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The photoproduction of ETA mesons at small angles
5] Nuclear
Physics B25 (1971) 510-518. North-Holland Publishing Company
THE P H O T O P R O D U C T I O N OF ETA MESONS AT SMALL ANGLES P. S. L. BOOTH, J.S. BARTON, L. J. CARROLL, J. R. HOLT, J. N. JACKSON, W. H. RANGE, K.A. SPRAKES and J. R. WORMALD Oliver Lodge Laboratory, The University of Liverpool Received 2 November 1970
1. I N T R O D U C T I O N In a p r e v i o u s p u b l i c a t i o n (Booth et al. [1]) we have r e p o r t e d the r e s u l t s of m e a s u r e m e n t s of the d i f f e r e n t i a l c r o s s s e c t i o n f o r p h o t o p r o d u c t i o n of eta m e s o n s f r o m p r o t o n s at i n c i d e n t e n e r g i e s b e t w e e n 950 MeV and 2.2 GeV f o r a r a n g e of a n g l e s g r e a t e r than 35 ° ( c . m . ) . A t h e o r e t i c a l fit to t h i s d a t a and o t h e r d a t a below 1.4 GeV w a s m a d e by B a j p a i and D o n n a c h i e [2] on the b a s i s of an i n t e r f e r e n c e m o d e l u s i n g r e s o n a n c e s and R e g g e i z e d p a r t i c l e e x c h a n g e . With the $11(1550 ) and P l 1 ( 1 7 8 5 ) r e s o n a n c e s i n the d i r e c t c h a n n e l and e i t h e r w o r p t o g e t h e r with B in the t - c h a n n e l , a good fit to the d a t a f r o m t h r e s h o l d to a b o u t 1.5 GeV (1920 MeV t o t a l m a s s ) could be o b t a i n e d on the a s s u m p t i o n of z e r o p h a s e d i f f e r e n c e s b e t w e e n the two r e s o n a n c e s and the R e g g e b a c k g r o u n d . The a v a i l a b l e i n f o r m a t i o n on the a n g u l a r v a r i a t i o n of c r o s s s e c t i o n w a s n o t s u f f i c i e n t to t e s t t h i s a s s u m p t i o n . O u r d a t a a b o v e 1.5 GeV could n o t be f i t t e d w i t h o u t i n v o k i n g a n o t h e r r e s o n a n c e o r e x c h a n g e t e r m and it w a s c l e a r that m o r e i n f o r m a t i o n on the a n g u l a r v a r i a t i o n w a s n e e d e d o v e r the whole r a n g e of e n e r g i e s . M o r e r e c e n t l y B a j p a i and D o n n a c h i e [3] have b e e n v e r y s u c c e s s f u l in f i t t i n g the d a t a on p i - z e r o p h o t o p r o d u c t i o n a b o v e the r e s o n a n c e r e g i o n by u s i n g a c o m b i n a t i o n of ¢v and p R e g g e i s e d e x c h a n g e . With the s a m e m o d e l they w e r e a b l e to fit the e t a p h o t o p r o d u c t i o n c r o s s s e c t i o n s at 4 GeV [4] and 6 GeV [5], a l t h o u g h this w a s a l s o p o s s i b l e with the c o m b i n a t i o n s w + B o r p+ B. H o w e v e r , with e i t h e r of t h e s e it w a s not p o s s i b l e to fit o u r d a t a in the r e g i o n of 2 GeV, w h e r e a s with the c o m b i n a t i o n w + p a f a i r m e a s u r e of a g r e e m e n t could be o b t a i n e d . In the p r e s e n t e x p e r i m e n t we have m a d e m e a s u r e m e n t s at s m a l l a n g l e s i n the r e g i o n of the P l 1 ( 1 7 8 5 ) r e s o n a n c e (1.22 GeV) and at h i g h e r e n e r g i e s (1.51 GeV and 1.85 GeV) in o r d e r to t e s t f u r t h e r the t h e o r e t i c a l i n t e r p r e t a t i o n s m e n t i o n e d above.
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2. M E T H O D In o u r f i r s t e x p e r i m e n t the p r o c e s s ~,p - pT? ( 7 / - 2~) w a s d e t e c t e d t h r o u g h a d o u b l e c o i n c i d e n c e b e t w e e n a p r o t o n and on e of the d e c a y p h o t o n s of the e t a m e s o n . H o w e v e r , at s m a l l a n g l e s the e n e r g y of the p r o t o n b e c o m e s too s m a l l f o r d e t e c t i o n so it i s then n e c e s s a r y to m a k e u s e of a c o i n c i d e n c e b e t w e e n the two d e c a y p h o t o n s . If the d i r e c t i o n s and e n e r g i e s of t h e s e two p h o t o n s a r e d e t e r m i n e d , the d i r e c t i o n and e n e r g y of the m e s o n and i t s r e s t m a s s can be found. T h e f o l l o w i n g a r e the e x p r e s s i o n s f o r the e n e r g y E , the r e s t m a s s ~ and the d i r e c t i o n of the m e s o n : 1
1
;~[(E 1 / E 2)~ + (E 2/E1)~ 1 E= 1 2 sin ~ 0
m 2 =2 E I E 2 ( 1 - c o s ~ ) , s in 81
E2
sin(6 - 81) - E 1 ' w h e r e E 1 and E 2 a r e the e n e r g i e s of the two d e c a y p h o t o n s , 0 i s the a n g l e b e t w e e n t h e m , and 81 i s the a n g l e b e t w e e n o n e of the p h o t o n s and the m e s o n d i r e c t i o n . A l l q u a n t i t i e s a r e m e a s u r e d in the l ab s y s t e m . It i s to b e n o t e d that an a b s o l u t e e n e r g y c a l i b r a t i o n of t h e photon " d e t e c t o r s i s r e q u i r e d only f o r the d e t e r m i n a t i o n of the r e s t m a s s of the m e s o n and a l s o t h a t E i s m u c h m o r e s e n s i t i v e to the a n g u l a r m e a s u r e m e n t than to the v a l u e s of the e n e r g y r a t i o s when t h e s e a r e c l o s e to unity. F r o m the e n e r g y , r e s t m a s s and d i r e c t i o n of the m e s o n the i n c i d e n t photon e n e r g y can be found on the a s s u m p t i o n that the m e s o n i s p r o d u c e d in a t w o - b o d y p r o cess.
3. D E T E C T O R S T h e photon d e t e c t o r s w e r e two h o d o s c o p e s of l e a d - g l a s s ~ e r e n k o v c o u n t e r s . E a c h h o d o s c o p e c o n s i s t e d of a 6 × 4 a r r a y of b l o c k s , e a c h b l o c k 35 c m l o n g by 8 c m s q u a r e and v i e w e d by an RCA 8575 p h o t o m u l t i p l i e r . T h e s e 24 b l o c k s w e r e m o u n t e d in a s t e e l box s c r e e n e d w i t h 5 c m of l e a d at the s i d e s and h a v i n g a l e a d d e f i n i n g a p e r t u r e 41 c m × 25 c m in f r o n t . A s c i n t i l l a t i o n c o u n t e r to v e t o c h a r g e d p a r t i c l e s w a s p l a c e d b e t w e e n the a p e r t u r e and the b l o c k s . T h e two h o d o s c o p e s w e r e s u p p o r t e d o n e a b o v e the o t h e r on a s t a n d in s u c h a m a n n e r that t h e i r h e i g h t s and a n g l e s of t i l t co u l d be a d j u s t e d to e n a b l e t h e m to be p o s i t i o n e d s y m m e t r i c a l l y a bo u t the h o r i z o n t a l p l a n e c o n t a i n i n g the b e a m and p o i n t e d t o w a r d s the t a r g e t . T h i s w a s a c h i e v e d by f i x i n g e a c h b o x at o n e s i d e to a h o r i z o n t a l b e a r i n g to p r o v i d e the t i l t a d j u s t m e n t w h i l e t h e b e a r i n g i t s e l f c o u l d be m o v e d v e r t i c a l l y in a s l i d e a t t a c h e d to a j a c k s c r e w . T h e s u p p o r t f r a m e w a s p r o v i d e d w i t h b a l l c a s t o r s so that it
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could be m o v e d into any p o s i t i o n on the s t e e l f l o o r of the e x p e r i m e n t a l hall. D u r i n g the e x p e r i m e n t the l e a d - g l a s s d e t e c t o r s w e r e p l a c e d with t h e i r f r o n t f a c e s 2 m f r o m the t a r g e t with an o p e n i n g a n g l e w h i c h v a r i e d b e t w e e n 30 ° and 58 °. The t a r g e t w a s of l i q u i d h y d r o g e n 10 c m i n length. At a n g l e s of e m i s s i o n of the eta g r e a t e r than a b o u t 30 ° c . m . the r e c o i l p r o t o n s w e r e d e t e c t e d with a s c i n t i l l a t i o n c o u n t e r 30 c m x 20 c m x 1.2 c m p l a c e d 40 cm f r o m the t a r g e t .
