Volume 31B, number 7 P H Y S I C S L E T T E R S 30 March 1970

T H E ~ - p ~ u n C R O S S S E C T I O N I N A S M A L L T R A N S F E R R A N G E A T

J. HLADKY, A. M. BALDIN, M. N. K H A C H A T U R Y A N , M. S. KHVASTUNOV Joint Institute f o r Nuclear Research, Dubna, USSR

and

L. N. SHTARKOV P. N. Lebedev Institute of Physics , Moscow, USSR

Received 12 Februa ry 1970

4 G e V / c

The react ion ~--+p-*??+ n, 77 ~ 27 has been studied in a 0 --< It I "-< 0.24 (GeV/ct 2 range at 4.0 GeV/c using spa rk chambers and Cerenkov total absorpt ion g a m m a s p e c t r o m e t e r s . The coefficients a = 4.3 ± 0.8 (GeV/c) -2 and b = 190 ± 18 pb/(GeV/c) 2 f rom the equation d(~/dt = b exp (at) were es t imated.

A p r o g r a m m e of e x p e r i m e n t s on t h e o b s e r v a - t i o n of t h e e l e c t r o m a g n e t i c d e c a y s of m e s o n r e s - o n a n c e s i s b e i n g p e r f o r m e d u s i n g t h e J I N R p r o - t o n - s y n c h r o t o n in Dubna . As a p a r t of t h i s p r o - g r a m m e , t he 7--* 27 d e c a y w a s o b s e r v e d .

In t h i s p a p e r t he r e s u l t s f r o m t he r e a c t i o n

n- +p-~n+ ~1, z?~27 (i)

at a T--meson momentum of 4 GeV/c ± 1.5% in the range of the transfer momentum 0 --< Itl --< 0.24 (GeV/c)2 are discussed. The pre- liminary data have been presented at the Lund Conference [i]. This paper has three improve- ments in comparison with the preliminary one: i) the statistics was increased by about 50~c; 2) the number of Monte-Carlo events in the de- tection probability calculations was also in- creased by a factor of five. The precise knowl- edge of this parameter is of great importance. For this reason the data from the Monte-Carlo programme were tested by the other used in JINR for many years [2]. Making these tests, good agreement has been obtained. Finally, 3) the interval for the dcr/dt histogram was di- minished, in order to have the possibility of studying better the differential cross section plot structure.

The reaction (i) is very interesting from the point of view of the simple Regge-pole model, especially in the range of I t r ~ 0 because it in- volves only the A2-trajectory.

In practice, the only experimental data for the reaction (I) treated in all theoretical papers are given in ref.3, when the reaction (1) was investigated in wide ranges of 7T--meson ener-

g i e s and s q u a r e d m o m e n t u m t r a n s f e r s . T h e f o r w a r d p e a k in t he d i f f e r e n t i a l c r o s s s e c t i o n d ~ / d t and i t s f l a t t e n i n g b e t w e e n I tl = 0.2 and 0 ( G e V / c ) 2 w a s o b s e r v e d a t a l l m o m e n t a .

O u r e x p e r i m e n t a l a r r a n g e m e n t u s i n g s p a r k c h a m b e r s and ¢ e r e n k o v t o t a l a b s o r p t i o n g a m m a - s p e c t r o m e t e r s h a s b e e n d e s c r i b e d e l s e w h e r e [4]. M e a s u r i n g the o p e n i n g a n g l e of t h e 77~ 27 d e c a y and t h e e n e r g y of e a c h g a m m a , we get t he a c c u - r a c y Gt in I t l : £ t = + 0 .015 ( G e V / c ) 2 a t It l ~ 0 ( G e V / c ) 2 and zkt = ± 0 .030 ( G e V / c ) 2 a t It j ~ 0 . 2 4 ( G e V / c ) 2.

T h i s a l l o w e d u s to i n v e s t i g a t e t he r e a c t i o n (1) a t l t i ~ 0 w i th b e t t e r a c c u r a c y &t t h a n in r e f .3 .

