 1 . I f t h el e p t o n d o e s n o t c h a n g e i t s i d e n t i t y d u r i n g t h e s c a t t e r i n g p r o c e s s , t h e r e a c t i o n i s l a b e l e dn e u t r a l c u r r e n t ( N C ) , a s e it h e r a v i r t u a l p h o t o n o r a Z ~ b o s o n c a n b e e x c h a n g e d . W h e nt h e i d e n t i t y o f t h e l e p t o n c h a n g e s i n t h e p r o c e s s , t h e r e a c t i o n i s c a l le d c h a r g e d c u r r e n t( C C ) a n d a c h a r g e d W + b o s o n i s e x c h a n g e d . D u r i n g t h i s t a l k w e w i ll d i s c u s s o n l y N Cp r o c e s s e s . U s i n g t h e f o u r v e c t o r s a s i n d i c a t e d i n t h e f i gu r e, o n e c a n d e fi n e t h e u s u a lD I S v a r ia b l e s : Q 2 = _ q 2 , t h e ' v i r t u a l i t y ' o f t h e e x c h a n g e d b o s o n , x = Q 2 / ( 2 P . q ) , t h ef r a c t io n o f t h e p r o t o n m o m e n t u m c a r r ie d b y th e i n t e r a c t i n g p a r t o n , y = ( P . q ) / ( P , k ) ,t h e i n e l a st i c it y , a n d W 2 = (q + p ) 2 , t h e b o s o n - p r o t o n c e n t e r o f m a s s e n e r g y s q u a r e d .*This work was partially supp orted by the German-Israel Foundation(GIF), by the U .S.-Israel BinationalFoundation (BS F) and by the Israel Science Foundation (ISF). The financial support of my visit to Jap anby JSPS is highly appreciated.


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F i g u r e 1 . A d i a g r a m d e s c r i b i n g t h e p r o -c e ss o f d e e p i n e l a s t ic s c a t t e r i n g ( D I S ) . T h ef o u r v e c t o r o f t h e i n c o m i n g a n d o u t g o -i n g l e p t o n s a r e k a n d k ' , t h a t o f t h e e x -c h a n g e d b o s o n is q , a n d t h a t o f t h e i n-c o m i n g p r o t o n i s P . T h e f o u r m o m e n t u mo f t h e s t r u c k q u a r k is x P .

T h e i n t e r p r e t a t i o n o f t h e d i a g r a m d e s c r i b i n g a N C e v e n t i s t h e f o ll o w in g . T h e e l e c t r o nb e a m i s a s o u r c e o f p h o t o n s w i t h v i r t u a l i t y Q 2 . T h e s e v i r t u a l p h o t o n s ' l o o k ' a t t h e p r o t o n .A n y ' o b s e r v e d ' s t r u c t u r e b e l o n g s t o t h e p r o t o n . H o w c an w e b e s u r e t h a t w e a r e i n d e edm e a s u r i n g t h e s t r u c t u r e o f t h e p r o t o n ? V i r t u a l p h o t o n s h a v e n o s t r u c t u r e . I s t h a t a l w a y st r u e ? W e k n o w t h a t r e a l p h o t o n s h a v e s t ru c t u r e ; w e e v en m e a s u r e t h e p h o t o n s t r u c t u r ef u n c t i o n F ~ [ 4 ] . L e t u s d i s c u s s t h i s p o i n t f u r t h e r i n t h e n e x t s u b s e c t i o n s .2 .2 . T h e f l u c t u a t i n g p h o t o n

H o w i s i t p o s s i b l e t h a t t h e p h o t o n , w h i c h i s t h e g a u g e p a r t i c l e m e d i a t i n g t h e 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 , h a s a h a d r o n i c s t r u c t u r e ? I o ff e 's a r g u m e n t [ 6 ]: t h e p h o t o n c a nf luc tua te in to q0 pa i r s j u s t l ike it f l uc tua tes in to e+ e - pa i r s ( see f igu re 2 ). I f t he f luc-t u a t i o n t i m e , d e f i n e d i n t h e p r o t o n r e s t f r a m e a s t I ~ ( 2 E ~ ) / m ~ o , i s m u c h l a r g e r t h a nt h e i n t e r a c t i o n t i m e , t in t ~ rp , t h e p h o t o n b u i l d s u p s t r u c t u r e i n t h e i n t e r a c t i o n . H e r e ,E ~ i s t h e e n e r g y o f t h e f l u c t u a t i n g p h o t o n , mqct i s t h e m a s s i n t o w h i c h i t f l u c t u a t e s , a n drp is t h e r a d i u s o f t h e p r o t o n . T h e h a d r o n i c s t r u c t u r e o f t h e p h o t o n , b u i l t d u r i n g t h e

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F i g u r e 3 . A d i a g r a m d e s c r i b i n g a D I S p ro -c e s s o n a q u a s i - r e a l p h o t o n u s i n g t h e r e -a c t i o n e + e - ~ e + e - X .

i n t e r a c t i o n , c a n b e s t u d i e d b y m e a s u r i n g t h e p h o t o n s t r u c t u r e f u n c t i o n F ~ i n a D I S t y p eo f e x p e r i m e n t w h e r e a q u a s i - re a l p h o t o n is p r o b e d b y a v i rt u a l p h o t o n , b o t h o f w h i c h a r eem i t t e d in e+ e - co l li s ions , as desc r ibed in f igu re 3. T h i s d i ag ram i s very s imi l a r t o th a ti n D I S o n a p r o t o n t a r g e t ( f i g u r e 1 ) .