4. E L E C T R O N I C S The l i n e a r o u t p u t s f r o m the 24 m u l t i p l i e r s in e a c h h o d o s c o p e w e r e added t o g e t h e r and a f t e r s u i t a b l e d i s c r i m i n a t i o n the two p u l s e s f r o m the h o d o s c o p e s w e r e t a k e n to a c o i n c i d e n c e c i r c u i t with 20 n s r e s o l v i n g t i m e to p r o v i d e the t r i g g e r s i g n a l f o r an e v e n t . T h e d i s c r i m i n a t o r s y s t e m w a s s u c h that a r a t h e r low l e v e l w a s s e t on the i n d i v i d u a l o u t p u t s of the two h o d o s c o p e s b u t a high l e v e l , e q u a l to a b o u t half the m a x i m u m p u l s e h e i g h t p o s s i b l e for an eta, on the s u m of the two. T h i s w a s i m p o r t a n t in r e d u c i n g u n w a n t e d e v e n t s w h i l e m a i n t a i n i n g m a x i m u m e f f i c i e n c y f o r eta d e t e c t i o n , s i n c e the s u m i s j u s t a m e a s u r e of the e n e r g y of the e t a , w h e r e a s the i n d i v i d u a l o u t p u t s v a r y w i d e l y d e p e n d i n g on the way in w h i c h the d e c a y e n e r g y d i v i d e s , in the l a b s y s t e m , b e t w e e n the two p h o t o n s . A s e c o n d o u t p u t f r o m e a c h p h o t o m u l t i p l i e r w a s u s e d to d i g i t i s e the c h a r g e f r o m e a c h ~ e r e n k o v c o u n t e r u s i n g 48 a n a l o g u e - t o - d i g i t a l c o n v e r t e r s . T i m e t o - d i g i t a l c o n v e r t e r s w i t h a r e s o l u t i o n of 0.3 n s w e r e u s e d to give the r e l a t i v e t i m e b e t w e e n the s u m m e d o u t p u t s f r o m the a r r a y s and any s i g n a l in the v e t o c o u n t e r s o r the p r o t o n c o u n t e r , when the l a t t e r w a s in u s e . The a b o v e d a t a , t o g e t h e r with the p u l s e h e i g h t in the p r o t o n c o u n t e r and the t i m e of e a c h e v e n t r e l a t i v e to the a c c e l e r a t o r c y c l e , w e r e fed into a P D P 8 c o m p u t e r . T h i s c o m p u t e r p r o v i d e d r u n n i n g d i s p l a y s f o r m o n i t o r i n g p u r p o s e s d u r i n g the e x p e r i m e n t and r e c o r d e d a l l the i n f o r m a t i o n on m a g n e t i c tape f o r l a t e r a n a l ysis.
5. C A L I B R A T I O N AND O P E R A T I O N T h e a b s o l u t e e n e r g y c a l i b r a t i o n and r e s o l u t i o n of a s i n g l e b l o c k of g l a s s w e r e d e t e r m i n e d u s i n g e l e c t r o n s o~f k n o w n e n e r g y . T h e G a u s s i a n half w i d t h of the p e a k w a s found to b e 8.8 E - g % , w h e r e E i s the e l e c t r o n e n e r g y in GeV. T h e p r o c e d u r e f o r e q u a l i s i n g the g a i n s of a l l the p h o t o m u l t i p l i e r s w a s a s f o l l o w s . T h e two l e a d - g l a s s a r r a y s w e r e p o s i t i o n e d a s c l o s e l y a s p o s s i b l e to the d i r e c t i o n of the photon b e a m f r o m the s y n c h r o t r o n . A s t o p p e r of l e a d 80 c m t h i c k w a s m o v e d into the b e a m s e v e r a l m e t r e s u p s t r e a m of the c o u n t e r s . The s p r a y of p a r t i c l e s e m e r g i n g f r o m the l e a d c o n s i s t e d l a r g e l y of m u o n s and t h e s e , p a s s i n g t h r o u g h the b l o c k s of g l a s s , p r o d u c e d ~ e r e n k o v p u l s e s of s t a n d a r d s i z e . T h e 48 p u l s e - h e i g h t s p e c t r a w e r e s i m u l t a n e o u s l y r e c o r d e d on m a g n e t i c t a p e and a f t e r a r u n of half an h o u r , d u r i n g w h i c h a
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total of a b o u t 50 000 m u o n s w e r e d e t e c t e d , the tape w a s p r o c e s s e d on a 3 6 0 / 6 5 c o m p u t e r to p r o d u c e p r i n t - o u t s of a l l the s p e c t r a . The p o s i t i o n s of the p e a k s could be d e t e r m i n e d to ± 4 2 and c o r r e c t i o n s to the m u l t i p l i e r v o l t a g e s w e r e then m a d e on the b a s i s of a p r e v i o u s l y d e t e r m i n e d r e l a t i o n b e t w e e n v o l t a g e and p u l s e height. T h i s c a l i b r a t i o n w a s c a r r i e d out at i n t e r v a l s of a few d a y s d u r i n g a r u n and it w a s u s u a l l y n e c e s s a r y to m a k e a d j u s t m e n t s of a few p e r c e n t to a s m a l l p r o p o r t i o n of the p h o t o m u l t i p l i e r s . T h e e x p e r i m e n t was o p e r a t e d f o r a total of 250 h o u r s with a photon b e a m of a b o u t 3.109 e q u i v a l e n t q u a n t a p e r s e c o n d h a v i n g a p u l s e d u r a t i o n of a b o u t 2 m s at the m a c h i n e r e p e t i t i o n f r e q u e n c y of 53 Hz. The r a t e of eta e v e n t s w a s a b o u t 15 p e r hour.
6. DATA R E D U C T I O N The f i r s t s t e p in p r o c e s s i n g the d a t a w a s to d e t e r m i n e the p u l s e h e i g h t s due to s h o w e r s in the two a r r a y s by a d d i n g the p u l s e s f r o m the n i n e b l o c k s in the v i c i n i t y of e a c h s h o w e r . The g e n e r a l b a c k g r o u n d of s m a l l , r a n d o m p u l s e s in the r e m a i n i n g b l o c k s w a s a v e r a g e d and s u b t r a c t e d f r o m this. The d i r e c t i o n of e a c h photon w a s t a k e n to be that c o r r e s p o n d i n g to the c e n t r e of the b l o c k s h o w i n g the l a r g e s t p u l s e . The m o m e n t u m and a n g l e of e m i s s i o n of the e t a w e r e n e x t c a l c u l a t e d . S i n c e the a n g u l a r r a n g e c o v e r e d at e a c h p o s i t i o n of the a p p a r a t u s w a s a b o u t 30 ° c . m . the d a t a w a s d i v i d e d into e i t h e r 3 o r 4 a n g l e b i n s . The a c c e p t e d m o m e n t u m r a n g e w a s r e s t r i c t e d to v a l u e s g r e a t e r than 150 M e V / c b e l o w the l i m i t s e t by the b r e m s s t r a h l u n g cut-off. T h i s e n s u r e s that e t a s p r o d u c e d in a s s o c i a t i o n with o n e o r m o r e p i o n s a r e not d e t e c t e d . The e n e r g y of the i n c i d e n t photon w a s c a l c u l a t e d on the a s s u m p t i o n of s i n g l e e t a p r o d u c t i o n and the e v e n t s s e p a r a t e d into two g r o u p s d e p e n d i n g on w h e t h e r this w a s below o r a b o v e the b r e m s s t r a h l u n g l i m i t . The t i m e s p e c t r u m of g a m m a - g a m m a c o i n c i d e n c e s w a s p l o t t e d out and the l i m i t s to be u s e d i n s e p a r a t i n g the p e a k due to " r e a l " e v e n t s f r o m the b a c k g r o u n d of " r a n d o m " e v e n t s w e r e d e c i d e d . An e f f e c t i v e t i m e window of 5 n s w a s thus o b t a i n e d . S i m i l a r l y , the t i m e s p e c t r a of the v e t o c o u n t e r s w e r e u s e d to d e c i d e the l i m i t s of the p e a k in e a c h c a s e r e p r e s e n t i n g the g e n u i n e v e t o p u l s e s s u p e r i m p o s e d on a b a c k g r o u n d of r a n d o m o n e s . The d a t a w a s then p r o c e s s e d a s e c o n d t i m e with t h e s e c u t s in the g a m m a g a m m a and v e t o t i m e s p e c t r a . E v e n t s a s s o c i a t e d with a g e n u i n e p u l s e in one o r both v e t o c o u n t e r s w e r e r e j e c t e d and the c o r r e c t i o n f o r r a n d o m v e t o s w a s d e t e r m i n e d . An e f f e c t i v e m e s o n m a s s w a s c a l c u l a t e d f o r e a c h e v e n t on the a s s u m p t i o n that it w a s p r o d u c e d by a m e s o n w h i c h d e c a y e d into two p h o t o n s . M a s s s p e c t r a w e r e p l o t t e d f o r e a c h a n g l e b i n f o r e v e n t s w i t h i n the p e a k in the g a m m a - g a m m a t i m e s p e c t r u m , f o r t h o s e o u t s i d e the p e a k and f o r t h o s e below and a b o v e the b r e m s s t r a h l u n g l i m i t . M a s s s p e c t r a c o r r e c t e d f o r r a n d o m e v e n t s w e r e p r o d u c e d f r o m t h e s e and a t y p i c a l p a i r of s p e c t r a a r e shown in fig. 1. The f i r s t of t h e s e , w h i c h c o r r e s p o n d s to c a l c u l a t e d v a l u e s of i n c i d e n t e n e r g y b e l o w the b r e m s s t r a h l u n g l i m i t , has a p e a k at the p o s i t i o n e x p e c t e d f o r the e t a m a s s , w h e r e a s the s e c o n d s p e c t r u m f o r i n c i d e n t e n e r g i e s a b o v e t h i s l i m i t , has no peak.