A f t e r a t w i c e s c a n n i n g p r o c e d u r e , a b o u t 9000 p i c t u r e s c o n t a i n i n g on ly c o n v e r s i o n of t he n e u - t r a l p a r t i c l e in e a c h c h a n n e l w e r e found. A p a r t , of a b o u t 4200 t w o - g a m m a e v e n t s , w a s m e a s u r e d w i t h a h a l f - a u t o m e t i c a l d e v i c e , and t h e t a p e w a s h a n d l e d by a c o m p u t e r . T h e g e o m e t r i c a l r e c o n - s t r u c t i o n p r o g r a m m e d e t e r m i n e s t h e po in t of t he t r a c k i n t e r s e c t i o n and f i t s t h e a n g u l a r p a r a - m e t e r s of t he t r a c k s . F o r f u r t h e r a n a l y s i s on ly t w o - g a m m a d e c a y s h a v i n g t he i n t e r s e c t i o n po in t w i t h i n the e f f e c t i v e t a r g e t v o l u m e w e r e s e l e c t e d . Only e v e n t s w i t h P(X 2) >I 1% w e r e t aken . T h e k i n e m a t i c s e l e c t i o n of t h e t w o - g a m m a e v e n t s w a s m a d e by t he r e a c t i o n - c h a n n e l i d e n t i f i c a t i o n p r o g r a m m e . T h u s , a b o u t 1500 e v e n t s w e r e d e - t e r m i n e d to fu l f i l t h e r e a c t i o n (1).

T h e r e a r e two s o u r c e s of t he b a c k g r o u n d in o u r s p e c t r u m : (a) T - + p ~ n + n ° + T ° ~ n + 2 7 and (b) ~ - + p ~ n + ¢ 0 - n + n ° 7 ~ n + 2 7 . T h e b a c k - g r o u n d i s f o r m e d w h e n t w o - o r o n e - g a m m a f r o m f o u r - o r t h r e e - g a m m a d e c a y s a r e not c o n v e r t e d

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Volume 31B, number 7 PHYSICS LETTERS 30 March 1970

T a b l e 1 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 r e a c t i o n (1).

Number of Iti [(GeV/c} 2] d(~ [dt] ~tb [(GeV/c)2] intervals

1 0 . 0 1 82 i 18 2 0 . 0 3 158 =~ 19 3 0 . 0 5 155 i 18 4 0 .07 143 i 20 5 0 . 0 9 144 • 17 6 0 . 1 1 108 • 15 7 0.13 112 i 17 8 0 . 1 5 106 i 17 9 0.17 94 • 18

i0 0.19 76 • 18

ii 0.21 69 :~ 19 12 0 .23 74 _~ 19

in a s p a r k c h a m b e r c o n v e r t e r o r have escaped . The ma in s o u r c e of the backg round is the f i r s t kind.

T h i s backg round was s u b t r a c t e d by u s ing the e x p e r i m e n t a l t h r e e - g a m m a even t s , d e t e c t e d in the s a m e runs , a s fo l lows: each t h r e e - g a m m a even t was sp l i t into the t w o - g a m m a even t s handled in the s a m e way as na tu r a l t w o - g a m m a events . Mul t ip ly ing t h e i r s p e c t r a by the (1-K)/K c o n v e r s i o n f a c t o r ( h e r e K is the p r o b a b i l i t y of o n e - g a m m a c o n v e r s i o n in the s p a r k c h a m b e r a s s e m b l y ) , the b a c k g r o u n d of about 25% has been ob ta ined and sub t r ac t ed . The backg round , (a) and (b), when s o m e of the g a m m a s have e s c a p e d , was e s t i m a t e d to be about 5% us ing the M o n t e - C a r l o ca l cu l a t i ons .

E a c h even t was we igh ted by i ts i n v e r s e d e - t e c t i on p robab i l i t y c a l c u l a t e d by the M o n t e - C a r l o method. 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 (a f te r b a c k g r o u n d sub t r ac t ion ) fo r r e a c t i o n (1) as a funct ion of the s q u a r e d m o m e n t u m t r a n s f e r (- t) is g iven in t ab le 1. The quoted e r r o r s a r e only due to s t a t i s t i c s . T h e s e r e s u l t s a r e a l so p lo t ted in fig. 1. F o r c o m p a r i s o n , the da ta f r o m ref . 3 at m o m e n t u m 3.72 G e V / c a r e a l so p r e s e n t e d . As

is s een , t h e r e i s no wide f l a t t en ing in the f o r w a r d peak. F o r the hypo the s i s of f l a t t en ing in the r a n g e 0 ~< it r --< 0.24 (GeV/c) 2 the va lue of ×2=28 by 9 d e g r e e s of f r e e d o m was obtained. It c o r r e - sponds to P(X 2) l e s s than 10 -3.