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2.3 . Structure of v ir tual photons?D o e s a v i r t u a l p h o t o n a ls o f l u c t u a te a n d a c q u ir e a h a d r o n i c s t r u c t u r e ? T h e f l u c t u a t i o n

t i m e o f a p h o t o n w i t h v i r t u a l i t y Q 2 is g i v e n b y t f ~ ( 2 E ~ ) /( m 2 q o + Q 2 ) , a n d t h u s a t v e r yh i g h Q 2 o n e d o e s n o t e x p e c t t h e c o n d i t i o n t I >> t int t o h o ld . H o w e v e r a t v e r y la r g e p h o t o ne n e r g ie s , o r a t v e r y l ow x, t h e f l u c t u a t i o n t i m e i s i n d e p e n d e n t o f Q 2 : t f ~ _ 1 / ( 2 m p x ) , w h e r em p is t h e p r o t o n m a s s , a n d t h u s e v e n h i g h l y v i r t u a l p h o t o n s c a n a c q u i r e s t r u c t u r e . F o ri n s ta n c e , a t H E R A p r e s e n t l y W ~ 2 0 0 - 3 00 G e V , a n d s in c e x ~ Q 2 / ( Q 2 + W 2 ) , z c a nbe as low as 0 .01 even fo r Q 2 = 1000 G e V 2. In th i s case , t he f luc tua t io n t im e w i ll bev e r y l a r g e c o m p a r e d t o t h e i n t e r a c t i o n t i m e a n d t h e h i g h l y v i r t u a l p h o t o n w i l l a c q u i r ea h a d r o n i c s t r u c t u r e . H o w d o w e i n t e r p r a t e t h e D I S d i a g r a m o f f i gu r e 1 i n t h i s c a se ?W h o s e s t r u c t u r e d o we m e a s u r e ? D o w e m e a s u r e t h e s t r u c t u r e o f t h e p r o t o n , f r o m th ev i e w p o i n t o f t h e p r o t o n i n f in i te m o m e n t u m f ra m e , o r do w e m e a s u r e t h e s t r u c t u r e o f t h ev i r t u a l p h o t o n , f r o m t h e p r o t o n r e s t f r a m e v i e w ? W h o i s p r o b i n g w h o m ?W h e n a s k e d t h i s q u e s t i o n , B j o r k e n a n s w e r e d [ 7 ] t h a t p h y s i c s c a n n o t b e f r a m e d e p e n -d e n t a n d t h e r e f o r e i t d o e s n ' t m a t t e r : w e c a n s a y t h a t w e m e a s u r e t h e s t r u c t u r e o f t h ep r o t o n o r we c a n s a y t h a t w e s t u d y t h e s t r u c t u r e o f t h e v i r t u a l p h o t o n . I w il l t r y t oc o n v i n c e y o u a t t h e e n d o f m y t a l k t h a t t h i s a n s w e r m a k e s s e n s e .3 . T H E S T R U C T U R E O F T H E P R O T O N

I n t h i s s e c t i o n w e w i l l r e f r a i n f r o m d i s c u s s i n g t h e q u e s t i o n p o s e d a b o v e a n d w i l l a c c e p tt h e i n t e r p r e t a t i o n o f m e a s u r i n g t h e s t r u c t u r e o f t h e p r o t o n v i a t h e D I S d i a g r a m i n f ig u re 1.W e p r e s e n t b e l o w i n f o r m a t i o n a b o u t t h e s t r u c t u r e o f t h e p r o t o n a s se e n fr o m t h e D I Ss t u d i e s a t H E R A .3 .1 . HERA

W i t h t h e a d v e n t o f t h e H E R A e p c o ll id e r t h e k i n e m a t i c p l a n e o f x - Q 2 h a s b e e n e x t e n d e db y 2 o r d e r s o f m a g n i t u d e i n b o t h v a r i a b l e s f r o m t h e e x i s t i n g f ix e d t a r g e t D I S e x p e r i m e n t s ,as dep ic t ed in f igu re 4 .

T h e D I S c r o s s s e c t i o n f o r el ) - - - . e X can be w r i t t e n ( for Q 2 0 , (3)

w h e r e t h e l o n g i t u d i n a l s t r u c t u r e f u n c t io n F L c o n t ri b u t e s i n a n i m p o r t a n t w a y o n ly a tl a rge y .


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Figure 4 . The x - Q 2 k inemat ic p laneof some of the f ixed targ et and of theHERA co l l ider DIS exper imen ts .

The mot iva t ion fo r measur ing F 2( x , Q 2) can be summar ized as follows: (a) t es t theva l id ity of per tu rba t ive QC D (pQC D) ca lcu la t ions , (b ) decompose the p ro ton in to quarksand g luons , and (c ) search fo r p ro ton subs t ruc tu re .3 .2 . Q C D e v o l u t i o n - s c a l in g v i o l a t io n

Q uar ks r adi ate g luons; g luons spl it and produ ce m ore g luons at low x and also q~ pairsat low x . This Q CD evolut ion chain is usual ly described in leading order by spl i t t ingfunc t ions Pij, as shown in f igure 5. This proc edur e leads to scal ing v io lat ion in the

g gp!0Pqg = =

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Figure 5 . Spl i t t ing funct ions Pi j in leadingorder, descr ib ing the sp l i t t ing o f par ton jin to par ton i .

fo l lowing way: there is an increase of F2 with Q2 at low x and a decrease at h igh x .Sca l ing ho lds a t abou t x=O.1. The data fo l lows th is predict ion of QCD, as can be seenin figure 6.3 . 3 . O v e r v i e w of F2