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300
500 MeV
Fig. l(a). Mass spectrum for events within the eta kinematic region. Fig. l(b). Mass spectrum for events outside the eta kinematic region. The s u b t r a c t i o n of the b a c k g r o u n d u n d e r n e a t h the e t a m a s s p e a k w a s p e r f o r m e d by a c u r v e f i t t i n g r o u t i n e on the c o m p u t e r . The p e a k and b a c k g r o u n d w e r e p a r a m e t r i s e d by a G a u s s i a n p l u s an e x p r e s s i o n of the f o r m a e x p ( - b x ) - c and a l e a s t s q u a r e s fit w a s u s e d to d e t e r m i n e the n u m b e r of e t a s in the p e a k ( s e e fig. 1). At a n g l e s w h e r e it w a s p o s s i b l e to d e t e c t the r e c o i l p r o t o n the d a t a w e r e p r o c e s s e d both with and w i t h o u t the r e q u i r e m e n t of a c o i n c i d e n t p u l s e f r o m the p r o t o n c o u n t e r . In a l l s u c h c a s e s the a g r e e m e n t b e t w e e n the f i n a l r e s u l t s w a s w i t h i n the e r r o r s of m e a s u r e m e n t . The r e l a t i o n s h i p b e t w e e n the n u m b e r of o b s e r v e d e t a s and the a b s o l u t e d i f f e r e n t i a l c r o s s s e c t i o n w a s d e t e r m i n e d by m e a n s of a Monte C a r l o p r o g r a m m e in w h i c h e v e n t s w e r e s i m u l a t e d and the d e t e c t i o n e f f i c i e n c i e s for e a c h r a n g e of a n g l e a n d m o m e n t u m w e r e d e r i v e d . The g e o m e t r y of the t a r get and c o u n t e r s , the e n e r g y r e s o l u t i o n and c a l i b r a t i o n of the l a t t e r , and the e n e r g y s p r e a d of the e l e c t r o n b e a m r e s u l t i n g f r o m the f i n i t e s p i l l t i m e w e r e u s e d in t h i s p r o g r a m m e .
7. R E S U L T S T h e d i f f e r e n t i a l c r o s s s e c t i o n s o b t a i n e d in t h i s w o r k a r e p r e s e n t e d in t a b l e 1. In o u r p r e v i o u s e x p e r i m e n t (Booth et al. [1]) d a t a w a s o b t a i n e d ~t l a r g e r a n g l e s u s i n g a c o m p l e t e l y d i f f e r e n t t e c h n i q u e f o r d e t e c t i n g the p r o c e s s . S o m e of t h i s d a t a i s i n c l u d e d h e r e in o r d e r to p r o v i d e a m o r e c o m p l e t e p i c t u r e of the b e h a v i o u r of the c r o s s s e c t i o n b e t w e e n 1.2 GeV and
P H O T O P R O D U C T I O N O F E T A MESONS
515
Table 1 Differential cross sections for yp ~ p~.
Ey
0 77
dO" da
1.22 1.21 1.22 1.22 1.52
13 19 26 33 8
0.085±0.028 0.093 ± 0.011 0.100±0.010 0.125±0.022 0.097±0.027
1.83 1.82 1.84 1.82 1.82
8 15 19 22 26
0.074 ± 0.024 0.095 ± 0.008 0.101±0.025 0.133±0.018 0.108±0.017
1.51 1.51 1.51 1.50 1.51
15 22 32 40 47
0.121±0.012 0.146±0.018 0.136±0.023 0.101 ± 0.012 0.084±0.020
1.83 1.83 1.82 1.84
32 34 38 46
0.130±0.023 0.105±0.022 0.120±0.015 0.095 ÷ 0.025
da
H e r e , E y is t h e m e a n i n c i d e n t e n e r g y (GeV), t o t a l bin w i d t h ~ 0.1 GeV; 8?? i s the m e a n a n g l e of e t a ( d e g r e e s c . m . ) , t o t a l bin w i d t h ~ 7o; and d(:r/d~ is the d i f f e r e n t i a l c r o s s s e c t i o n (t~b s r - 1 ) .
Table 2 D i f f e r e n t i a l c r o s s s e c t i o n s f o r y p -~ p r / .
1.23 1.34 1.33 1.32
64 45 50 65
0.179 0.156 0.180 0.173
± ± ± ±
0.018 0.020 0.016 0.018
0.148 0.126 0.172 0.173
± 0.023 ± 0.018 ± 0.025 ± 0.027"
1.33 1.41 1.51 1.50
83 65 41 66
0.189 0.149 0.157 0.096
± 0.013 ± 0.012 ± 0.013 ± 0.010
0.163 0.137 0.151 0.111
± 0.023 ± 0.021 ± 0.()28 -~ 0.015
1.50 1.59 1.70 1.64
74 63 38 51
0.141 0.082 0.128 0.092
± 0.012 ± 0.008 ± 0.010 ± 0.010
0.141 0.071 0.137 0.077
± 0.018 *" ± 0.010 ± 0.026 ± 0.017
1.68 1.88 1.83 1.85 2.02
67 35 46 56 52
0.064 0.137 0.081 0.052 0.095
± ± ± ± ±
0.056 0.148 0.060 0.052 0.100
± 0.014 ± 0.017 ± 0.015 ± 0.012 * ± 0.012
0.009 0.013 0.012 0.008 0.011
H e r e , (d(Y/d~)l i s the c r o s s s e c t i o n q u o t e d in r e f . [1]; (d(~/d~)2 i s the c r o s s s e c t i o n r e s u l t i n g f r o m r e a n a l y s i s of t h e d a t a of r e f . [1] ( p o i n t s m a r k e d w i t h an a s t e r i s k w e r e not r e a n a l y s e d but the e r r o r has been i n c r e a s e d ) .
516
P.S.L.
BOOTH et al.
F'
0.2
#_b sr
0.1 ET= 1.22 GeV
0 F i g . 2. D i f f e r e n t i a l
' cross
'
3~0~
'
'6'0
°.
' '
s e c t i o n s f o r i n c i d e n t e n e r g y 1.22 G e V . H e r e p r e s e n t e x p e r i m e n t , x r e f . [1].
'
o are the
/ /
02
Sr
0.1
ET= 1.33 GeV 0
L
F i g . 3. D i f f e r e n t i a l c r o s s
'
3~
L
e,
I
6~ °
,
L
s e c t i o n s f o r i n c i d e n t e n e r g y 1.33 G e V f r o m r e f . [1].
0.2
ET= 1.51 GeV
ST
0.1
o
F i g . 4. D i f f e r e n t i a l c r o s s
'
'
3'o~
'
'
~
'
'
s e c t i o n s f o r i n c i d e n t e n e r g y 1.51 G e V . H e r e o a r e t h e p r e s e n t e x p e r i m e n t , × r e f . [1].
