c

Volume 39B, number 3

SMALL

1~ H Y S I C S L E T T E R S

ANGLE

PROTON-PROTON FROM 9 TO

70

ELASTIC GeV/c

1May 1972

SCATTERING

G. G. BEZNOGIKH, A. BUJAK, L. F. KIRILLOVA, B . A . MOROZOV, V . A . NIKITIN, P. V. NOMOKONOV, A. SANDACZ, M. G. SHAFRANOVA, V.A. SVIRIDOV, TRUONG BIEN, V . I . ZAYACHKI, N . K . ZHIDKOV and L . S . ZOLIN Laboratory of High Energies, Joint Institute for Nuclear Research, Dubna, USSR Received 22 March 1972

Proton-l~roton elastic scattering has been measured over the four-momentum transfer squared 0.0007 ~< t ~< 0.02 GeV2/c2. A gas hydrogen jet has been used as an internal target of the accelerator. The results indicate that the ratio of the real to the imaginary part of the proton-proton forward scattering amplitude rises smoothly with increasing energy from ot = -0.35 =~0.05 at p = 9.39 GeV/c to (x = -0.092 ± 0.011 at p = 69.8 GeV/c.

T h i s l e t t e r p r e s e n t s the r e s u l t s of the e x p e r i m e n t p e r f o r m e d at the 70 GeV Serpukhov a c c e l e r a t o r . The r e a l p a r t p a r a m e t e r c~ = Re A / I m A of the p r o t o n - p r o t o n f o r w a r d e l a s t i c s c a t t e r i n g a m p l i t u d e has been m e a s u r e d . T h i s w o r k is a continuation and d e v e l o p m e n t of o u r e a r l y exp e r i m e n t at the 10 GeV Dubna P r o t o n S y n c h r o t r o n [1]. T h e new data c o v e r the m o m e n t u m r a n g e '9 --< p --< 70 G e V / c . P r e l i m i n a r y data f r o m a p a r t of runs w e r ~ p r e s e n t e d a t the 1970 Kiev C o n f e r e n c e [2]. The method and e x p e r i m e n t a l technique w e r e s i m i l a r to t h o s e used by o u r group in p r e v i o u s slope p a r a m e t e r m e a s u r e m e n t s [3]. The hydrogen jet t a r g e t was used instead of a (CH2) n film. T h e d e t a i l s of the e x p e r i m e n t a l method can be found in ref. [4]. A b r i e f d e s c r i p t i o n of the app a r a t u s is given below. The s p e c i a l d e v i c e with a c r y o g e n i c liquid h e l i u m pump f o r m e d the gas h y d r o g e n jet in the a c c e l e r a t o r v a c u u m c h a m b e r . The h y d r o g e n d e n s i t y in the j et was about 10 -7 g / c m 3. The p r o t o n b e a m - h y d r o g e n jet i n t e r s e c t i o n r e g i o n was a c y l i n d e r 2 c m long, 0.8 cm in d i a m e t e r with the axis o r i e n t e d along the b e a m d i r e c t i o n . The jet t a r g e t o p e r a t e d 2 o r 3 t i m e s p e r c y c l e (~ 2500 m s e c ) of a c c e l e r a t i o n . The duration of each such jet was only 200 m s e c in o r d e r not to i n c r e a s e the background due to the i n t e r a c t i o n of the b e a m with the r e s i d u a l h y d r o g e n gas in the a c c e l e r a t o r v a c u u m c h a m b e r . F o r 200 m s e c the b e a m p r o t o n s have p a s s e d through the jet about 4 × 104 t i m e s . Eight s e m i c o n d u c t o r S i - d e t e c t o r s w e r e p l a c e d in the e v a c u a t e d r e c o i l proton tube at 352 cm

