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Inelastic electron-photon scattering
Volume 36B, number 2
PHYSICS LETTERS
INELASTIC
ELECTRON-PHOTON
23 August 1971
SCATTERING
T. F. WALSH
Deutsches Elektronen-SynchrotronDESY, Hamburg, Germany Received 19 March 1971
It is suggested that colliding e+e- beam machines may be used to study inelastic electron-photon scattering.
T h e r e have been r e c e n t l y a p p e a r e d s u g g e s t i ons [1] that co l l i d i n g e+e - and e - e - b e a m m a c h i n e s may p r o v e useful in i n v e s t i g a t i n g photonphoton c o l l i s i o n s . The i d e a i s to use as photon b e a m s the i n t en s e v i r t u a l photon s p e c t r u m a c c o m p a n y i n g the e l e c t r o n or p o s i t r o n b e a m s in t he se m a c h i n e s . The v i r u a l photon s p e c t r u m has a ln(E/m e) dependence and the r e s u l t i n g total c r o s s s e c t i o n for the p r o c e s s e+e - --* e+e - + h a d r o n s r i s e s slowly with e n e r g y . T h i s i s in cont r a s t to the one photon annihilation c r o s s s e c t i o n s which d e c r e a s e as E -2 or f a s t e r . The f i r s t sugg e s t i o n s of this kind w e r e made by Low [2] and by C a l a g e r o and Z e m a c h [3]. N u m e r o u s photonphoton r e a c t i o n s can be i n v e s t i g a t e d : 7~/~ 7T°, and o t h e r s . The c r o s s s e c t i o n s a r e all l a r g e enough to be m e a s u r a b l e with e a s e (e.g. that f o r pOpO is = 10 -34 cm 2 at E = 3 GeV). It i s s e n s i b l e , t h e r e f o r e , to see what o th e r p r o c e s s e s of this g e n e r a l s o r t may e x i s t . T h i s note c o n c e r n s one of t h e s e : i n e l a s t i c e l e c t r o n photon s c a t t e r i n g . The i d e a h e r e i s to use the v i r t u a l photon s p e c t r u m on one b e a m as a t a r g e t f o r the other beam of e l e c t r o n s (or p o s i t r o n s ) . One then o b s e r v e s an e l e c t r o n s c a t t e r e d at l a r g e angle with some e n e r g y l o s s t o g e t h e r with a s y s t e m of h a d r o n s (probably pions). We will a s s u m e that the e l e c t r o n which supplies the v i r t u a l photon and i s t h e r e b y s c a t t e r e d at s m a l l (0 ~< 0.1) a n g l e s i s not o b s e r v e d and that the v i r t u a l photons a r e t r a n s v e r s e l y p o l a r i z e d . The r e a s o n for this a s s u m p tion is to enhance the o b s e r v a b i l i t y of the effect by i n t e g r a t i n g o v e r the v i r t u a l photon s p e c t r u m . O t h e r w i s e the c r o s s s e c t i o n s depend s e n s i t i v e l y on the k i n e m a t i c cuts and a r e s i g n i f i c a n t l y s m a l l e r . T h i s a s s u m p t i o n a l s o allows us to use the W e i z a c k e r - V ¢ i l l i a m s a p p r o x i m a t i o n so as to get m o r e t r a n s p a r e n t r e s u l t s . The e r r o r made in this a p p r o x i m a t i o n i s t y p ic a l ly 15% or so
around E = 3 GeV beam e n e r g y . The W e i z a c k e r W i l l i a m s a p p r o x i m a t i o n has been v e r y nicely d i s c u s s e d by K e s s l e r [4] and we r e f e r the r e a d e r to that p a p e r for r e l e v a n t d e t a i l s . The c r o s s sect i o n ai f o r the p r o c e s s e + e e + e + h ad r o n s w h e r e one e l e c t r o n i s s c a t t e r e d , u n o b s e r v e d , at s m a l l angles and the other i s s c a t t e r e d at angle 0 with e n e r g y E ' < E i s given
by [2] d2cri
dQ2dEm= 2 fdk o P(ko)~
(I)
d2
--,
~(e+Vko e ' + h a d r o n s )
with k o the v i r t u a l photon e n e r g y (k 2 = 0), and w h e r e we take f o r the s p e c t r u m