The f ixed ta rge t exper imen ts p rov ided in fo rmat ion a t re la t ive ly h igh x and thus enab ledthe s tudy o f the be hav iour o f va lence quarks . The f ir st H ER A resu l t s showed a su rpr is ing ly


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F i g u r e 6 . C o m p a r i s o n o f t h e s c a l i n g v i o l a t io n b e h a v i o u r o f F 2 w i t h t h e r e s u l t s o f a n e x t -t o - le a d i n g o r d e r D G L A P e v o l u ti o n e q u a ti o n.

s t r o n g r i s e o f F 2 a s x d e c r e a s e s . A n e x a m p l e o f s u c h a r i s e i s g i v e n i n f ig u r e 7 w h e r e / 1 2i n c r e a s e s a s x d e c r e a s e s , f or a f ix e d v a l u e o f Q 2 = 1 5 G e V 2. T h i s i n c r e a s e i s t h e r e s u l t

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F i g u r e 7 . T h e p r o t o n s t r u c t u r e f u n c t io nF 2 , a s func t ion o f x , a t Q2 = 1 5 G eV 2 , f o rH E R A a n d s o m e fix e d ta r g e t d a t a.

o f t h e r is i n g g l u o n d e n s i t y a t lo w x . N o t e t h e g o o d a g r e e m e n t b e t we e n b o t h H E R Ae x p e r i m e n t s , H 1 a n d Z E U S , a n d a l s o b e t w e en H E R A a n d th e fi xe d t ar g e t d a t a .3 . 4 . E v o l u t i o n o f F 2

T h e m e a s u r e m e n t s o f F 2 a s f u n c ti o n o f x a n d Q 2 c a n b e u s e d t o o b t a i n i n f or m a t io na b o u t t h e p a r t o n d e n s i t i es i n t h e p r o t o n. T h i s is d o n e b y u s in g t h e p Q C D D G L A Pe v o l u t i o n e q u a t i o n s . O n e c a n n o t c a lc u l a t e e v e r y t h i n g fr o m f ir s t p r i n c i p le s b u t n e e d s a si n p u t f r o m t h e e x p e r i m e n t t h e p a r t o n d e n s i t i e s a t a s c a l e Q g, u s u a l l y t a k e n a s a fe w G e V 2 ,a b o v e w h i c h p Q C D is b e li e v e d t o b e a pp l ic a b le .


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T h e r e a r e s e v e r a l g r o u p s w h i c h p e r f o r m Q C D f i ts , t h e m o s t n o t a b l e a r e M R S T [ 10 ] a n dC T E Q [ 1 1 ] . T h e y p a r a m e t e r i z e t h e z d e p e n d e n c e o f t h e p a r t o n d e n s i t i e s a t Q02 i n t h ef o r m ,x q ( x , Q 2 ) r ~ X ~ 1 9 (1 - z ) '7 2 . f ~ o o t h ( z ) . (4)T h e f r e e p a r a m e t e r s l i k e 7 1 1 an d r /2 a re a d ju s t e d to f it t he d a t a fo r Q 2 > Q o . A n ex am ple

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, ~ . . .. . . .. . ~ . . . . . . . . . . . . . . . . . . . , . . . . .. . .. , . . .. . . .. .2i '45 0 1200 0"--20O0 O'--3O0OJ--e50 O'--800 O'--SO0)

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . . .1 0 " l O ' G 1 0 " e l O ' 4 I 1 0 - ' 1 0 " ~ 1 0 " 4 1 0 ' I I 0 " 1 0 ' 4 1 0 " m | 0 " * 1 l O " * l O ' m t O 4 t O - ~ 1 1 0 " * 1 0 " m ) 0 " ~ t % 1

9 Z E U S 9 4 N V X1m Z E U S 9 4 ~ - H1 9 4 ( ( ~ i n p o r e n , w h e r e d i f f e r e n t )9 Z E U S g 4 I SR :3 ~ D M S , N M C . E 6 6 5

Figu re 8 . F2 as func-t ion o f z , fo r fixed Q 2va lues ( in G e V 2 ) as i n -d ica t ed in the f igu re , fo rt h e H E R A '9 4 d a t a t o -g e t h e r w i t h s o m e f i x e dt a r g e t d a t a . T h e c u r v esa r e t h e r e s u l t o f a N L OQ C D f i t .

o f s u c h a n e v o l u t i o n s t u d y c a n b e s e e n i n f i g u r e 8 w h e r e t h e F 2 d a t a a r e p r e s e n t e d a sfunc t ion o f z fo r fixed Q 2 va lues . T h e increase o f F2 w i th d ecrea s ing z i s seen over thew h o l e r a n g e o f m e a s u r e d Q 2 v a lu e s . T h e p Q C D f it s g iv e a g o o d d e s c r i p t i o n o f t h e d a t ad o w n t o s u r p r i s i n g l y l o w Q 2 v a l u e s .