PHOTOPRODUCTION OF ETA MESON8
517
E;r= 1.68 GeV SF
0.1
o
j J
I
J
3o°
i
6~00
i
Fig. 5. Differential c r o s s sections for incident energy 1.68 GeV from ref. [11.
$r
0.1
o
~
F__7=1.85GeV
3'O
Fig. 6. Differential c r o s s sections for incident energy 1.85 GeV. Here o are the p r e s e n t experiment, × ref. [1]. 1.9 GeV. In t h i s e a r l i e r w o r k the s u b t r a c t i o n of the b a c k g r o u n d b e n e a t h the e t a p e a k had b e e n d o n e by hand and the c o n t r i b u t i o n of the u n c e r t a i n t y in t h i s to the s t a n d a r d d e v i a t i o n of the r e s u l t w a s e s t i m a t e d . As a c h e c k on t h i s p r o c e d u r e it s e e m e d w o r t h w h i l e r e a n a l y s i n g s o m e of the d a t a f r o m the f i r s t e x p e r i m e n t u s i n g "the c o m p u t e r c u r v e f i t t i n g p r o c e d u r e e m p l o y e d in the p r e s e n t i n v e s t i g a t i o n . In t a b l e 2 we show the c r o s s s e c t i o n s r e s u l t i n g f r o m t h i s r e a n a l y s i s , t o g e t h e r w i t h the p r e v i o u s v a l u e s . T h e c h a n g e s in c r o s s s e c t i o n a r e not l a r g e but t h e r e is a g e n e r a l i n c r e a s e in the v a l u e s of the s t a n d a r d deviation. T h e t h r e e p o i n t s m a r k e d w i t h a s t e r i s k s in t a b l e 2 and the r e s t of the d a t a f r o m the f i r s t e x p e r i m e n t h a v e not b e e n s u b j e c t e d to r e a n a l y s i s . S i n c e the c h i e f r e s u l t of r e a n a l y s i s w a s an i n c r e a s e in the s t a n d a r d d e v i a t i o n it s e e m e d r e a s o n a b l e in t h e s e c a s e s to l e a v e the c r o s s s e c t i o n s u n c h a n g e d but to i n c r e a s e t h e s t a n d a r d d e v i a t i o n s by 5 0 ~ T h e d a t a f r o m the p r e s e n t e x p e r i m e n t and the r e v i s e d d a t a f r o m the e a r l i e r o n e a r e d i s p l a y e d in f i g s . 2 to 6 a s a n g u l a r d i s t r i b u t i o n s f o r m e a n e n e r g i e s of 1.22 GeV, 1.33 GeV, 1.51 GeV, 1.68 GeV and 1.83 GeV. T h e p r e s e n t d a t a p o i n t s a r e m a r k e d a s c i r c l e s , t h e e a r l i e r o n e s as c r o s s e s . T h e c u r v e d r a w n in fig. 6 i s a t h e o r e t i c a l c u r v e o b t a i n e d by B a j p a i and D o n n a c h i e [3] by f i r s t f i t t i n g the d a t a at 4 G eV and 6 G e V a s s u m i n g the ex-
518
P . S . L . BOOTH et al.
c h a n g e of R e g g e i z e d co- a n d p - m e s o n s and then e x t r a p o l a t i n g d o w n w a r d s in e n e r g y to 1.85 GeV. It i s i n t e r e s t i n g that the d a t a a g r e e so w e l l with the p r e d i c t i o n of the e x c h a n g e m o d e l at s u c h a c o m p a r a t i v e l y low e n e r g y . T h i s i s p o s s i b l y c o n n e c t e d w i t h an a b s e n c e of l a r g e c o n t r i b u t i o n s f r o m T = ½ r e s o n a n c e s in eta p h o t o p r o d u c t i o n at t h i s e n e r g y . At 2.03 GeV, n e a r the p e a k of the G17(2190 ) r e s o n a n c e o u r old d a t a p o i n t s (Booth et al. [1]) a r e h i g h e r than the t h e o r e t i c a l c u r v e ( B a j p a i and D o n n a c h i e [3]) and we i n t e n d to m a k e f u r t h e r m e a s u r e m e n t s at s m a l l a n g l e s t h r o u g h o u t the r e g i o n of this r e s o nance. The c u r v e s in figs. 2 to 5 w e r e d e r i v e d f r o m the g e n e r a l i s e d i n t e r f e r e n c e m o d e l of B a j p a i and D o n n a c h i e [2], u s i n g a m p l i t u d e s r e p r e s e n t i n g the P l 1 ( 1 7 8 5 ) and S l 1 ( 1 5 5 0 ) r e s o n a n c e s p l u s t h o s e of the Regge e x c h a n g e p r o c e s s m e n t i o n e d above. As d e s c r i b e d in ref. [2], the e n e r g i e s and w i d t h s of the r e s o n a n c e s w e r e t a k e n f r o m the r e s u l t s of ~p p h a s e - s h i f t a n a l y s e s , l e a v i n g a s f r e e p a r a m e t e r s the p r o d u c t of the 7P and UP p a r t i a l w i d t h s f o r e a c h r e s o n a n c e and the r e l a t i v e p h a s e s of the r e s o n a n c e s and R e g g e b a c k g r o u n d . The a v a i l a b l e d a t a w e r e s a t i s f a c t o r i l y fitted in ref. [2] on the a s s u m p t i o n of r e l a t i v e p h a s e d i f f e r e n c e s of z e r o . O u r p r e s e n t r e s u l t s at 1.22 GeV, n e a r the p e a k of the P l l r e s o n a n c e , show that the c r o s s s e c t i o n d e c r e a s e s at s m a l l a n g l e s , i n d i c a t i n g d e s t r u c t i v e i n t e r f e r e n c e b e t w e e n t h i s s t a t e and the t a i l of the S l 1 ( 1 5 5 0 ). U s i n g the p r e s e n t d a t a and all o u r old d a t a b e t w e e n 960 MeV and 1.9 GeV t o g e t h e r with d a t a f r o m o t h e r s o u r c e s [2] b e t w e e n t h r e s h o l d and 960 MeV, the c u r v e s shown w e r e o b t a i n e d a s b e s t fits w i t h the f o u r p a r a m e t e r s s p e c i f i e d a b o v e a s v a r i a b l e s . The p h a s e d i f f e r e n c e b e t w e e n the r e s o n a n t a m p l i t u d e s w a s 180 ° r a t h e r than z e r o . It i s a p l e a s u r e to t h a n k P r o f . A. D o n n a c h i e f o r p r o v i d i n g the t h e o r e t i c a l f i t s to o u r d a t a u s i n g his i n t e r f e r e n c e m o d e l . We w i s h a l s o to t h a n k M e s s r s . D. C a r s o n and P. Noake f o r help in s e t t i n g up the c o u n t e r s and e l e c t r o n i c s and D r . E. G. H. W i l l i a m s f o r a s s i s t a n c e d u r i n g r u n n i n g . P r o f . B. C o l l i n g e w a s r e s p o n s i b l e f o r the d e s i g n of s o m e of the e l e c t r o n i c c i r c u i t s . We a r e i n d e b t e d to the s t a f f of the D a r e s b u r y e l e c t r o n s y n c h r o t r o n f o r t h e i r e f f o r t s on o u r b e h a l f and to the S c i e n c e R e s e a r c h C o u n c i l f o r the p r o v i s i o n of f a c i l i t i e s and f i n a n c i a l s u p p o r t , i n c l u d i n g a s t u d e n t s h i p f o r J. S. B.
REFERENCES [1] P . S . L . Booth, M.F. Butler, L . J . Carroll, J. R. Holt, J. N. Jackson, W. H. Range, E. G. H. Williams, J. R. Wormald and N. lq. S. Tait, Nuovo Cim. Letters 2 {1969) 66. [2] R. P. Bajpai and A. Donnachie, Nucl. Phys. B12 {1969) 274. [3] R. P. Bajpai and A. Donnachie, Daresbury Laboratory preprint DNPL/P 15, 1969. [4] D. Bellenger, S. Deutsch, D. Luckey, L.S. Osborne and R. Schwitters, Phys. Rev. Letters 21 (1968) 1205. [5] R. Anderson, D. Gustavson, J. Johnson, D. Ritson, W. G. Jones, D. Kreinick, F. Murphy and R.Weinstein, Phys. Rev. Letters 21 {1968) 384.