P(ko ) =2a_~leo1E2+(E-ko) 2 22E lnt
~
sin ~10M }
r e t a i n i n g only the leading l o g a r i t h m i c dependence on e n e r g y . T h e r e i s a cutoff on the angle of the u n o b s e r v e d s c a t t e r e d e l e c t r o n 0 M ~ 0.1. Note that we can expect for the total c r o s s sect i o n s o m e t h i n g of the o r d e r of magnitude ( ~ a4 Q ~ i n In (E/m e) w h e r e Q 2 i n i s the l o w e r l i m i t on the s q u a r e d four m o m e n t u m t r a n s f e r ( Q 2 i n ~ 1 GeV 2). The c r o s s s e c t i o n for e + Yk --* e ' + . . . d i f f e r s o f r o m that f o r i n e l a s t i c e l e c t r o n - p r o t o n s c a t t e r i n g in two r e s p e c t s . The proton m a s s is r e p l a c e d by the photon e n e r g y as a s c a l e f o r the t a r g e t s y s t e m , and the l a b o r a t o r y s y s t e m i s not r e l a t e d to the c e n t e r of m o m e n t u m s y s t e m f o r the v i r t u a l photon k and the f a r off m a s s sh el l photon q(k 2=0, q 2 = _ Q 2 = _ 4 E E , sin 2½0) by a s i m p l e boost along q with the t h r e e - m o m e n t a all c o l l i n e a r . One useful f o r m u l a for this c r o s s sect i o n Js (with P=p .Lp', PO=E, P'o = E ' ) 121
Volume 36B, number 2
PHYSICS LETTERS
d2<7(ey ~ e ' + . . . ) ~Ta2 1 1 [ W(~)(k.q,q2) dQ2dE' (Q2)2 E 2 2k o Q2 + ½[-(k. q)2 + (k. p)2]
W~7) (k. q,
and another (which shows how the fined) i s
q2)]
W(7) a r e
(2) de-
d2cr(ey~e'+...) 2va 2 E ' 1 dQ2dE, =(Q2)2 E- 2k~ ×
[ 2 sin2 ½OW~Y)(k'q ,q2) +4k2 cos2 ½OW2( k.q ,q2) ] . We wish now to define the new functions
F(.y)
such that the c r o s s s e c t i o n s b e c o m e s d2cr/ a3 1 f~[l+(l_pP~l) dQ2dE , ~ ~ ~-~ P l
~tot (P°P°)/CLot (pOp) = 2/3
We will just a s s u m e that F(~ ° ) ~ 0.3 for l a r g e enoughp>po(Po~ 1) and. f u r t h e r F(~°) up~ FP,'(o)z c o r r e s p o n d i n g to spin 1/2 c o n s t i t u e n t s for the pO. If we pick out only the leading l o g a r i t h m i c d e pendence a s E ~ ¢o the c r o s s s e c t i o n t a k e s on a s i m p l e f o r m which e x p l i c i t l y e x h i b i t s the "pointlike" behavior we a r e a s s u m i n g :
2
i /Pmax\
] In(E-)
lp-lFi')(p,O2)+½(-l+(kk3-q)2)F2(P,O2) f
×
(4)
The v a r i a b l e p can be w r i t t e n p = k. q/Q2 = and the i n t e g r a n d in (4) will vanish u n l e s s the c e n t e r of m o m e n t u m e n e r g y W 2 = (k+q) 2 i s sufficiently l a r g e , and will extend to a m a x i m u m d e t e r m i n e d by the k i n e m a t i c s ,
½(I~-W2/Q2)
2Pmax --- 1 +
Fi(P°)/F~p) = Crtot (~P°)/Crtot(H))
a4 F~ p°) d~i •4 In(~ee) dQ2 (Q2)2 f2/4 v
p =- k'q/Q2
P ~
where the Q~ are the squared charges of the quarks. Alternatively, we might argue from vector dominance and the quark model that
=
(3)
23 August 1971
2Pl ~
I+4E(E-E')/Q2;
4E2/Q 2 .
It i s useful to t r y and obtain a total c r o s s s e c tion by making f u r t h e r a s s u m p t i o n s and i n t r o ducing a p p r o x i m a t i o n s . We will try to r e l a t e the s t r u c t u r e functions to h a d r o n i c ones by using the v e c t o r d o m i n a n c e model for the t a r g e t photon. N a m e l y , we set
and a s s u m e f u r t h e r that s o m e f o r m of s c a l i n g h o l d s T h i s m e a n s that the functions F : (n O2/ = Fi(P,Q~)) for s o m e Q2 ~ 1GeV 2 and a l l Q2 ~ Q2o. If we f u r t h e r a s s u m e that the h a d r o n s a r e built out of q u a r k s , then t h e s e functions should not v a n i s h if those for the p r o t o n do not vanish. The r a t i o of the functions F i for the po and p r o ton i s given by
F
_
[ln(9max')
_
.