T h e r e s u l t i n g p a r t o n d e n s it ie s f r o m t h e M R S T p a r a m e t e r i z a t i o n a t Q 2 = 2 0 G e V 2 a r es h o w n i n f ig u r e 9. O n e s e e s t h e d o m i n a n c e o f t h e u v a l e nc e q u a r k a t h i g h x a n d t h e s h a r pr i se o f t h e s e a q u a r k s a t l ow x . I n p a r t i c u l a r , t h e g l u o n d e n s i t y a t l o w x r is e s v e r y s h a r p l yan d h as a va lue o f mo re th an 20 g luons pe r un i t o f r ap id i ty a t x ~ 10 -4 . In figu re 10 ones e es t h e e x t r a c t e d g l u o n d e n s i t y b y t h e H 1 e x p e r i m e n t [ 12 ] a t t h r e e d i f fe r e n t Q 2 v a l ue s .T h e d e n s i t y o f t h e g l u o n s a t a g i v e n lo w x in c r e a s e s s t r o n g l y w i t h Q 2.3 . 5 . R i s e o f F2 w i t h d e c r e a s i n g x

T h e r a t e o f t h e r i s e o f F 2 w i t h d e c r e a s i n g x i s Q 2 d e p e n d e n t . T h i s c a n b e c l e a r l y s e e nin figu re 11 w h ere F2 i s p lo t t ed as a func t ion o f z fo r t h ree Q 2 va lues . T h e r a t e o f r i sed e c r e a s e s a s Q 2 g e t s s m a l le r . W h a t c a n w e s a y a b o u t t h e r a t e o f r is e ? T o w h a t c a n o n e


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c o m p a r e i t ?~o~(~*p), T h e p r o t o n s t r u c t u r e f u n c t i o n F 2 i s r e l a t e d t o t h e t o t a l 7 * P c r o s s s e c t i o nQ2(1 - z) Q2 Q2

F2 = 47r2a Q2 + 4m ~,z2 ~Ttot(~/*P) ~ 47c2c a to t (7*P) , (5)w he re the ap pro x im ate s ign ho lds for l ow x . S ince w e have a be t t e r f ee l ing fo r t hebe hav iou r o f t he to t a l c ro ss sec t ion w i th energy , w e p lo t i n f igu re 12 the F2 da ta conv er t edt o (Ttot(~*p) as func t ion o f W 2 fo r f ixed va lues o f Q 2 . Fo r com par i so n w e p lo t a l so theto t a l ~/p c ross sec t ion . O ne sees th a t t he sha l low W be hav iou r o f t he to t a l 7p c rosss e c t i o n c h a n g e s t o a s t e e p e r b e h a v i o u r a s Q2 i n c re a s e s . T h e c u r v e s a r e t h e r e s u l t s o f t h eA L L M 9 7 [1 3] p a r a m e t e r i z a t i o n ( se e b e l ow ) w h i c h g i ve s a g o o d d e s c r i p t i o n o f t h e t r a n s i t i o ns e e n i n t h e d a t a .3 . 6 . T h e t r a n s i t i o n r e g i o n

T h e d a t a p r e s e n t e d a b o v e s h o w a c l e a r c h a n g e o f t h e W d e p e n d e n c e w i t h Q 2. A t Q 2 = 0t h e p r o c e s s e s a r e d o m i n a n t l y n o n - p e r t u r b a t i v e a n d t h e r e s u l t i n g r e a c t i o n s a r e u s u a l l yn a m e d a s ' s o f t' p h y s ic s . T h i s d o m a i n i s w e ll d e s c r i b e d i n t h e R e g g e p ic t u r e . A s Q2i n c r ea s e s , t h e e x c h a n g e d p h o t o n i s e x p e c t e d t o s h r in k a n d o n e e x p e c t s p Q C D t o t a k e


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o v e r. T h e r e a c t i o n s a r e s a i d t o b e ' h a r d ' . W h e r e d o e s th e t r a n s i t i o n f r o m s o f t t o h a r dp h y s i c s t a k e p l a c e ? I s i t a s m o o t h o r a b r u p t o n e ? I n t h e f o ll o w in g w e d e s c r i b e t w op a r a m e t e r i z a t i o n s , o n e f u l l y b a s e d o n t h e R e g g e p i c t u r e w h i l e t h e o t h e r c o m b i n e s t h eR e g g e a p p r o a c h w i t h a Q C D m o t i v a t e d o n e .3 . 7 . E x a m p l e o f t w o p a r a m e t e r i z a t i o n s

D o n n a c h i e a n d L a n d s h o f f ( D L ) [ 14 ] s u c c e e d e d t o d e s c r i b e al l e x i s t i n g h a d r o n - p r o t o nt o t a l c r o s s s e c t i o n d a t a i n a s im p l e R e g g e p i c t u r e b y u s i n g a c o m b i n a t i o n o f a P o m e r o na n d a R e g g e o n e x c h a n g e , t h e f o r m e r r i si n g sl o w ly w h i le t h e l a t t e r d e c r e a s i n g w i t h e n e r g y ,( 7 t o t ~ - - - X s 0 " 0 8 J r - y s -0.45, (6)w h e r e s i s t h e s q u a r e o f t h e t o t a l c e n t e r o f m a s s e n e r gy . T h e t w o n u m e r i c a l p a r a m e t e r ,r e l a t e d t o t h e i n t e r c e p t s c ~( 0) o f t h e P o m e r o n a n d R e g g e o n t r a j e c t o r i e s , r e s p e c t iv e l y , a r et h e r e s u l t o f f i t t in g t h i s s i m p l e e x p r e s s i o n t o a l l av a i la b l e d a t a , s o m e o f w h i c h a r e s h o w nin the f i rs t tw o p lo t s i n f igu re 13 . T he se p ara m ete r s g ive a l so a go od desc r ip t io n o f t het o t a l ~ /p c r o s s s e c t i o n d a t a w h i c h w e r e n o t u s e d i n t h e f i t a n d a r e a l s o s h o w n o n t h e r i g h th a n d s i de o f t h e f ig u re . D o n n a c h i e a n d L a n d s h o f f w a n t e d t o e x t e n d t h i s p i c t u r e a l so t ov i r t u a l p h o t o n s [ 15 ] ( fo r Q 2 < 1 0 G e V 2 ) , k e e p i n g t h e p o w e r o f W 2, w h i c h i s r e l a t e d t o