Physics B25 (1971) 510-518. North-Holland Publishing Company
THE P H O T O P R O D U C T I O N OF ETA MESONS AT SMALL ANGLES P. S. L. BOOTH, J.S. BARTON, L. J. CARROLL, J. R. HOLT, J. N. JACKSON, W. H. RANGE, K.A. SPRAKES and J. R. WORMALD Oliver Lodge Laboratory, The University of Liverpool Received 2 November 1970
1. I N T R O D U C T I O N In a p r e v i o u s p u b l i c a t i o n (Booth et al. [1]) we have r e p o r t e d the r e s u l t s of m e a s u r e m e n t s of the d i f f e r e n t i a l c r o s s s e c t i o n f o r p h o t o p r o d u c t i o n of eta m e s o n s f r o m p r o t o n s at i n c i d e n t e n e r g i e s b e t w e e n 950 MeV and 2.2 GeV f o r a r a n g e of a n g l e s g r e a t e r than 35 ° ( c . m . ) . A t h e o r e t i c a l fit to t h i s d a t a and o t h e r d a t a below 1.4 GeV w a s m a d e by B a j p a i and D o n n a c h i e [2] on the b a s i s of an i n t e r f e r e n c e m o d e l u s i n g r e s o n a n c e s and R e g g e i z e d p a r t i c l e e x c h a n g e . With the $11(1550 ) and P l 1 ( 1 7 8 5 ) r e s o n a n c e s i n the d i r e c t c h a n n e l and e i t h e r w o r p t o g e t h e r with B in the t - c h a n n e l , a good fit to the d a t a f r o m t h r e s h o l d to a b o u t 1.5 GeV (1920 MeV t o t a l m a s s ) could be o b t a i n e d on the a s s u m p t i o n of z e r o p h a s e d i f f e r e n c e s b e t w e e n the two r e s o n a n c e s and the R e g g e b a c k g r o u n d . The a v a i l a b l e i n f o r m a t i o n on the a n g u l a r v a r i a t i o n of c r o s s s e c t i o n w a s n o t s u f f i c i e n t to t e s t t h i s a s s u m p t i o n . O u r d a t a a b o v e 1.5 GeV could n o t be f i t t e d w i t h o u t i n v o k i n g a n o t h e r r e s o n a n c e o r e x c h a n g e t e r m and it w a s c l e a r that m o r e i n f o r m a t i o n on the a n g u l a r v a r i a t i o n w a s n e e d e d o v e r the whole r a n g e of e n e r g i e s . M o r e r e c e n t l y B a j p a i and D o n n a c h i e [3] have b e e n v e r y s u c c e s s f u l in f i t t i n g the d a t a on p i - z e r o p h o t o p r o d u c t i o n a b o v e the r e s o n a n c e r e g i o n by u s i n g a c o m b i n a t i o n of ¢v and p R e g g e i s e d e x c h a n g e . With the s a m e m o d e l they w e r e a b l e to fit the e t a p h o t o p r o d u c t i o n c r o s s s e c t i o n s at 4 GeV [4] and 6 GeV [5], a l t h o u g h this w a s a l s o p o s s i b l e with the c o m b i n a t i o n s w + B o r p+ B. H o w e v e r , with e i t h e r of t h e s e it w a s not p o s s i b l e to fit o u r d a t a in the r e g i o n of 2 GeV, w h e r e a s with the c o m b i n a t i o n w + p a f a i r m e a s u r e of a g r e e m e n t could be o b t a i n e d . In the p r e s e n t e x p e r i m e n t we have m a d e m e a s u r e m e n t s at s m a l l a n g l e s i n the r e g i o n of the P l 1 ( 1 7 8 5 ) r e s o n a n c e (1.22 GeV) and at h i g h e r e n e r g i e s (1.51 GeV and 1.85 GeV) in o r d e r to t e s t f u r t h e r the t h e o r e t i c a l i n t e r p r e t a t i o n s m e n t i o n e d above.
PHOTOPRODUCTION OF ETA MESONS
511
2. M E T H O D In o u r f i r s t e x p e r i m e n t the p r o c e s s ~,p - pT? ( 7 / - 2~) w a s d e t e c t e d t h r o u g h a d o u b l e c o i n c i d e n c e b e t w e e n a p r o t o n and on e of the d e c a y p h o t o n s of the e t a m e s o n . H o w e v e r , at s m a l l a n g l e s the e n e r g y of the p r o t o n b e c o m e s too s m a l l f o r d e t e c t i o n so it i s then n e c e s s a r y to m a k e u s e of a c o i n c i d e n c e b e t w e e n the two d e c a y p h o t o n s . If the d i r e c t i o n s and e n e r g i e s of t h e s e two p h o t o n s a r e d e t e r m i n e d , the d i r e c t i o n and e n e r g y of the m e s o n and i t s r e s t m a s s can be found. T h e f o l l o w i n g a r e the e x p r e s s i o n s f o r the e n e r g y E , the r e s t m a s s ~ and the d i r e c t i o n of the m e s o n : 1
1
;~[(E 1 / E 2)~ + (E 2/E1)~ 1 E= 1 2 sin ~ 0
m 2 =2 E I E 2 ( 1 - c o s ~ ) , s in 81
E2
sin(6 - 81) - E 1 ' w h e r e E 1 and E 2 a r e the e n e r g i e s of the two d e c a y p h o t o n s , 0 i s the a n g l e b e t w e e n t h e m , and 81 i s the a n g l e b e t w e e n o n e of the p h o t o n s and the m e s o n d i r e c t i o n . A l l q u a n t i t i e s a r e m e a s u r e d in the l ab s y s t e m . It i s to b e n o t e d that an a b s o l u t e e n e r g y c a l i b r a t i o n of t h e photon " d e t e c t o r s i s r e q u i r e d only f o r the d e t e r m i n a t i o n of the r e s t m a s s of the m e s o n and a l s o t h a t E i s m u c h m o r e s e n s i t i v e to the a n g u l a r m e a s u r e m e n t than to the v a l u e s of the e n e r g y r a t i o s when t h e s e a r e c l o s e to unity. F r o m the e n e r g y , r e s t m a s s and d i r e c t i o n of the m e s o n the i n c i d e n t photon e n e r g y can be found on the a s s u m p t i o n that the m e s o n i s p r o d u c e d in a t w o - b o d y p r o cess.
3. D E T E C T O R S T h e photon d e t e c t o r s w e r e two h o d o s c o p e s of l e a d - g l a s s ~ e r e n k o v c o u n t e r s . E a c h h o d o s c o p e c o n s i s t e d of a 6 × 4 a r r a y of b l o c k s , e a c h b l o c k 35 c m l o n g by 8 c m s q u a r e and v i e w e d by an RCA 8575 p h o t o m u l t i p l i e r . T h e s e 24 b l o c k s w e r e m o u n t e d in a s t e e l box s c r e e n e d w i t h 5 c m of l e a d at the s i d e s and h a v i n g a l e a d d e f i n i n g a p e r t u r e 41 c m × 25 c m in f r o n t . A s c i n t i l l a t i o n c o u n t e r to v e t o c h a r g e d p a r t i c l e s w a s p l a c e d b e t w e e n the a p e r t u r e and the b l o c k s . T h e two h o d o s c o p e s w e r e s u p p o r t e d o n e a b o v e the o t h e r on a s t a n d in s u c h a m a n n e r that t h e i r h e i g h t s and a n g l e s of t i l t co u l d be a d j u s t e d to e n a b l e t h e m to be p o s i t i o n e d s y m m e t r i c a l l y a bo u t the h o r i z o n t a l p l a n e c o n t a i n i n g the b e a m and p o i n t e d t o w a r d s the t a r g e t . T h i s w a s a c h i e v e d by f i x i n g e a c h b o x at o n e s i d e to a h o r i z o n t a l b e a r i n g to p r o v i d e the t i l t a d j u s t m e n t w h i l e t h e b e a r i n g i t s e l f c o u l d be m o v e d v e r t i c a l l y in a s l i d e a t t a c h e d to a j a c k s c r e w . T h e s u p p o r t f r a m e w a s p r o v i d e d w i t h b a l l c a s t o r s so that it
512
P . S . L . BOOTH et al.
could be m o v e d into any p o s i t i o n on the s t e e l f l o o r of the e x p e r i m e n t a l hall. D u r i n g the e x p e r i m e n t the l e a d - g l a s s d e t e c t o r s w e r e p l a c e d with t h e i r f r o n t f a c e s 2 m f r o m the t a r g e t with an o p e n i n g a n g l e w h i c h v a r i e d b e t w e e n 30 ° and 58 °. The t a r g e t w a s of l i q u i d h y d r o g e n 10 c m i n length. At a n g l e s of e m i s s i o n of the eta g r e a t e r than a b o u t 30 ° c . m . the r e c o i l p r o t o n s w e r e d e t e c t e d with a s c i n t i l l a t i o n c o u n t e r 30 c m x 20 c m x 1.2 c m p l a c e d 40 cm f r o m the t a r g e t .