When this i n t e g r a t e d down to Q2 = 1 GeV 2 at E = 3 GeV we find a total c r o s s s e c t i o n cri ~ 3 × 10 -35 cm 2 [5]• If the colliding beam m a chines under c o n s t r u c t i o n r e a c h l u m i n o s i t i e s ~ 1033 cm -2 sec -1, this should be o b s e r v a b l e , depending on the s e v e r i t y of the background. We conclude with s o m e c o m m e n t s : (i) Eq. (4) can be used for the c a s e w h e r e a s m a l l - a n g l e e l e c t r o n i s a l s o d e t e c t e d . One then s i m p l y i n t r o d u c e s the a p p r o p r i a t e l i m i t s on the i n t e g r a l over p and the r e l e v a n t value of 0 M. In o r d e r to e n s u r e that the v i r t u a l photons a r e unp o l a r i z e d , an a v e r a g e over the a z i m u t a l angle of the s c a t t e r e d e l e c t r o n should be u n d e r s t o o d . Note that k o = ED/Pl . (it) It wouh~ .~e of obvious)intergs)t if the e x t r e m e c a s e s Flay = 0 andF~V = F~Y could be d i s t i n g u i s h e d e x p e r i m e n t a l l y . T h i s would involve the m e a s u r e m e n t of the c r o s s s e c t i o n in a r e g i o n w h e r e it i s s m a l l . (iii) If the t r a n s v e r s e m o m e n t a of the p r o d u c e d h a d r o n s i s s m a l l , the e v e n t s (at high enough ene r g y ) would be confined n e a r the plane defined by
~ ~ - . I _ ......... k( k ~ ~ , ~ q = p
Fig.
i.
p~ =E')
_0~ H
po 122
×
p(po=E) p (qZ• IGeV2)
Volume 36H, number 2
PHYSICS LETTERS
t h e s c a t t e r e d e l e c t r o n E ' and the b e a m . (iv) It w o u l d be p r e m a t u r e to c o m m e n t e x t e n s i v e l y on the b a c k g r o u n d to t h i s p r o c e s s . We m e r e l y n o t e t h a t the p u r e l y e l e c t r o d y n a m i c p r o c e s s e s w h i c h c o n t a m i n a t e the s m a l l - a n g l e e v e n t s in (i) do not l e a d to h a d r o n i c t r i g g e r s , and t h a t t h e p r o d u c t i o n of C = - h a d r o n s t a t e s p l u s an e l e c t r o n w i t h Q2 > 1 GeV 2 i s p r o b a b l y s m a l l . H o p e f u l l y the b a c k g r o u n d due to e l e c t r o p r o d u c t i o n on r e s i d u a l g a s c a n be c o n t r o l l e d . Of c o u r s e , t h i s e x p e r i m e n t i s c l e a n e s t if p e r f o r m e d w i t h e - e - o r e+e+ b e a m s .
In s u m m a r y , we h a v e s u g g e s t e d t h a t the s t r u c t u r e f u n c t i o n s of the p h o t o n c a n be m e a s u r e d with colliding b e a m m a c h i n e s . This would r e q u i r e d e t e c t i n g an e l e c t r o n s c a t t e r e d at s m a l l
23 August 1971
a n g l e s . An i n t e g r a l o v e r the s t r u c t u r e f u n c t i o n s * c a n be o b t a i n e d w i t h o u t d e t e c t i n g t h i s e l e c t r o n , and w o u l d t e s t f o r p o i n t l i k e s t r u c t u r e in the p h o t o n . * This is much l a r g e r than the c r o s s section we would have obtained by assuming vector dominance for the inelastic scattering structure functions.
References [1] P . C . de Celles and J. E. Goehl J r . , Phys. Rev. 184 (1969) 1612; A. J a c c a r i n i e t a l . , Nuovo Cimento 4 (1970) 933. S. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. L e t t e r s 25 (1970) 972; V. M. Budnev and I. F. Ginsberg, Novosibirsk P r e print TP-55. [2] F. Low, Phys. Rev. 120 (1960) 582. [3] F. Calogero and C. Zemaeh, Phys. Rev. 120 (1960) 582. [4] P . K e s s l e r , Nuovo Cimento 17 (1960) 809.
