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Inelastic screening in high-energy pion-deuteron scattering
Volume 32B, n u m b e r 1
INELASTIC
PHYSICS
SCREENING
IN
LETTERS
HIGH-ENERGY
25 May 1970
PION-DEUTERON
SCATTERING
S. A. G U R V I T S and M. S. MARINOV
Institute for Theoretical and Experimental Physics, Moscow, USSR Received 10 April 1970
By means of the Gribov theory and with experimental data on inelastic v-p interactions it is shown that the nuclear s c r e e n i n g in v - d s c a t t e r i n g at 16 G e V / e with account of the inelastic channels is about 50~ higher than the elastic shadow effect. With the energy rise to 65 GeV (the Serpukhov limit) the inelastic s c r e e n i n g may be expected to d e c r e a s e .
D a t a on t o t a l c r o s s s e c t i o n s of v - , K- a n d interactions with protons and deuterons at energ i e s u p to 65 G e V h a v e b e e n p u b l i s h e d r e c e n t l y [1]. T h e n e u t r o n t o t a l c r o s s s e c t i o n s a r e e x t r a c t e d f r o m t h e d a t a w i t h a c c o u n t of t h e s h a d o w effect, derived from the Glauber formula when t h e F e r m i m o t i o n a n d t h e r e a l p a r t s of t h e 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 s a r e n e g l e c t e d : ¢y,~ = = C r p + C r n - 6 ; 6 = ( 4 v ) - l ( r - 2 } d crl~ "n F o r t h e deuteron radius the value consistent with the d a t a a t few G e V [2] w a s u s e d : < r - 2 } ~ = 0 . 0 3 0 ± ± 0.005 m b -1. H o w e v e r , a s G r i b o v ° h a s p o i n t e d out [3], a t t h e e n e r g i e s ~ 10 G e V a n d m o r e t h e s c r e e n i n g i s a r e s u l t of b o t h t h e e l a s t i c r e s c a t tering and virtual inelastic processes. The s c r e e n i n g e f f e c t m a y be r e p r e s e n t e d a s A = a p + cfn - crd = 2 fdTp(~')dcr/dT
(1)
w h e r e p(~-) i s t h e d e u t e r o n f o r m f a c t o r , dcr/dT i s t h e s u m of a l l t h e c r o s s s e c t i o n s of p a r t i c l e i n t e r actions with the nucleon at the fixed momentum t r a n s f e r s q u a r e d , r . (At h i g h e n e r g i e s t h e d i f ference between neutron and proton cross sections may be neglected). For GeV energies dcr/dT i s t h e e l a s t i c 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 n d e q . ( 1 ) m a y b e r e d u c e d to t h e c o n v e n t i o n a l s h a d o w f o r m u l a . A s G r i b o v n o t e d , t h e s i m p l e eq.(1) i s b a s e d on s o m e r e a s o n a b l e , t h o u g h n o n - s t r i c t , a s s u m p t i o n s a n d it i s s c a r c e l y p r e c i s e . N e v e r t h e l e s s it e n a b l e s o n e to e s t i m a t e t h e e f f e c t of inelastic screening provided the necessary inf o r m a t i o n on i n e l a s t i c p r o c e s s e s i s a v a i l a b l e . T h i s i s t h e p u r p o s e of t h e p r e s e n t n o t e . I n t e r e s t i n g d a t a o n 7r-p i n t e r a c t i o n s a t 16 G e V / c a r e p u b l i s h e d r e c e n t l y [4] by t h e c o l l a b o r a t i o n o p e r a t i n g t h e 2 - m H B C a t C E R N . D u e to t h e f o r m f a c t o r , o n l y t h o s e r e a c t i o n s i n r e f [1] a r e e s s e n tial that proceed with small momentum transfer
to the nucleon. With this in mind, we neglect the inelastic charge exchange and the strange particle production, though these processes contribute considerably to the total cross section. Consider only the pionisation processes: ~-p ~pTr- + mTr. Very important is the fact that a sharp maximum at low T is seen in the experiment. The cross section may be described by the formula d~/dT = ~A
m ~m exp[-Am(T-Tm)]
(2)
reasonably enough, as the experimental cross s e c t i o n s d e c r e a s e e x p o n e n t i a l l y w i t h T. In e q . ( 2 ) a m i s t h e t o t a l c r o s s s e c t i o n of m ~ p r o d u c t i o n , Tm i s t h e b o u n d a r y m o m e n t u m t r a n s f e r : Tm = = [ ( m ~ 1 ) 2 - 1 1 2 / x 2 / 4 E 2, E i s t h e l a b . e n e r g y , p is the pion mass. Only data on reactions without n e u t r a l p a r t i c l e s (m e v e n ) , o r w i t h o n e n ° (m odd) a r e a v a i l a b l e . In o r d e r to f i n d crm w e a s s u m e t h a t t h e t r a n s i t i o n ~ - ~ n - + mTr p r o c e e d s w i t h o u t c h a n g e of t h e i s o s p i n , a n d a p p l y t h e s t a t i s t i c a l m o d e l [5]. T h e n a t m = 1 , 2 , 3 , 4 , 5 , 6 w e g e t f o r b r a n c h i n g r a t i o s of t h e c h a r g e d p i o n s 1, 3 / 5 , 4 / 5 , 2/7, 15/28 and 5/39, respectively. F o r t h e d e u t e r o n f o r m f a c t o r p u t cr(~-) = = exp(-a~) with the parameter a in accordance w i t h t h e nd d a t a i n t h e G e V r e g i o n : a = 3 5 ( G e V ) -2 ( n u c l e a r p h y s i c s p r e d i c t s a n e a r v a l u e [6]). F r o m e q s . (1) a n d (2) we g e t
a =2~m~mAm(a+Am)-lexp(-a-rm ).