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2 0 1 0 0 , a ' 5 1 0 " ' ' ' ' | ' ' ' 5 " ' ' ' 0 1 " 0 0 ' ' '6 10 100 5 0 0"Js (eeV) W[GeV]F ig u r e 1 3 . T h e t o t a l c r o s s s e c t i o n d a t a o f pp, pp, 7r+p and ~ /p as func t ion o f the cen te r o fm a s s e n e r g y. T h e d i ff e re n t l in e s a r e t h e r e s u l ts o f p a r a m e te r i z a t i o n s t o t h e s e d a t a ( se et e x t ) .

t h e P o m e r o n in t e r c e p t , f ix e d w i th Q 2 . T h e i r m o t iv a t i o n w a s t o s ee w h a t i s t h e e x p e c t e dc o n t r i b u t io n f r o m n o n - p e r tu r b a t i v e p h y si c s, o r s o ft p h y s ic s a s w e c a l le d i t a b o v e , a t h ig h e rQ2.

T h e o th e r e x a m p le i s t h a t o f A b r a m o w ic z , L e v in , L ev y , M a o r ( A L L M ) [ 16 ], w h ic h w a su p d a t e d b y A b r a m o w i c z a n d L e v y ( A L L M 9 7 ) [ 13 ]. T h i s p a r a m e t e r i z a t i o n u s es a R e g gem o t i v a t e d a p p r o a c h a t l o w z t o g e t h e r w i t h a Q C D m o t i v a t e d o n e a t h ig h z t o p a r a m e t e r i z ethe w ho le ( z , Q2) phas e space , f i t t ing a ll ex is t ing F2 da ta . Th is pa ram ete r iza t ion uses aso -ca l led in te rp l ay o f so f t and hard phys ics ( see [17 ]) .

T h e tw o p a r a m e te r i z a t i o n s a r e c o m p a r e d [1 8] t o t h e lo w Q 2 H E R A d a t a t o g e th e r w i thth a t o f the f ixed ta rge t E665 expe r ime n t in f igu re 14. Here one sees aga in how the c rosssec t ion ch anges f rom a (W2) ~176 eha v iou r a t ve ry low Q2 to a (W 2) 0"2-0"4 as Q2 increases .T h e s i m p l e D L p a r a m e t e r i z a t i o n a s im p l e m e n t e d b y Z E U S ( Z E U S R E G G E i n t h e f ig u re )f a il s to de scr ibe th e da ta above Q2 N 1 GeV 2. AL LM 97 descr ibes the da ta w el l in thew h o le r e g io n . D L 9 8 [ 1 9] , w h ic h a d d s t o t h e s of t P o m e r o n a n a d d i t i o n a l h a r d P o m e r o n ,can a l so descr ibe the da ta , b u t lo ses the s impl ic i ty o f the o r ig ina l DL one .

O n e c a n q u a n t i f y t h e c h a n g e i n t h e r a t e o f i n c re a s e b y u s in g t h e p a r a m e te r A. S in ce( T t o t ~ " (W2) a (0 )- I th i s impl ies th a t F2 ~ x - a . The f i t t ed va lue o f A as func t ion o f Q2 isshow n in f igu re 15 fo r the ZEU S [20] (upper ) and th e H1 [21] ( lower ) expe r ime n ts . Ones e es a c l e a r i n c re a s e o f A w i th Q 2 w h ic h c a n n o t b e r e p r o d u c e d b y t h e s im p le R e g g e p i c tu r ebu t ne eds an app roac h in wh ich there i s the in te rp lay o f so f t and h ard phys ics [17] .3 .8 . W h a t h a v e w e l e a r n e d a b o u t t h e s t r u c t u r e o f t h e p r o t o n ?

L e t u s s u m m a r i z e w h a t w e ha v e l e a r n e d so f a r a b o u t t h e s t r u c tu r e o f t h e p r o to n .9 T h e d e n s i t y o f p a r to n s i n t h e p r o to n i n c r e as e s w i th d e c r e a s ing z .

The r a te o f increase i s Q2 depe nden t ; a t h igh Q2 the increase fo llows the e xpe c ta t io nsf r o m th e p Q C D h a r d p h y s ic s w h i le a t l o w Q2 th e r a t e is d e sc r ib e d b y t h e s o f t p h y s i c sb e h a v io u r e x p e c t e d b y t h e R e g g e p h e n o m e n o lo g y .Th ou gh there seems to be a t r a ns i t i on in the r eg ion o f Q2 N 1 -2 GeV 2, there i s anin t e r p l a y b e tw e e n th e s o f t a n d h a r d p h y s i c s i n b o th r e g io n s .


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F i g u r e 1 5. T h e Q 2 d e p e n d e n c e o f t h e p a -r a m e t e r A, d e t e r m i n e d f r o m a f it o f t h eform F2 ~ x -x at f ixed Q2 values .