In the f i r s t i n t e r v a l , up to I tl = 0.02 (GeV/c ) 2, 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 d e c r e a s e s wi th I ti ~ 0. The v a l u e d(~/dt in the f i r s t i n t e r v a l was s y s t e m a t i c a l l y l o w e r in a l l the runs of our e x p e r i m e n t ind ica t ing the change of s l ope fo r s m a l l v a l u e s of i t i . In the r ange 0.02 ~< It i ~< --< 0.24 (GeV/c) 2 (e.g. when the f i r s t point i s e x - c luded) the data w e r e a p p r o x i m a t e d by

d(~/dt = b exp (at) (2)

The fo l lowing r e s u l t s have been ob ta ined by the b e s t fit p r o c e d u r e : ~ = 4.3 ± 0.8 (GeV/c) -2 b = 190 ± 18 t tb / (Ge~/c) 2 by ×2 = 2.1 (9 d e - g r e e s of f r eedom) .

T h e s lope a is in good a g r e e m e n t wi th the s lope f r o m re f .3 ob ta ined in the g r e a t e r r a n g e of t: 0.2 --< iti < 0.7 (GeV/c ) 2.

The m e a s u r e m e n t s of r e a c t i o n (1) in the r a n g e of s m a l l It I v a l u e s a r e v e r y i m p o r t a n t fo r the p a r a m e t r i z a t i o n of the r e s i d u e funct ion in the R e g g e - p o l e mode l . A s e r i e s of a n a l y s e s [5 - 7] u s ing both e x p e r i m e n t a l and t h e o r e t i c a l data f r o m ~ N and KN i n t e r a c t i o n s , in the R e g g e - po le m o d e l p a r a m e t r i z a t i o n has b e e n p e r f o r m e d dur ing r e c e n t y e a r s . The data in the high e n e r g y r e g i o n w e r e c o m p l e t e d by the data in the low e n e r g y r e g i o n on the b a s i s of the f in i te e n e r g y sum r u l e s [8]. It is p o s s i b l e to a n a l y s e the data fo r the r e a c t i o n (1), w h e r e only the A 2 - m e s o n c o n t r i b u t e s , on the b a s i s of a o n e - p o l e exchange formula:

dcr/dt = F(t) E 2(~(t)-2 (3)

The funct ion F(t) is s t r o n g l y dependen t un the m o d e l used. It con ta ins the h e l i c i t y f l ip and non- f l ip a m p l i t u d e s and g h o s t - k i l l i n g f a c t o r s . The

L~j

2OO

/no

5 0

2 0

"/C , h 0.1

OUR OATA

~ GUISAN ET AL

' 0'. 2 ' O' 3 ' ' ' ~ - - ' ~ ' 04 05 06

-TRANSFER ,'/C'JM. £.(GEV/c)~

F i g . 1. 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 f o r t h e r e a c t i o n 7 r - + p ~ n + ~, 17~2~ . T h e s q u a r e s a r e f r o m the p r e s e n t p a p e r , The c i rc les are from ref. [3] at 3.72 GeV/c.

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Volume 31B, number 7 P H Y S I C S L E T T E R S 30 March 1970

m a i n u n c e r t a i n t y of F(t) is the e x p o n e n t i a l f a c - t o r s in the a m p l i t u d e s of the t ype exp (ct). It i s i m p o s s i b l e to e x p l o r e the a A 2 - t r a j e c t o r y wi thout t h e i r d e t e r m i n a t i o n . U n f o r t u n a t e l y , t i l l now, t h e r e a r e no e x p e r i m e n t a l da ta in the r a n g e of s m a l l it] 7r -meson e n e r g i e s E wi th s u f f i c i e n t a c c u r a c y fo r s u c h a n a l y s e s .

References 1. J. Hladk] et al. Lund Con~renee , Lund, 1969.

2. V. E. Komolova, G. I. Kopylov. Prepr in t JINR P-2027, Dubna. 1965.

3. O. Guisan et al. Phys. Let ters 18 (1965) 200. 4. M. N. Khaehgturyan et al. Phys. Let ters 24B (1967)

349. 5. G.V. Dass. C. Michael and R. J. N. Phillips.

Nucl. Phys. B9 (1969) 549. 6. R . J .N . Phillips and W. Rarita. Phys. Rev. Let ters

15 (1965) 807. 7. K.A. Ter -Mar t i ros ian . Prepr in t ITEF (1968). 8. A. A. Logunov, L. D. Soloviev and A. N. Tavkhelidze.

Phys. Let ters 24B (1967) 181.

477