123
PHYSICS LETTERS
INELASTIC
ELECTRON-PHOTON
23 August 1971
SCATTERING
T. F. WALSH
Deutsches Elektronen-SynchrotronDESY, Hamburg, Germany Received 19 March 1971
It is suggested that colliding e+e- beam machines may be used to study inelastic electron-photon scattering.
T h e r e have been r e c e n t l y a p p e a r e d s u g g e s t i ons [1] that co l l i d i n g e+e - and e - e - b e a m m a c h i n e s may p r o v e useful in i n v e s t i g a t i n g photonphoton c o l l i s i o n s . The i d e a i s to use as photon b e a m s the i n t en s e v i r t u a l photon s p e c t r u m a c c o m p a n y i n g the e l e c t r o n or p o s i t r o n b e a m s in t he se m a c h i n e s . The v i r u a l photon s p e c t r u m has a ln(E/m e) dependence and the r e s u l t i n g total c r o s s s e c t i o n for the p r o c e s s e+e - --* e+e - + h a d r o n s r i s e s slowly with e n e r g y . T h i s i s in cont r a s t to the one photon annihilation c r o s s s e c t i o n s which d e c r e a s e as E -2 or f a s t e r . The f i r s t sugg e s t i o n s of this kind w e r e made by Low [2] and by C a l a g e r o and Z e m a c h [3]. N u m e r o u s photonphoton r e a c t i o n s can be i n v e s t i g a t e d : 7~/~ 7T°, and o t h e r s . The c r o s s s e c t i o n s a r e all l a r g e enough to be m e a s u r a b l e with e a s e (e.g. that f o r pOpO is = 10 -34 cm 2 at E = 3 GeV). It i s s e n s i b l e , t h e r e f o r e , to see what o th e r p r o c e s s e s of this g e n e r a l s o r t may e x i s t . T h i s note c o n c e r n s one of t h e s e : i n e l a s t i c e l e c t r o n photon s c a t t e r i n g . The i d e a h e r e i s to use the v i r t u a l photon s p e c t r u m on one b e a m as a t a r g e t f o r the other beam of e l e c t r o n s (or p o s i t r o n s ) . One then o b s e r v e s an e l e c t r o n s c a t t e r e d at l a r g e angle with some e n e r g y l o s s t o g e t h e r with a s y s t e m of h a d r o n s (probably pions). We will a s s u m e that the e l e c t r o n which supplies the v i r t u a l photon and i s t h e r e b y s c a t t e r e d at s m a l l (0 ~< 0.1) a n g l e s i s not o b s e r v e d and that the v i r t u a l photons a r e t r a n s v e r s e l y p o l a r i z e d . The r e a s o n for this a s s u m p tion is to enhance the o b s e r v a b i l i t y of the effect by i n t e g r a t i n g o v e r the v i r t u a l photon s p e c t r u m . O t h e r w i s e the c r o s s s e c t i o n s depend s e n s i t i v e l y on the k i n e m a t i c cuts and a r e s i g n i f i c a n t l y s m a l l e r . T h i s a s s u m p t i o n a l s o allows us to use the W e i z a c k e r - V ¢ i l l i a m s a p p r o x i m a t i o n so as to get m o r e t r a n s p a r e n t r e s u l t s . The e r r o r made in this a p p r o x i m a t i o n i s t y p ic a l ly 15% or so
around E = 3 GeV beam e n e r g y . The W e i z a c k e r W i l l i a m s a p p r o x i m a t i o n has been v e r y nicely d i s c u s s e d by K e s s l e r [4] and we r e f e r the r e a d e r to that p a p e r for r e l e v a n t d e t a i l s . The c r o s s sect i o n ai f o r the p r o c e s s e + e e + e + h ad r o n s w h e r e one e l e c t r o n i s s c a t t e r e d , u n o b s e r v e d , at s m a l l angles and the other i s s c a t t e r e d at angle 0 with e n e r g y E ' < E i s given
by [2] d2cri
dQ2dEm= 2 fdk o P(ko)~
(I)
d2
--,
~(e+Vko e ' + h a d r o n s )
with k o the v i r t u a l photon e n e r g y (k 2 = 0), and w h e r e we take f o r the s p e c t r u m