4 . T H E S T R U C T U R E O F T H E P H O T O NI n th i s p a r t w e w i ll d e s c r i b e w h a t i s p r e s e n t l y k n o w n a b o u t t h e s t r u c t u r e o f t h e p h o t o n ,

b o t h f r o m e + e - e x p e r i m e n t s a s w e ll a s f r o m H E R A .4 . 1 . P h o t o n s t r u c t u r e f r o m e + e -

T h e h a d r o n i c s t r u c t u r e f u n c t i o n o f t h e p h o t o n , F ~ , w a s m e a s u r e d i n e + e - c o ll is i on sw h ich can be in t e rp re t ed as dep ic t ed in f igu re 3 . A h igh ly v i r tua l 7 " w i th l a rge Q 2 p robesa quas i - r ea l 7 w i th p2 ~ 0 .

T h e m e a s u r e m e n t s o f F s ~ s h o w e d a d if f er e n t b e h a v i o u r t h a n t h a t o f t h e p r o t o n s t r u c t u r efunc t ion . F ro m the Q 2 depe nden ce , show n in f igu re 16 [4] , one sees pos i t i ve sca l ing v io la -t i o n f or a ll x . T h i s d i f fe r e n t b e h a v i o u r c a n b e u n d e r s t o o d a s c o m i n g f r o m a n a d d i t i o n a lsp l i t t i ng to the ones p resen t i n the p ro to n case ( see f igure 5 ) . In the ph o to n case , t hep h o t o n c a n s p l i t i n t o a q ~ p a i r , ~ / ~ q ~. T h e c o n t r i b u t i o n r e s u l t i n g f ro m t h i s s p li t ti n g ,ca l l ed the ' box d i ag ram ' , causes pos i t i ve sca l ing v io l a t ion fo r a l l x . In add i t ion , and aga in


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- - - - - - - - ~ + 4 t =. 8 3 0 = = 1 , 3 . 7 6 . . . ~ + _ ~:1 2= 4 . 3. .. +_ + ~ p { .] + 4 p ~ t 0 = = T + 5 " 0 9 1 0 = = -- ~ l -M p S " 0 = 4 ~ ._ ~ ._ + _ _ {.=. 3 .

~ ' ~ IY : : : . '. : ( ~ P A L : " _ L : d P a L i : J ' O L U ~ '6 L _ X L E b ' H : _ _ : L 3 : : : _ ' . : d e , ~ h , '_Q = 6 . 8 @ = 7 . 5 ~ L 0 = = 9 ] 0 = = 9 . 2 . . 0 = = 9 . 9 . 0 = = 1 0 . 8 0 = = 1 2 :. . , .~EL~'hl ' 'ALEON '4 dPAL' '4 'OPAL' " :_ ~ lS.3 -- ~bPX~ ' XLEPN0 = = 1 3 Q = = 1 3 . 7 _ 0 = = 1 4 - . 5 0 = = 1 4 . 7 . (:} 2 = 1 6 Q = = 2 0 . 7. . . . . - . . - ++ + _ . r

:% i- I L ' ,J P A L _ 6 f L ~ ' h lg _ l _ # ~ l L I 3 I I , I , ' 'TASSu JrL Q A ~ L . E s ~ 6 !" : _ . : ~ P A L = : :. " A ~ f " (' I _ .~ . ~ '" ~ A O _ ~ 0 = = 9 9 , Q ' = I O 0 + 1 . Q :L _ _ ~ , - b + ~

F i gure 1 7 . F ~ , a s func t ion o f x , f o r f ixedQ~ a s g iv en i n the fi gure . T he d ata po i nt sh a v e b e e n t a k e n f r o m t h e n u m e r i c a l ta b l e sin [4].

c o n t r a r y t o t h e p r o t o n c a s e , i t a l s o c a u s e s t h e p h o t o n s t r u c t u r e f u n c t i o n t o b e l a r g e f o rh i g h x v a l u e s , a s c a n b e s e e n i n f i g u r e 1 7 w h e r e F ~ i s p l o t t e d a s f u n c t i o n o f x f o r f i x e dQ 2 v a l u e s . F r o m t h i s f i g u r e o n e c a n a l s o s e e t h a t t h e r e e x i s t v e r y l i t t l e d a t a i n t h e l o w xr e g i o n .

4 . 2 . P h o t o n s t r u c t u r e f r o m H E R AAt HERA, the structure of the photon can be studied by selecting events in which the

exchanged photon is quasi-real and the probe is provided by a large transverse momentumpar ton from the proton. The probed photon can parti cipate in the process in two ways.In one, the interaction takes place before it fluctuates into a q~ pair and thus the wholeof the photon parti cipates in the interaction. Such a process is called a 'direct' photoninteraction. In the other case, the photon first fluctuates into partons and only one ofthese parton s participates in the interaction while the rest continue as the photon remnant.This process is said to be a 'resolved' photon interaction. An example of leading orderdiagrams describing dijet photoproduction for the two processes is shown in figure 18.If one defines a variable x~ as the fraction of the photon momentum taking part in adijet process, we expect xz ~ 1 in the direct case, while x~


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t o p r o d u c t i o n a s f u n ct i o n o f z ~ a n d t o s u b t r a c t t h e c o n t r i b u t i o n c o m i n g f ro m t h e d i r ec tph o to n re a c t io n s . Th i s i s s h o wn in f ig u re 2 0, wh e re th e m e a s u re m e n ts a re p re s e n te d a t

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Fig ure 20. D istr ibu tio ns of ~?'~~ for differentth re s h o ld s o n th e h ig h e s t t r a n s v e rs e e n e rg y j e t.T h e o p e n h i s t o g r a m is t h e p r e d i c t i o n o f t h e M C ,a n d th e s h a d e d pa r t i s th e d i re c t ph o to n c o m-p o n e n t o f t h e M C .