f r o m the b e a m - j e t i n t e r s e c t i o n r~gion. Moving to round a c i r c l e c e n t e r e d at the t a r g e t t h e s e d e t e c t o r s c o v e r e d an i n t e r v a l of r e c o i l proton angles f r o m 91 ° to 84 °. The e n e r g y r e s o l u t i o n s of the d e t e c t o r s used w e r e 6 0 - 100 keY; t h e i r d i m e n s i o n s w e r e 5 (along the beam) × 25 m m 2" the t h i c k n e s s e s of the d e t e c t o r s ' s e n s i t i v e l a y e r w e r e f r o m 0.1 to 3.0 m m . Th e r e c o i l proton was a n a l y s e d f o r 10 c y c l e s of a c c e l e r a t i o n , and then the d e t e c t o r s w e r e shifted by 1.4 ° to m e a s u r e the background (5 c y c l e s ) . T y p i c a l l y the n o r m a l r a t e s in the d e t e c t o r s w e r e of the o r d e r of s o m e hundreds p e r second. T h i s a r r a n g e m e n t allowed the p r o t o n - p r o t o n e l a s t i c s c a t t e r i n g d i f f e r e n t i a l c r o s s - s e c t i o n to be m e a s u r e d o v e r a I t l - r a n g e f r o m 0.0007 to 0.02 G e V 2 / c 2. T h r e e co u n t er t e l e s c o p e s w e r e i n s t a l l e d at the angle of 65 ° to the b e a m to look at the b e a m jet i n t e r a c t i o n region. The si g n al s f r o m t h ese c o u n t e r s w e r e used to c o n t r o l the i n t e r a c t i o n r a t e and for the r e l a t i v e n o r m a l i z a t i o n of the runs with d i f f e r e n t d e t e c t o r a n g u l a r p o s i t i o n s . Th e d e t e c t o r s i g n a l s w e r e t r a n s f e r r e d to a b u f f e r m e m o r y through 8 s p e c t r o m e t r i c t r a c k s , a d e t e c t o r n u m b e r c o d e r and a n a l o g u e - t o - d i g i t a l c o n v e r t o r . The content of the buffer m e m o r y was r e c o r d e d on m a g n e t i c tape through an o n - l i n e c o m p u t e r . Th e t i m e c o d e r g e n e r a t e d 64 t i m i n g m a r k e r s with the i n t e r v a l of 32 m s e c and it was t r i g g e r e d by a s t a r t pulse f r o m the a c c e l e r a t o r . S i m u l t a n e o u s l y with the t i m i n g m a r k e r g e n e r a t i o n , the contents of the t e l e s c o p e co u n t er s c a l e r s w e r e r e a d into a c o m p u t e r . T h e typical e n e r g y s p e c t r u m of r e c o i l p a r t i c l e s taken by the s e m i c o n d u c t o r d e t e c t o r is p r e s e n t e d 411

Volume 39B, n u m b e r 3

PHYSICS

-*,N

,,j,

7O

I

p_p 55.3oev/c ~=-0.0014(oev/c~~

50

30

to

oo %

zo

Fig. 1. Energy s p e c t r u m of the recoil p a r t i c l e s . in fig. 1. It i s s e e n t h a t t h e b a c k g r o u n d is l e s s t h a n 1 0 % of t h e e f f e c t . T h e w i d t h of t h e e l a s t i c p p s c a t t e r i n g p e a k is m a i n l y due to t h e d i m e n s i o n of t h e b e a m - t a r g e t i n t e r a c t i o n r e g i o n . T h e s a m p l e of r e c o i l p a r t i c l e s p e c t r a w a s p r o c e s s e d o f f - l i n e to o b t a i n 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 for elastic pp scattering. This analysis also perf o r m e d t h e c o n t r o l a n d c o r r e c t i o n of t h e m a i n a p p a r a t u s p a r a m e t e r s : c a l i b r a t i o n c o n s t a n t s of the spectrometric tracks, the target coordinate a n d i t s g a s d i s t r i b u t i o n s h a p e a n d s o on. The proton-proton differential cross-section