4. E L E C T R O N I C S The l i n e a r o u t p u t s f r o m the 24 m u l t i p l i e r s in e a c h h o d o s c o p e w e r e added t o g e t h e r and a f t e r s u i t a b l e d i s c r i m i n a t i o n the two p u l s e s f r o m the h o d o s c o p e s w e r e t a k e n to a c o i n c i d e n c e c i r c u i t with 20 n s r e s o l v i n g t i m e to p r o v i d e the t r i g g e r s i g n a l f o r an e v e n t . T h e d i s c r i m i n a t o r s y s t e m w a s s u c h that a r a t h e r low l e v e l w a s s e t on the i n d i v i d u a l o u t p u t s of the two h o d o s c o p e s b u t a high l e v e l , e q u a l to a b o u t half the m a x i m u m p u l s e h e i g h t p o s s i b l e for an eta, on the s u m of the two. T h i s w a s i m p o r t a n t in r e d u c i n g u n w a n t e d e v e n t s w h i l e m a i n t a i n i n g m a x i m u m e f f i c i e n c y f o r eta d e t e c t i o n , s i n c e the s u m i s j u s t a m e a s u r e of the e n e r g y of the e t a , w h e r e a s the i n d i v i d u a l o u t p u t s v a r y w i d e l y d e p e n d i n g on the way in w h i c h the d e c a y e n e r g y d i v i d e s , in the l a b s y s t e m , b e t w e e n the two p h o t o n s . A s e c o n d o u t p u t f r o m e a c h p h o t o m u l t i p l i e r w a s u s e d to d i g i t i s e the c h a r g e f r o m e a c h ~ e r e n k o v c o u n t e r u s i n g 48 a n a l o g u e - t o - d i g i t a l c o n v e r t e r s . T i m e t o - d i g i t a l c o n v e r t e r s w i t h a r e s o l u t i o n of 0.3 n s w e r e u s e d to give the r e l a t i v e t i m e b e t w e e n the s u m m e d o u t p u t s f r o m the a r r a y s and any s i g n a l in the v e t o c o u n t e r s o r the p r o t o n c o u n t e r , when the l a t t e r w a s in u s e . The a b o v e d a t a , t o g e t h e r with the p u l s e h e i g h t in the p r o t o n c o u n t e r and the t i m e of e a c h e v e n t r e l a t i v e to the a c c e l e r a t o r c y c l e , w e r e fed into a P D P 8 c o m p u t e r . T h i s c o m p u t e r p r o v i d e d r u n n i n g d i s p l a y s f o r m o n i t o r i n g p u r p o s e s d u r i n g the e x p e r i m e n t and r e c o r d e d a l l the i n f o r m a t i o n on m a g n e t i c tape f o r l a t e r a n a l ysis.
5. C A L I B R A T I O N AND O P E R A T I O N T h e a b s o l u t e e n e r g y c a l i b r a t i o n and r e s o l u t i o n of a s i n g l e b l o c k of g l a s s w e r e d e t e r m i n e d u s i n g e l e c t r o n s o~f k n o w n e n e r g y . T h e G a u s s i a n half w i d t h of the p e a k w a s found to b e 8.8 E - g % , w h e r e E i s the e l e c t r o n e n e r g y in GeV. T h e p r o c e d u r e f o r e q u a l i s i n g the g a i n s of a l l the p h o t o m u l t i p l i e r s w a s a s f o l l o w s . T h e two l e a d - g l a s s a r r a y s w e r e p o s i t i o n e d a s c l o s e l y a s p o s s i b l e to the d i r e c t i o n of the photon b e a m f r o m the s y n c h r o t r o n . A s t o p p e r of l e a d 80 c m t h i c k w a s m o v e d into the b e a m s e v e r a l m e t r e s u p s t r e a m of the c o u n t e r s . The s p r a y of p a r t i c l e s e m e r g i n g f r o m the l e a d c o n s i s t e d l a r g e l y of m u o n s and t h e s e , p a s s i n g t h r o u g h the b l o c k s of g l a s s , p r o d u c e d ~ e r e n k o v p u l s e s of s t a n d a r d s i z e . T h e 48 p u l s e - h e i g h t s p e c t r a w e r e s i m u l t a n e o u s l y r e c o r d e d on m a g n e t i c t a p e and a f t e r a r u n of half an h o u r , d u r i n g w h i c h a
PHOTOPRODUCTION OF ETA MESONS
513
total of a b o u t 50 000 m u o n s w e r e d e t e c t e d , the tape w a s p r o c e s s e d on a 3 6 0 / 6 5 c o m p u t e r to p r o d u c e p r i n t - o u t s of a l l the s p e c t r a . The p o s i t i o n s of the p e a k s could be d e t e r m i n e d to ± 4 2 and c o r r e c t i o n s to the m u l t i p l i e r v o l t a g e s w e r e then m a d e on the b a s i s of a p r e v i o u s l y d e t e r m i n e d r e l a t i o n b e t w e e n v o l t a g e and p u l s e height. T h i s c a l i b r a t i o n w a s c a r r i e d out at i n t e r v a l s of a few d a y s d u r i n g a r u n and it w a s u s u a l l y n e c e s s a r y to m a k e a d j u s t m e n t s of a few p e r c e n t to a s m a l l p r o p o r t i o n of the p h o t o m u l t i p l i e r s . T h e e x p e r i m e n t was o p e r a t e d f o r a total of 250 h o u r s with a photon b e a m of a b o u t 3.109 e q u i v a l e n t q u a n t a p e r s e c o n d h a v i n g a p u l s e d u r a t i o n of a b o u t 2 m s at the m a c h i n e r e p e t i t i o n f r e q u e n c y of 53 Hz. The r a t e of eta e v e n t s w a s a b o u t 15 p e r hour.
6. DATA R E D U C T I O N The f i r s t s t e p in p r o c e s s i n g the d a t a w a s to d e t e r m i n e the p u l s e h e i g h t s due to s h o w e r s in the two a r r a y s by a d d i n g the p u l s e s f r o m the n i n e b l o c k s in the v i c i n i t y of e a c h s h o w e r . The g e n e r a l b a c k g r o u n d of s m a l l , r a n d o m p u l s e s in the r e m a i n i n g b l o c k s w a s a v e r a g e d and s u b t r a c t e d f r o m this. The d i r e c t i o n of e a c h photon w a s t a k e n to be that c o r r e s p o n d i n g to the c e n t r e of the b l o c k s h o w i n g the l a r g e s t p u l s e . The m o m e n t u m and a n g l e of e m i s s i o n of the e t a w e r e n e x t c a l c u l a t e d . S i n c e the a n g u l a r r a n g e c o v e r e d at e a c h p o s i t i o n of the a p p a r a t u s w a s a b o u t 30 ° c . m . the d a t a w a s d i v i d e d into e i t h e r 3 o r 4 a n g l e b i n s . The a c c e p t e d m o m e n t u m r a n g e w a s r e s t r i c t e d to v a l u e s g r e a t e r than 150 M e V / c b e l o w the l i m i t s e t by the b r e m s s t r a h l u n g cut-off. T h i s e n s u r e s that e t a s p r o d u c e d in a s s o c i a t i o n with o n e o r m o r e p i o n s a r e not d e t e c t e d . The e n e r g y of the i n c i d e n t photon w a s c a l c u l a t e d on the a s s u m p t i o n of s i n g l e e t a p r o d u c t i o n and the e v e n t s s e p a r a t e d into two g r o u p s d e p e n d i n g on w h e t h e r this w a s below o r a b o v e the b r e m s s t r a h l u n g l i m i t . The t i m e s p e c t r u m of g a m m a - g a m m a c o i n c i d e n c e s w a s p l o t t e d out and the l i m i t s to be u s e d i n s e p a r a t i n g the p e a k due to " r e a l " e v e n t s f r o m the b a c k g r o u n d of " r a n d o m " e v e n t s w e r e d e c i d e d . An e f f e c t i v e t i m e window of 5 n s w a s thus o b t a i n e d . S i m i l a r l y , the t i m e s p e c t r a of the v e t o c o u n t e r s w e r e u s e d to d e c i d e the l i m i t s of the p e a k in e a c h c a s e r e p r e s e n t i n g the g e n u i n e v e t o p u l s e s s u p e r i m p o s e d on a b a c k g r o u n d of r a n d o m o n e s . The d a t a w a s then p r o c e s s e d a s e c o n d t i m e with t h e s e c u t s in the g a m m a g a m m a and v e t o t i m e s p e c t r a . E v e n t s a s s o c i a t e d with a g e n u i n e p u l s e in one o r both v e t o c o u n t e r s w e r e r e j e c t e d and the c o r r e c t i o n f o r r a n d o m v e t o s w a s d e t e r m i n e d . An e f f e c t i v e m e s o n m a s s w a s c a l c u l a t e d f o r e a c h e v e n t on the a s s u m p t i o n that it w a s p r o d u c e d by a m e s o n w h i c h d e c a y e d into two p h o t o n s . M a s s s p e c t r a w e r e p l o t t e d f o r e a c h a n g l e b i n f o r e v e n t s w i t h i n the p e a k in the g a m m a - g a m m a t i m e s p e c t r u m , f o r t h o s e o u t s i d e the p e a k and f o r t h o s e below and a b o v e the b r e m s s t r a h l u n g l i m i t . M a s s s p e c t r a c o r r e c t e d f o r r a n d o m e v e n t s w e r e p r o d u c e d f r o m t h e s e and a t y p i c a l p a i r of s p e c t r a a r e shown in fig. 1. The f i r s t of t h e s e , w h i c h c o r r e s p o n d s to c a l c u l a t e d v a l u e s of i n c i d e n t e n e r g y b e l o w the b r e m s s t r a h l u n g l i m i t , has a p e a k at the p o s i t i o n e x p e c t e d f o r the e t a m a s s , w h e r e a s the s e c o n d s p e c t r u m f o r i n c i d e n t e n e r g i e s a b o v e t h i s l i m i t , has no peak.