(3)
T e r m s w i t h m > 6 a r e s u p p r e s s e d h e r e by t h e e x p o n e n t . T h e r e s u l t * i s A ~ 1.6 5 = 2.3 m b . * Note that with account of the inelastic s c r e e n i n g the ~'-n c r o s s section at 20 GeV extracted from the Serpukhov data is in perfect a g r e e m e n t with the ~+p c r o s s section m e a s u r e d at Brookhaven. 55
Volume 32B, number ]
PHYSICS
T h e p r i n c i p a l a s s u m p t i o n f o r eq.(1) i s t h a t t h e ~N i n t e r a c t i o n a m p l i t u d e i s p u r e i m a g i n a r y . It i s v a l i d , in p a r t i c u l a r , if t h e i n t e r a c t i o n i s d u e to t h e v a c u u m R e g g e p o l e . Such a m e c h a n i s m m a y w e l l d o m i n a t e the p r o c e s s e s w i t h e v e n m, low T a n d h i g h E . A s f o r odd m , t h e w p o l e i s e v i d e n t l y t h e d o m i n a t i n g one a n d the r a t i o R e / I m i s not s m a l l . T h i s r e s u l t s in s u p p r e s s i n g t h e c o n t r i b u t i o n f r o m p r o c e s s e s w i t h odd m . N o t e , h o w e v e r , t h a t t h e c o n t r i b u t i o n i s s m a l l : if it v a n i s h e s t h e r e s u l t would be A ~ 1.4 5 = 2 rob. Now t r y to s p e c u l a t e on t h e i n e l a s t i c s c r e e n i n g at Serpukhov energies. Neglect the K-meson and n u c l e o n p a i r p r o d u c t i o n (the l a s t i s c o r r e c t i n v i e w of t h e d e u t e r o n f o r m f a c t o r up to 70 GeV). T h e c r o s s s e c t i o n of the ~ - p - - p ~ - ~ - ~ + r e a c t i o n t h a t c o n t r i b u t e s t h e m a i n p a r t of the i n e l a s t i c s c r e e n i n g a t 16 GeV f a l l s , e v i d e n t l y , to o n e h a l f of i t s v a l u e w h e n e n e r g y r i s e s f r o m 16 up to 65 GeV (the r e s u l t d e d u c e d e x t r a p o l a t i n g t h e c u r v e s i n r e f . [4]). M e a n w h i l e , t h e e l a s t i c c r o s s s e c t i o n d o e s not v a r y e s s e n t i a l l y . In t h e f r a m e w o r k of the Regge pole model, the slopeA 2 may increase f r o m 7 up to 8.5 GeV - 2 , but A o a l s o i n c r e a s e s and the ratio is likely constant. The result is t h a t t h e c o n t r i b u t i o n f r o m (~2 f a l l s f r o m 0.3 up to 0.15 5. As f o r o t h e r p r o c e s s e s , no i n f o r m a t i o n on t h e i r h i g h e n e r g y b e h a v i o u r i s n o w a v a i l a b l e . T h e p e r i p h e r a l p r o d u c t i o n w i t h odd m i s e x p e c t e d to d e c r e a s e due to t h e a b s e n c e of t h e v a c u u m
56
LETTERS
2 5 M a y 1970
p o l e . T h e c r o s s s e c t i o n f o r e v e n m d o e s not i n c r e a s e l a s t l y a s no e s s e n t i a l r i s e of t h e m e a n p i o n multiplicity is observed: production processes a r i s i n g at t h r e s h o l d e n e r g i e s a m o u n t to r a t h e r low p r o b a b i l i t i e s a n d t h e n f a l l . E s t i m a t i n g t h e c o n t r i b u t i o n f r o m p i o n i z a t i o n w i t h e v e n m by m e a n s of t h e P o i s s o n d i s t r i b u t i o n we g e t a r e s u l t of few p e r c e n t . In c o n c l u s i o n n o t e t h a t w i t h a c c o u n t of i n e l a s t i c s c r e e n i n g t h e d i f f e r e n c e cr(~-p) - ~(~-n) a t E = = 16 GeV e q u a l s to 1.4 m b a n d f a l l s by ~ 3 0 % a t E = 65 G e V ( i n s t e a d of 2.1 m b a n d f a l l to i t s h a l f w h e n c a l c u l a t e d by m e a n s of t h e s i m p l e s h a d o w f o r m u l a [1]. D i s c u s s i o n s w i t h D r . A. B. K a y d a l o v a n d P r o f . K. A. T e r - M a r t i r o s y a n are greatly acknowledged.