i May 1972

LETTERS

o b t a i n e d in o n e of t h e r u n s a t 70 G e V i s p l o t t e d v e r s u s It[ in fig. 2 (full d a t a w i l l b e p u b l i s h e d e l s e w h e r e ) . T h e a n a l y s i s ol t h e d i f f e r e n t i a l cross-sections used the well-known Bethe formul a [5] a n d w a s s i m i l a r to t h a t i n o u r e a r l y p a p e r s [1]. T h e m a i n s y s t e m a t i c e r r o r s in t h e r e a l p a r t p a r a m e t e r ~ w e r e due to t h e u n c e r t a i n t y in t h e a r e a of t h e d e t e c t o r s , t h e u n c e r t a i n t y in t h e detectors' coordinates and the apparatus faults connected with electronics overload. The rootm e a n - s q u a r e of a l l t h e s e e r r o r s i s A~ = 0.028. T h e r e s u l t s f o r ~ (the r a t i o b e t w e e n t h e r e a l a n d t h e i m a g i n a r y p a r t s of t h e p r o t o n - p r o t o n f o r w a r d s c a t t e r i n g a m p l i t u d e ) a r e g i v e n in t a b l e 1 a n d p l o t t e d v e r s u s l a b . m o m e n t u m in fig. 3. T h e t o t a l pp e l a s t i c c r o s s - s e c t i o n d a t a ~el = = ( d a / d t ) o p t (1 + a 2 ) / b + A w h e r e t h e s l o p e p a r a m e t e r b w a s t a k e n f r o m o u r p r e v i o u s p a p e r [3] a r e a l s o g i v e n . T h e c o r r e c t i o n A t a k i n g into a c c o u n t t h e t - d e p e n d e n c e of t h e s l o p e p a r a m e t e r Table 1 The r e a l p a r t p a r a m e t e r ~ = R e A / I m A and the total elastic c r o s s - s e c t i o n for proton-proton scattering. NN

p(GeV/c)

1 2 3 4 5 6 7 8

9.39 19.07 38.03 40.03 50.63 55.33 59.43 69.83

ol ± ,xel "~ -0.351 -0.258 -0.171 -0.168 -0.159 -0.154 -0.122 -0.092

(:Tel(mb)

4- 0.048 ± 0.020 ± 0.029 ± 0.015 ± 0.030 ± 0.022 ± 0.020 ± 0.011

± ± ± ± ± ± ±

8.47 7.64 7.61 7.34 7.35 7.20 7.12

0.34 0.31 0.30 0.29 0.29 0.29 0.28

~t Statistical e r r o r s are shown.

8

4500

i

i

6 t0 ,

,

,

i

2.0 ,

i

PG6V/C O0 00t00

40 ~

,

i

i

,

,

1000 N "~'600

P-P 70oev

~0

-O.Z

2.00

-O.4

dpp

"c1400

~..-- . . . .

5(

0

o.oos

"_~._'--. ~ = . ~ o.o,

o.o,5

o.o2

-ac(oev/c)2 Fig. 2. P r o t o n - p r o t o n elastic s c a t t e r i n g differential c r o s s - s e c t i o n at 70 GeV. 412

.:/'[L ] . -

Fig. 3. Real p a r t paTameter ~ = R e A / I m A for pp s c a t t e r i n g v e r s u s lab. momentum. The solid line shows the d i s p e r s i o n r e l a t i o n calculations. The dotted line is the complex momentum t h e o r y prediction [12]. The dotdashed line is the d i s p e r s i o n r e l a t i o n calculation by S~ding [10]

Volume 39B, n u m b e r 3

LETTERS

PHYSICS

Table 2 The r e s u l t s of the d i s p e r s i o n r e l a t i o n calculation of the r a t i o between the r e a l and the i m a g i n a r y part,of the pp forward elastic s c a t t e r i n g amplitude 4.

(GeV/c)

~(p) = Re (i)

P

A/Im A (ii)