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Fig u re 21 . Co m pa r i s o n o f th e ph o -to n g lu o n d e n s i ty , d e te rmin e d f ro md i - j e t ph o to pro d u c t io n e v e n t s t a k e nin 1 9 9 6 , w i th e a r l i e r me a s u re me n tsof H1. Th e curves a re the expe c ta -t io n s o f di f fe ren t pa ra m e te r i z a t io n s .

f i x e d v a l u e s o f t h e h a r d s c a l e , w h i c h i s t a k e n a s t h e h i g h e s t t r a n s v e r s e e n e r g y j e t [ 2 3 ] . O n ec a n g o o n e s t e p f u r t h e r b y a s s u m i n g l e a d i n g o r d e r Q C D a n d M o n t e C a r l o ( M C ) m o d e l st o e x t r a c t t h e e f f e c t i v e p a r t o n d e n s i t i e s i n t h e p h o t o n . A n e x a m p l e o f t h e e x t r a c t e d g l u o nd e n s i t y i n t h e p h o t o n [ 2 4 ] i s s h o w n i n f i g u r e 2 1 . T h e g l u o n d e n s i t y i n c r e a s e s w i t h d e -c r e a s i n g x , a s i m i l a r b e h a v i o u r t o t h a t o f t h e g l u o n d e n s i t y i n t h e p r o t o n . T h e d a t a h a v e


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t h e p o t e n t i a l o f d i f f e r e n t i a t i n g b e t w e e n 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 o f t h e p a r t o n d e n s i t i e si n t h e p h o t o n , a s c a n b e s e e n i n t h e s a m e f i g u r e .4 . 3 . V i r t u a l p h o t o n s a t H E R AO n e c a n s t u d y t h e s t r u c t u r e o f v i r t u a l p h o t o n s i n a s i m i l a r w a y a s d e s c r i b e d a b o v e . I nt h i s c a se , t h e Q 2 o f t h e v i r t u a l p h o t o n h a s t o b e m u c h s m a l l e r t h a n t h e t r a n s v e r s e e n e r g ys q u a r e d o f t h e j e t , E t2, w h ich p rov ides the h ard sca l e o f t he p robe . Such a s tu dy [25 ]i s p re sen ted in figu re 22, w here the d i j e t c ro ss sec t ion i s p lo t t ed as func t ion o f x~ fo rd i f f e ren t r eg ions in Q 2 and E t2. O ne sees a c l ea r excess over the ex pec ta t io n o f d i r ec tp h o t o n r e a c t i o n s , i n d i c a t i n g t h a t v i r t u a l p h o t o n s a l s o h a v e a r e s o l v e d p a r t . T h i s f a c t c a n

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F i g u r e 2 3 . T h e r a t i o o f t h e r e s o l v e d t od i r e c t p h o t o n c o m p o n e n t , a s f u n c t i o n o ft h e v i r t u a l i t y Q 2 ( i n G e V 2 ) o f t h e p h o t o n .

a l so bee n seen in f igu re 23 w he re the r a t io o f r eso lved to d i r ec t ph o to n in t e rac t ions i sp l o t t e d a s fu n c t i o n o f t h e v i r t u a l i t y Q 2 of t h e p r o b e d p h o t o n [ 26 ]. O n e s e e s t h a t a l t h o u g hthe r a t io decreases w i th Q 2 , i t r emains non -zero even a t r e l a t ive ly h igh Q 2 va lues .4 . 4 . V i r t u a l p h o t o n s a t L E P

T h e s t u d y o f t h e s t r u c t u r e o f v i r t u a l p h o t o n s i n e + e - r e a c t i o n s w a s d o r m a n t f or m o r et h a n 1 5 y e a r s fo l lo w i ng t h e m e a s u r e m e n t d o n e b y t h e P L U T O c o l l a b o r a t i o n [ 27 ]. R e c e n t l y ,h o w e v e r, t h e L 3 c o l l a b o r a t i o n a t L E P [2 8] m e a s u r e d t h e s t r u c t u r e f u n c t i o n o f p h o t o n s w i t ha v i r tu a l i t y o f 3 .7 G eV 2, u s ing as p robes pho tons w i th a v i r tu a l i t y o f 120 G eV 2. In thes a m e e x p e r i m e n t , t h e s t r u c t u r e f u n c t i o n o f r e a l p h o t o n s w a s a ls o m e a s u r e d . B o t h r e s u l t s


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c a n b e s e e n i n f i g u r e 2 4 a n d w i t h i n e r r o r s t h e s t r u c t u r e f u n c t i o n o f t h e v i r t u a l p h o t o n s i so f t h e s a m e o r d e r o f m a g n i t u d e a s t h a t o f t h e r e a l o n e s . T h e e f f e c t i v e s t r u c t u r e f u n c t i o ni s a l s o p r e s e n t e d a s f u n c t i o n o f t h e v i r t u a l i t y o f t h e p r o b e d p h o t o n p 2 i n f i g u r e 2 5 a n ds h o w v e r y l i t t l e d e p e n d e n c e o n p 2 u p t o v a l u e s o f ~ 6 G e V 2 [ 2 7 , 2 8 ] .4 . 5 . W h a t h a v e w e l e a r n e d a b o u t t h e s t r u c t u r e o f t h e p h o t o n ?