P(ko ) =2a_~leo1E2+(E-ko) 2 22E lnt
~
sin ~10M }
r e t a i n i n g only the leading l o g a r i t h m i c dependence on e n e r g y . T h e r e i s a cutoff on the angle of the u n o b s e r v e d s c a t t e r e d e l e c t r o n 0 M ~ 0.1. Note that we can expect for the total c r o s s sect i o n s o m e t h i n g of the o r d e r of magnitude ( ~ a4 Q ~ i n In (E/m e) w h e r e Q 2 i n i s the l o w e r l i m i t on the s q u a r e d four m o m e n t u m t r a n s f e r ( Q 2 i n ~ 1 GeV 2). The c r o s s s e c t i o n for e + Yk --* e ' + . . . d i f f e r s o f r o m that f o r i n e l a s t i c e l e c t r o n - p r o t o n s c a t t e r i n g in two r e s p e c t s . The proton m a s s is r e p l a c e d by the photon e n e r g y as a s c a l e f o r the t a r g e t s y s t e m , and the l a b o r a t o r y s y s t e m i s not r e l a t e d to the c e n t e r of m o m e n t u m s y s t e m f o r the v i r t u a l photon k and the f a r off m a s s sh el l photon q(k 2=0, q 2 = _ Q 2 = _ 4 E E , sin 2½0) by a s i m p l e boost along q with the t h r e e - m o m e n t a all c o l l i n e a r . One useful f o r m u l a for this c r o s s sect i o n Js (with P=p .Lp', PO=E, P'o = E ' ) 121
Volume 36B, number 2
PHYSICS LETTERS
d2<7(ey ~ e ' + . . . ) ~Ta2 1 1 [ W(~)(k.q,q2) dQ2dE' (Q2)2 E 2 2k o Q2 + ½[-(k. q)2 + (k. p)2]
W~7) (k. q,
and another (which shows how the fined) i s
q2)]
W(7) a r e
(2) de-
d2cr(ey~e'+...) 2va 2 E ' 1 dQ2dE, =(Q2)2 E- 2k~ ×
[ 2 sin2 ½OW~Y)(k'q ,q2) +4k2 cos2 ½OW2( k.q ,q2) ] . We wish now to define the new functions
F(.y)
such that the c r o s s s e c t i o n s b e c o m e s d2cr/ a3 1 f~[l+(l_pP~l) dQ2dE , ~ ~ ~-~ P l
~tot (P°P°)/CLot (pOp) = 2/3
We will just a s s u m e that F(~ ° ) ~ 0.3 for l a r g e enoughp>po(Po~ 1) and. f u r t h e r F(~°) up~ FP,'(o)z c o r r e s p o n d i n g to spin 1/2 c o n s t i t u e n t s for the pO. If we pick out only the leading l o g a r i t h m i c d e pendence a s E ~ ¢o the c r o s s s e c t i o n t a k e s on a s i m p l e f o r m which e x p l i c i t l y e x h i b i t s the "pointlike" behavior we a r e a s s u m i n g :
2
i /Pmax\
] In(E-)
lp-lFi')(p,O2)+½(-l+(kk3-q)2)F2(P,O2) f
×
(4)
The v a r i a b l e p can be w r i t t e n p = k. q/Q2 = and the i n t e g r a n d in (4) will vanish u n l e s s the c e n t e r of m o m e n t u m e n e r g y W 2 = (k+q) 2 i s sufficiently l a r g e , and will extend to a m a x i m u m d e t e r m i n e d by the k i n e m a t i c s ,
½(I~-W2/Q2)
2Pmax --- 1 +
Fi(P°)/F~p) = Crtot (~P°)/Crtot(H))
a4 F~ p°) d~i •4 In(~ee) dQ2 (Q2)2 f2/4 v
p =- k'q/Q2
P ~
where the Q~ are the squared charges of the quarks. Alternatively, we might argue from vector dominance and the quark model that
=
(3)
23 August 1971
2Pl ~
I+4E(E-E')/Q2;
4E2/Q 2 .
It i s useful to t r y and obtain a total c r o s s s e c tion by making f u r t h e r a s s u m p t i o n s and i n t r o ducing a p p r o x i m a t i o n s . We will try to r e l a t e the s t r u c t u r e functions to h a d r o n i c ones by using the v e c t o r d o m i n a n c e model for the t a r g e t photon. N a m e l y , we set
and a s s u m e f u r t h e r that s o m e f o r m of s c a l i n g h o l d s T h i s m e a n s that the functions F : (n O2/ = Fi(P,Q~)) for s o m e Q2 ~ 1GeV 2 and a l l Q2 ~ Q2o. If we f u r t h e r a s s u m e that the h a d r o n s a r e built out of q u a r k s , then t h e s e functions should not v a n i s h if those for the p r o t o n do not vanish. The r a t i o of the functions F i for the po and p r o ton i s given by
F
_
[ln(9max')
_
.