2.2 3.1 4.5 5.0

-0.177 -0.331 -0.369 -0.414

± 0.094 ~- 0.071 ± 0.052 ± 0.047

-0.321 -0.439 -0.448 -0.439

± ± ± ±

0.076 0.058 0.042 0.038

5.5 8.0 ii.0 15.0

-0.363 -0.330 -0.324 -0.262

± ± ± ±

0.043 0.030 0.022 0.016

-0.429 -0.377 -0.328 -0.287

± ± ± ±

0.035 0.025 0.018 0.013

25.0 35.0 45.0 55.0

-0.208 -0.175 -0.152 -0.134

± 0.010 =~0.007 ± 0.006 ± 0.005

-0.223 -0.186 -0.160 -0.142

± ± ± ±

0.008 0.006 0.005 0.004

65.0 75.0 150.0 300.0

-0.121 ± 0.004 -0.113 ± 0.003 -0.066 -0.036

-0.127 ± 0.003 -0.115 ± 0.002 -0.069 -0.037

450.0

-0.023

-0.023

I000.0 3000.0

+0.001 +0.011

-0.001 +0.010

9000.0

+0.022

+0.022

1 May 1972

of t h e r e a l p a r t p a r a m e t e r a n d t h e t o t a l c r o s s section energy dependence. T h e r e a l p a r t p a r a m e t e r c~ w a s c a l c u l a t e d from the dispersion relation, working in the s c h e m e of r e f . [10] a n d u s i n g t h e r e c e n t S e r p u k h o v total cross section data Ill]. The asymptotic energy total cross section behaviour was taken f r o m r e f . [12]. T h e r e s u l t s of t h e s e c a l c u l a t i o n s a r e g i v e n in t a b l e 2 a n d d i s p l a y e d in fig. 3 ( s o l i d l i n e ) . T h e d o t t e d l i n e is t h e c o m p l e x m o m e n t u m t h e o r y p r e d i c t i o n [12]. A s i s s e e n f r o m fig. 3, t h e a g r e e m e n t b e t w e e n t h e c a l c u l a t i o n s a n d t h e e x p e r i m e n t a l d a t a i s good in t h e r a n g e of e n e r g y e x p l o r e d . A g a i n up to 70 G e V / c t h e r e i s no r e a s o n to d o u b t in v a l i d i t y of l o c a l quantum field theory from which the dispersion relation is derived. W e w o u l d l i k e to t h a n k P r o f e s s o r s A. M. Bald±n, I. V. C h u v i l o , A . A . L o g u n o v , A . A . N a u m o v , Yu. D. P r o k o s h k i n a n d R . M. S u l y a e v f o r t h e i r c o n t i n u o u s support during the experiment. Without the effort of t h e c r e w of t h e S e r p u k h o v a c c e l e r a t o r t h e experiment would not have been possible.

The s u b t r a c t i o n constant was calculated using (i) the e x p e r i m e n t a l data at p = 1.7 GeV/c, and (ii) the data at p = 10 GeV/c. The e r r o r s a r e due to the u n c e r tainty in the s u b s t r a e t i o n constant determination.

b(t) w a s e v a l u a t e d f r o m t h e d a t a of r e f s . [6, 7]. O n e c a n s e e f r o m fig. 3 t h a t t h e r e a l p a r t of the amplitude is negative over the investigated m o m e n t u m r a n g e up to 70 G e V / c . I n a b s o l u t e v a l u e a(p) f a l l s m o n o t o n i c a l l y w i t h i n c r e a s i n g e n e r g y f r o m I s I = 0.35 ± 0.05 a t p = 9.39 G e V / c to Ic~ | = 0 . 0 9 2 ± 0 . 0 1 1 a t p = 6 9 . 8 GeY/c. T h e r e i s n o t h i n g u n u s u a l in s u c h a b e h a v i o u r of t h e r e a l p a r t p a r a m e t e r a(p). T h e f e a t u r e s a b o v e a r e i n good a g r e e m e n t w i t h t h e P o m e r a n c h u k t h e o r e m c o n d i t i o n s [8] a n d s u p p o r t t h e a x i o m a t i c f i e l d t h e o r y a s y m p t o t i c p r e d i c t i o n [9] of t h e c o n n e c t i o n b e t w e e n t h e e n e r g y b e h a v i o u r

References [1] L. F. Kirillova et al., Soviet Phys. J E T P 23 (1966) 52. [2] V. D. B a r t e n e v et al., 15th Int. Conf. on High energy phys., Kiev, 1970, sect. l(a), p a p e r 1. [3] G. G. Beznogikh et al., Phys. L e t t e r s 30B (1969) 274. [4] V. D. B a r t e n e v et al., Proc. Intern. Conf. on I n s t r u m e n t a t i o n for high energy phys., Dubna, USSR (1970), p.16, JINR D-5805 (1970). [5] H. Bethe, Ann. of Phys. 3 (1958) 190. [6] D. Harting et al. (Geneva - B o l o g n a - Liverpool Ann A r b o r - B e r k e l e y Collaboration), Nuovo Cimento 38 (1965) 60. [7] M. Holder et al., Phys. L e t t e r s 36B (1971) 400. [8] G. G. Volkov, A. A. Logunov, M. A. M e s t v i r i s h v i l i , TMT, 4 (1970) 196. [9] T. Khuri and T. Kinoshita, Phys. Rev. 137B (1965) 720; 140B (1965) 706; G. G. Volkov, P r e p r i n t IHEP, 71-8. [10] P. S~ding, Phys. L e t t e r s 8 (1963) 286. [11] S. P. Denisov et al., Phys. L e t t e r s 36B (1971) 415. [12] K. G. Boreskov, Yadern. Flz. 14 (1971) 814.

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413