L e t u s s u m m a r i z e w h a t w e h a v e l e a r n e d s o f a r a b o u t t h e s t r u c t u r e o f t h e p h o t o n .9 A t H E R A o n e c a n s e e c l e a r s i g n a l s o f t h e 2 - c o m p o n e n t s t r u c t u r e o f q u a s i - r e a l p h o -

t o n s , a d i r e c t a n d a r e s o l v e d p a r t .9 V i r t u a l p h o t o n s c a n a l s o h a v e a r e s o l v e d p a r t a t l o w x a n d f l u c t u a t e i n t o q q p a i r s .9 S t r u c t u r e o f v i r t u a l p h o t o n s h a s b e e n s e e n a l s o a t L E P .

5 . T H E A N S W E RF o l l o w i n g t h e t w o s e c t i o n s o n t h e s t r u c t u r e o f t h e p r o t o n a n d t h e p h o t o n , l e t u s r e m i n d

o u r s e l v e s a g a i n w h a t o u r o r i g i n a l q u e s t i o n w a s . A t l o w x w e h a v e s e e n t h a t a ~ 7 " c a nh a v e s t r u c t u r e . D o e s i t s t i l l p r o b e t h e p r o t o n i n a n e p D I S e x p e r i m e n t o r d o e s o n e o f t h ep a r t o n s o f t h e p r o t o n p r o b e t h e s t r u c t u r e o f t h e " 7 * ?


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T h e a n s w e r is j u s t a s B j o r k e n s a id : a t lo w x i t d o e s n o t m a t t e r . B o t h i n t e r p r e t a t i o na r e c o r r e c t . T h e e m p h a s i s i s h o w e v e r ' a t l ow x ' . A t l ow x t h e s t r u c t u r e f u n c t i o n s o f t h ep r o t o n a n d o f t h e p h o t o n c a n b e r e l a te d t h r o u g h G r i b o v f a c t o r iz a t i o n [ 29 ]. B y m e a s u r i n go n e , t h e o t h e r c a n b e o b t a i n e d f r o m i t t h r o u g h a s i m p l e r e l a t io n . T h i s c a n b e se e n asfollows.

G r ibo v s how ed [29 ] th a t t he 3 '~ , ~/P an d pp t o t a l c r o s s s e c t i o n s c a n b e r e l a t e d b y R e g g efac to r i za t ion as fo l low s :

~ , ( w ~ )~ ( w ~.) - . (7)~pp(W 2)T h i s r e l a t i o n c a n b e e x t e n d e d [ 1 ] t o t h e c a s e w h e r e o n e p h o t o n i s r e a l a n d t h e o t h e r i sv i r t u a l ,~ . ~ ( w ~ Q ~) - ~ . p ( w ~, Q ~ ) ~ p ( w ~) ( 8 )

o r t o t h e c a s e w h e r e b o t h p h o t o n s a r e v i r t u a l ,~ . ~ . ( w ~ , Q~ , p ~ ) = ~ -~ .p( ~ , Q ~ ) ~ . p ( w ~ , P~ )

~ , , p ( w 2 ) (9 )47r2o~S i n c e a t l ow x o n e h a s cr ~ ~ F 2 , o n e g e t s t h e f o ll o w in g r e l a t i o n s b e t w e e n t h e p r o t o n

s t r u c t u r e f u n c t i o n F ~ , t h e s t r u c t u r e f u n c t io n o f a r e a l p h o t o n , F ~ , a n d t h a t o f a v i r tu a lp h o t o n , F s

p ~ ( w ~ Q ~) = F ~ ( W ~ Q~) ~ ( w ~ ), , % ( w ~ ) , (10)

a n d4 ~ F f w ~., Q ~ ) F ~ ( w ~ , p ~ ) ( ~ )r ; ' * ( w ~ ' Q ~' P ~) = P ~ ~ ( w ~ ) "

T h e r e l a t i o n g i v e n i n e q u a t i o n ( 10 ) h a s b e e n u s e d [ 30 ] t o ' p r o d u c e ' F ~ ' d a t a ' f r o m w e llm e a s u r e d F ~~ d a t a i n t h e r e g i o n o f x < 0 . 0 1 , w h e r e t h e G r i b o v f a c t o r i z a t i o n i s e x p e c t e d t oh o l d . T h e r e s u l t s a r e p l o t t e d i n f ig u r e 2 6 t o g e t h e r w i t h d i r e c t m e a s u r e m e n t s o f F ~ . S i n c eno d i r ec t m ea su rem en t s ex i s t i n the very low x r eg ion fo r Q 2 > 4 G eV 2, i t is d if f icu l t t ot e s t t h e r e l a t i o n . H o w e v e r b o t h d a t a s e t s h a v e b e e n u s e d f o r a g l o b a l Q C D l e a d i n g o r d e ra n d h i g h e r o r d e r f i ts [ 3 1] t o o b t a i n p a r t o n d i s t r i b u t i o n s i n t h e p h o t o n . C l e a r l y t h e r e i s an e e d o f m o r e p r e c i s e d i r e c t F ~ d a t a f o r s u c h a s tu d y .I n a n y c a s e , o u r a n s w e r t o t h e q u e s t i o n w o u l d b e t h a t a t l o w x t h e v i r t u a l p h o t o n a n dt h e p r o t o n p r o b e t h e s t r u c t u r e o f e a c h o th e r . I n fa c t, w h a t o n e p r o b e s is t h e s t r u c t u r e o ft h e i n t e r a c t io n . A t h i g h x, t h e v i r tu a l p h o t o n c a n b e a s s u m e d t o b e s t r u c tu r e l e s s a n d i ts t u d i e s t h e s t r u c t u r e o f t h e p r o t o n .


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The Proton and the Photon Who is Probing Whom in Electroproduction

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