514
P . S . L . BOOTH et al.
120 HI,,
lOO
80
50
40
~
30
60 40
10
20 _L 700
500 MeV
300
500 MeV
Fig. l(a). Mass spectrum for events within the eta kinematic region. Fig. l(b). Mass spectrum for events outside the eta kinematic region. The s u b t r a c t i o n of the b a c k g r o u n d u n d e r n e a t h the e t a m a s s p e a k w a s p e r f o r m e d by a c u r v e f i t t i n g r o u t i n e on the c o m p u t e r . The p e a k and b a c k g r o u n d w e r e p a r a m e t r i s e d by a G a u s s i a n p l u s an e x p r e s s i o n of the f o r m a e x p ( - b x ) - c and a l e a s t s q u a r e s fit w a s u s e d to d e t e r m i n e the n u m b e r of e t a s in the p e a k ( s e e fig. 1). At a n g l e s w h e r e it w a s p o s s i b l e to d e t e c t the r e c o i l p r o t o n the d a t a w e r e p r o c e s s e d both with and w i t h o u t the r e q u i r e m e n t of a c o i n c i d e n t p u l s e f r o m the p r o t o n c o u n t e r . In a l l s u c h c a s e s the a g r e e m e n t b e t w e e n the f i n a l r e s u l t s w a s w i t h i n the e r r o r s of m e a s u r e m e n t . The r e l a t i o n s h i p b e t w e e n the n u m b e r of o b s e r v e d e t a s and the a b s o l u t e d i f f e r e n t i a l c r o s s s e c t i o n w a s d e t e r m i n e d by m e a n s of a Monte C a r l o p r o g r a m m e in w h i c h e v e n t s w e r e s i m u l a t e d and the d e t e c t i o n e f f i c i e n c i e s for e a c h r a n g e of a n g l e a n d m o m e n t u m w e r e d e r i v e d . The g e o m e t r y of the t a r get and c o u n t e r s , the e n e r g y r e s o l u t i o n and c a l i b r a t i o n of the l a t t e r , and the e n e r g y s p r e a d of the e l e c t r o n b e a m r e s u l t i n g f r o m the f i n i t e s p i l l t i m e w e r e u s e d in t h i s p r o g r a m m e .
7. R E S U L T S T h e d i f f e r e n t i a l c r o s s s e c t i o n s o b t a i n e d in t h i s w o r k a r e p r e s e n t e d in t a b l e 1. In o u r p r e v i o u s e x p e r i m e n t (Booth et al. [1]) d a t a w a s o b t a i n e d ~t l a r g e r a n g l e s u s i n g a c o m p l e t e l y d i f f e r e n t t e c h n i q u e f o r d e t e c t i n g the p r o c e s s . S o m e of t h i s d a t a i s i n c l u d e d h e r e in o r d e r to p r o v i d e a m o r e c o m p l e t e p i c t u r e of the b e h a v i o u r of the c r o s s s e c t i o n b e t w e e n 1.2 GeV and
P H O T O P R O D U C T I O N O F E T A MESONS
515
Table 1 Differential cross sections for yp ~ p~.
Ey
0 77
dO" da
1.22 1.21 1.22 1.22 1.52
13 19 26 33 8
0.085±0.028 0.093 ± 0.011 0.100±0.010 0.125±0.022 0.097±0.027
1.83 1.82 1.84 1.82 1.82
8 15 19 22 26
0.074 ± 0.024 0.095 ± 0.008 0.101±0.025 0.133±0.018 0.108±0.017
1.51 1.51 1.51 1.50 1.51
15 22 32 40 47
0.121±0.012 0.146±0.018 0.136±0.023 0.101 ± 0.012 0.084±0.020
1.83 1.83 1.82 1.84
32 34 38 46
0.130±0.023 0.105±0.022 0.120±0.015 0.095 ÷ 0.025
da
H e r e , E y is t h e m e a n i n c i d e n t e n e r g y (GeV), t o t a l bin w i d t h ~ 0.1 GeV; 8?? i s the m e a n a n g l e of e t a ( d e g r e e s c . m . ) , t o t a l bin w i d t h ~ 7o; and d(:r/d~ is the d i f f e r e n t i a l c r o s s s e c t i o n (t~b s r - 1 ) .
Table 2 D i f f e r e n t i a l c r o s s s e c t i o n s f o r y p -~ p r / .
1.23 1.34 1.33 1.32
64 45 50 65
0.179 0.156 0.180 0.173
± ± ± ±
0.018 0.020 0.016 0.018
0.148 0.126 0.172 0.173
± 0.023 ± 0.018 ± 0.025 ± 0.027"
1.33 1.41 1.51 1.50
83 65 41 66
0.189 0.149 0.157 0.096
± 0.013 ± 0.012 ± 0.013 ± 0.010
0.163 0.137 0.151 0.111
± 0.023 ± 0.021 ± 0.()28 -~ 0.015
1.50 1.59 1.70 1.64
74 63 38 51
0.141 0.082 0.128 0.092
± 0.012 ± 0.008 ± 0.010 ± 0.010
0.141 0.071 0.137 0.077
± 0.018 *" ± 0.010 ± 0.026 ± 0.017
1.68 1.88 1.83 1.85 2.02
67 35 46 56 52
0.064 0.137 0.081 0.052 0.095
± ± ± ± ±
0.056 0.148 0.060 0.052 0.100
± 0.014 ± 0.017 ± 0.015 ± 0.012 * ± 0.012
0.009 0.013 0.012 0.008 0.011
H e r e , (d(Y/d~)l i s the c r o s s s e c t i o n q u o t e d in r e f . [1]; (d(~/d~)2 i s the c r o s s s e c t i o n r e s u l t i n g f r o m r e a n a l y s i s of t h e d a t a of r e f . [1] ( p o i n t s m a r k e d w i t h an a s t e r i s k w e r e not r e a n a l y s e d but the e r r o r has been i n c r e a s e d ) .
516
P.S.L.
BOOTH et al.
F'
0.2
#_b sr
0.1 ET= 1.22 GeV
0 F i g . 2. D i f f e r e n t i a l
' cross
'
3~0~
'
'6'0
°.
' '
s e c t i o n s f o r i n c i d e n t e n e r g y 1.22 G e V . H e r e p r e s e n t e x p e r i m e n t , x r e f . [1].
'
o are the
/ /
02
Sr
0.1
ET= 1.33 GeV 0
L
F i g . 3. D i f f e r e n t i a l c r o s s
'
3~
L
e,
I
6~ °
,
L
s e c t i o n s f o r i n c i d e n t e n e r g y 1.33 G e V f r o m r e f . [1].