When this i n t e g r a t e d down to Q2 = 1 GeV 2 at E = 3 GeV we find a total c r o s s s e c t i o n cri ~ 3 × 10 -35 cm 2 [5]• If the colliding beam m a chines under c o n s t r u c t i o n r e a c h l u m i n o s i t i e s ~ 1033 cm -2 sec -1, this should be o b s e r v a b l e , depending on the s e v e r i t y of the background. We conclude with s o m e c o m m e n t s : (i) Eq. (4) can be used for the c a s e w h e r e a s m a l l - a n g l e e l e c t r o n i s a l s o d e t e c t e d . One then s i m p l y i n t r o d u c e s the a p p r o p r i a t e l i m i t s on the i n t e g r a l over p and the r e l e v a n t value of 0 M. In o r d e r to e n s u r e that the v i r t u a l photons a r e unp o l a r i z e d , an a v e r a g e over the a z i m u t a l angle of the s c a t t e r e d e l e c t r o n should be u n d e r s t o o d . Note that k o = ED/Pl . (it) It wouh~ .~e of obvious)intergs)t if the e x t r e m e c a s e s Flay = 0 andF~V = F~Y could be d i s t i n g u i s h e d e x p e r i m e n t a l l y . T h i s would involve the m e a s u r e m e n t of the c r o s s s e c t i o n in a r e g i o n w h e r e it i s s m a l l . (iii) If the t r a n s v e r s e m o m e n t a of the p r o d u c e d h a d r o n s i s s m a l l , the e v e n t s (at high enough ene r g y ) would be confined n e a r the plane defined by
~ ~ - . I _ ......... k( k ~ ~ , ~ q = p
Fig.
i.
p~ =E')
_0~ H
po 122
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p(po=E) p (qZ• IGeV2)
Volume 36H, number 2
PHYSICS LETTERS
t h e s c a t t e r e d e l e c t r o n E ' and the b e a m . (iv) It w o u l d be p r e m a t u r e to c o m m e n t e x t e n s i v e l y on the b a c k g r o u n d to t h i s p r o c e s s . We m e r e l y n o t e t h a t the p u r e l y e l e c t r o d y n a m i c p r o c e s s e s w h i c h c o n t a m i n a t e the s m a l l - a n g l e e v e n t s in (i) do not l e a d to h a d r o n i c t r i g g e r s , and t h a t t h e p r o d u c t i o n of C = - h a d r o n s t a t e s p l u s an e l e c t r o n w i t h Q2 > 1 GeV 2 i s p r o b a b l y s m a l l . H o p e f u l l y the b a c k g r o u n d due to e l e c t r o p r o d u c t i o n on r e s i d u a l g a s c a n be c o n t r o l l e d . Of c o u r s e , t h i s e x p e r i m e n t i s c l e a n e s t if p e r f o r m e d w i t h e - e - o r e+e+ b e a m s .
In s u m m a r y , we h a v e s u g g e s t e d t h a t the s t r u c t u r e f u n c t i o n s of the p h o t o n c a n be m e a s u r e d with colliding b e a m m a c h i n e s . This would r e q u i r e d e t e c t i n g an e l e c t r o n s c a t t e r e d at s m a l l
23 August 1971
a n g l e s . An i n t e g r a l o v e r the s t r u c t u r e f u n c t i o n s * c a n be o b t a i n e d w i t h o u t d e t e c t i n g t h i s e l e c t r o n , and w o u l d t e s t f o r p o i n t l i k e s t r u c t u r e in the p h o t o n . * This is much l a r g e r than the c r o s s section we would have obtained by assuming vector dominance for the inelastic scattering structure functions.
References [1] P . C . de Celles and J. E. Goehl J r . , Phys. Rev. 184 (1969) 1612; A. J a c c a r i n i e t a l . , Nuovo Cimento 4 (1970) 933. S. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. L e t t e r s 25 (1970) 972; V. M. Budnev and I. F. Ginsberg, Novosibirsk P r e print TP-55. [2] F. Low, Phys. Rev. 120 (1960) 582. [3] F. Calogero and C. Zemaeh, Phys. Rev. 120 (1960) 582. [4] P . K e s s l e r , Nuovo Cimento 17 (1960) 809.
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