0.2
ET= 1.51 GeV
ST
0.1
o
F i g . 4. D i f f e r e n t i a l c r o s s
'
'
3'o~
'
'
~
'
'
s e c t i o n s f o r i n c i d e n t e n e r g y 1.51 G e V . H e r e o a r e t h e p r e s e n t e x p e r i m e n t , × r e f . [1].
PHOTOPRODUCTION OF ETA MESON8
517
E;r= 1.68 GeV SF
0.1
o
j J
I
J
3o°
i
6~00
i
Fig. 5. Differential c r o s s sections for incident energy 1.68 GeV from ref. [11.
$r
0.1
o
~
F__7=1.85GeV
3'O
Fig. 6. Differential c r o s s sections for incident energy 1.85 GeV. Here o are the p r e s e n t experiment, × ref. [1]. 1.9 GeV. In t h i s e a r l i e r w o r k the s u b t r a c t i o n of the b a c k g r o u n d b e n e a t h the e t a p e a k had b e e n d o n e by hand and the c o n t r i b u t i o n of the u n c e r t a i n t y in t h i s to the s t a n d a r d d e v i a t i o n of the r e s u l t w a s e s t i m a t e d . As a c h e c k on t h i s p r o c e d u r e it s e e m e d w o r t h w h i l e r e a n a l y s i n g s o m e of the d a t a f r o m the f i r s t e x p e r i m e n t u s i n g "the c o m p u t e r c u r v e f i t t i n g p r o c e d u r e e m p l o y e d in the p r e s e n t i n v e s t i g a t i o n . In t a b l e 2 we show the c r o s s s e c t i o n s r e s u l t i n g f r o m t h i s r e a n a l y s i s , t o g e t h e r w i t h the p r e v i o u s v a l u e s . T h e c h a n g e s in c r o s s s e c t i o n a r e not l a r g e but t h e r e is a g e n e r a l i n c r e a s e in the v a l u e s of the s t a n d a r d deviation. T h e t h r e e p o i n t s m a r k e d w i t h a s t e r i s k s in t a b l e 2 and the r e s t of the d a t a f r o m the f i r s t e x p e r i m e n t h a v e not b e e n s u b j e c t e d to r e a n a l y s i s . S i n c e the c h i e f r e s u l t of r e a n a l y s i s w a s an i n c r e a s e in the s t a n d a r d d e v i a t i o n it s e e m e d r e a s o n a b l e in t h e s e c a s e s to l e a v e the c r o s s s e c t i o n s u n c h a n g e d but to i n c r e a s e t h e s t a n d a r d d e v i a t i o n s by 5 0 ~ T h e d a t a f r o m the p r e s e n t e x p e r i m e n t and the r e v i s e d d a t a f r o m the e a r l i e r o n e a r e d i s p l a y e d in f i g s . 2 to 6 a s a n g u l a r d i s t r i b u t i o n s f o r m e a n e n e r g i e s of 1.22 GeV, 1.33 GeV, 1.51 GeV, 1.68 GeV and 1.83 GeV. T h e p r e s e n t d a t a p o i n t s a r e m a r k e d a s c i r c l e s , t h e e a r l i e r o n e s as c r o s s e s . T h e c u r v e d r a w n in fig. 6 i s a t h e o r e t i c a l c u r v e o b t a i n e d by B a j p a i and D o n n a c h i e [3] by f i r s t f i t t i n g the d a t a at 4 G eV and 6 G e V a s s u m i n g the ex-
518
P . S . L . BOOTH et al.
c h a n g e of R e g g e i z e d co- a n d p - m e s o n s and then e x t r a p o l a t i n g d o w n w a r d s in e n e r g y to 1.85 GeV. It i s i n t e r e s t i n g that the d a t a a g r e e so w e l l with the p r e d i c t i o n of the e x c h a n g e m o d e l at s u c h a c o m p a r a t i v e l y low e n e r g y . T h i s i s p o s s i b l y c o n n e c t e d w i t h an a b s e n c e of l a r g e c o n t r i b u t i o n s f r o m T = ½ r e s o n a n c e s in eta p h o t o p r o d u c t i o n at t h i s e n e r g y . At 2.03 GeV, n e a r the p e a k of the G17(2190 ) r e s o n a n c e o u r old d a t a p o i n t s (Booth et al. [1]) a r e h i g h e r than the t h e o r e t i c a l c u r v e ( B a j p a i and D o n n a c h i e [3]) and we i n t e n d to m a k e f u r t h e r m e a s u r e m e n t s at s m a l l a n g l e s t h r o u g h o u t the r e g i o n of this r e s o nance. The c u r v e s in figs. 2 to 5 w e r e d e r i v e d f r o m the g e n e r a l i s e d i n t e r f e r e n c e m o d e l of B a j p a i and D o n n a c h i e [2], u s i n g a m p l i t u d e s r e p r e s e n t i n g the P l 1 ( 1 7 8 5 ) and S l 1 ( 1 5 5 0 ) r e s o n a n c e s p l u s t h o s e of the Regge e x c h a n g e p r o c e s s m e n t i o n e d above. As d e s c r i b e d in ref. [2], the e n e r g i e s and w i d t h s of the r e s o n a n c e s w e r e t a k e n f r o m the r e s u l t s of ~p p h a s e - s h i f t a n a l y s e s , l e a v i n g a s f r e e p a r a m e t e r s the p r o d u c t of the 7P and UP p a r t i a l w i d t h s f o r e a c h r e s o n a n c e and the r e l a t i v e p h a s e s of the r e s o n a n c e s and R e g g e b a c k g r o u n d . The a v a i l a b l e d a t a w e r e s a t i s f a c t o r i l y fitted in ref. [2] on the a s s u m p t i o n of r e l a t i v e p h a s e d i f f e r e n c e s of z e r o . O u r p r e s e n t r e s u l t s at 1.22 GeV, n e a r the p e a k of the P l l r e s o n a n c e , show that the c r o s s s e c t i o n d e c r e a s e s at s m a l l a n g l e s , i n d i c a t i n g d e s t r u c t i v e i n t e r f e r e n c e b e t w e e n t h i s s t a t e and the t a i l of the S l 1 ( 1 5 5 0 ). U s i n g the p r e s e n t d a t a and all o u r old d a t a b e t w e e n 960 MeV and 1.9 GeV t o g e t h e r with d a t a f r o m o t h e r s o u r c e s [2] b e t w e e n t h r e s h o l d and 960 MeV, the c u r v e s shown w e r e o b t a i n e d a s b e s t fits w i t h the f o u r p a r a m e t e r s s p e c i f i e d a b o v e a s v a r i a b l e s . The p h a s e d i f f e r e n c e b e t w e e n the r e s o n a n t a m p l i t u d e s w a s 180 ° r a t h e r than z e r o . It i s a p l e a s u r e to t h a n k P r o f . A. D o n n a c h i e f o r p r o v i d i n g the t h e o r e t i c a l f i t s to o u r d a t a u s i n g his i n t e r f e r e n c e m o d e l . We w i s h a l s o to t h a n k M e s s r s . D. C a r s o n and P. Noake f o r help in s e t t i n g up the c o u n t e r s and e l e c t r o n i c s and D r . E. G. H. W i l l i a m s f o r a s s i s t a n c e d u r i n g r u n n i n g . P r o f . B. C o l l i n g e w a s r e s p o n s i b l e f o r the d e s i g n of s o m e of the e l e c t r o n i c c i r c u i t s . We a r e i n d e b t e d to the s t a f f of the D a r e s b u r y e l e c t r o n s y n c h r o t r o n f o r t h e i r e f f o r t s on o u r b e h a l f and to the S c i e n c e R e s e a r c h C o u n c i l f o r the p r o v i s i o n of f a c i l i t i e s and f i n a n c i a l s u p p o r t , i n c l u d i n g a s t u d e n t s h i p f o r J. S. B.
REFERENCES [1] P . S . L . Booth, M.F. Butler, L . J . Carroll, J. R. Holt, J. N. Jackson, W. H. Range, E. G. H. Williams, J. R. Wormald and N. lq. S. Tait, Nuovo Cim. Letters 2 {1969) 66. [2] R. P. Bajpai and A. Donnachie, Nucl. Phys. B12 {1969) 274. [3] R. P. Bajpai and A. Donnachie, Daresbury Laboratory preprint DNPL/P 15, 1969. [4] D. Bellenger, S. Deutsch, D. Luckey, L.S. Osborne and R. Schwitters, Phys. Rev. Letters 21 (1968) 1205. [5] R. Anderson, D. Gustavson, J. Johnson, D. Ritson, W. G. Jones, D. Kreinick, F. Murphy and R.Weinstein, Phys. Rev. Letters 21 {1968) 384.