References [1] A[labi et al. (IHEP-CERN Collaboration) Phys. L e t t e r s 30B (1969) 500. [2] A b r a m s et al. Phys. Rev. L e t t e r s 18 (1967) 1209. [3] V.N.Gribov, J Expl. Theor. Physics (USSR), 56 (1969) 892. ['41 Honeeker et al. (Aaehen-Berlin-CERN-CrakowHeidelberg-Warsaw Co[tab.). NucL Phys. B13 (1969) 571. [5] F. Ceru[us, Nuovo Cimento 19 {1961) 528. [6] M. Verde, He[v. Phys. Acta 22 (1949) 339.
INELASTIC
PHYSICS
SCREENING
IN
LETTERS
HIGH-ENERGY
25 May 1970
PION-DEUTERON
SCATTERING
S. A. G U R V I T S and M. S. MARINOV
Institute for Theoretical and Experimental Physics, Moscow, USSR Received 10 April 1970
By means of the Gribov theory and with experimental data on inelastic v-p interactions it is shown that the nuclear s c r e e n i n g in v - d s c a t t e r i n g at 16 G e V / e with account of the inelastic channels is about 50~ higher than the elastic shadow effect. With the energy rise to 65 GeV (the Serpukhov limit) the inelastic s c r e e n i n g may be expected to d e c r e a s e .
D a t a on t o t a l c r o s s s e c t i o n s of v - , K- a n d interactions with protons and deuterons at energ i e s u p to 65 G e V h a v e b e e n p u b l i s h e d r e c e n t l y [1]. T h e n e u t r o n t o t a l c r o s s s e c t i o n s a r e e x t r a c t e d f r o m t h e d a t a w i t h a c c o u n t of t h e s h a d o w effect, derived from the Glauber formula when t h e F e r m i m o t i o n a n d t h e r e a l p a r t s of t h e 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 s a r e n e g l e c t e d : ¢y,~ = = C r p + C r n - 6 ; 6 = ( 4 v ) - l ( r - 2 } d crl~ "n F o r t h e deuteron radius the value consistent with the d a t a a t few G e V [2] w a s u s e d : < r - 2 } ~ = 0 . 0 3 0 ± ± 0.005 m b -1. H o w e v e r , a s G r i b o v ° h a s p o i n t e d out [3], a t t h e e n e r g i e s ~ 10 G e V a n d m o r e t h e s c r e e n i n g i s a r e s u l t of b o t h t h e e l a s t i c r e s c a t tering and virtual inelastic processes. The s c r e e n i n g e f f e c t m a y be r e p r e s e n t e d a s A = a p + cfn - crd = 2 fdTp(~')dcr/dT
(1)
w h e r e p(~-) i s t h e d e u t e r o n f o r m f a c t o r , dcr/dT i s t h e s u m of a l l t h e c r o s s s e c t i o n s of p a r t i c l e i n t e r actions with the nucleon at the fixed momentum t r a n s f e r s q u a r e d , r . (At h i g h e n e r g i e s t h e d i f ference between neutron and proton cross sections may be neglected). For GeV energies dcr/dT i s t h e e l a s t i c 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 n d e q . ( 1 ) m a y b e r e d u c e d to t h e c o n v e n t i o n a l s h a d o w f o r m u l a . A s G r i b o v n o t e d , t h e s i m p l e eq.(1) i s b a s e d on s o m e r e a s o n a b l e , t h o u g h n o n - s t r i c t , a s s u m p t i o n s a n d it i s s c a r c e l y p r e c i s e . N e v e r t h e l e s s it e n a b l e s o n e to e s t i m a t e t h e e f f e c t of inelastic screening provided the necessary inf o r m a t i o n on i n e l a s t i c p r o c e s s e s i s a v a i l a b l e . T h i s i s t h e p u r p o s e of t h e p r e s e n t n o t e . I n t e r e s t i n g d a t a o n 7r-p i n t e r a c t i o n s a t 16 G e V / c a r e p u b l i s h e d r e c e n t l y [4] by t h e c o l l a b o r a t i o n o p e r a t i n g t h e 2 - m H B C a t C E R N . D u e to t h e f o r m f a c t o r , o n l y t h o s e r e a c t i o n s i n r e f [1] a r e e s s e n tial that proceed with small momentum transfer
to the nucleon. With this in mind, we neglect the inelastic charge exchange and the strange particle production, though these processes contribute considerably to the total cross section. Consider only the pionisation processes: ~-p ~pTr- + mTr. Very important is the fact that a sharp maximum at low T is seen in the experiment. The cross section may be described by the formula d~/dT = ~A
m ~m exp[-Am(T-Tm)]
(2)
reasonably enough, as the experimental cross s e c t i o n s d e c r e a s e e x p o n e n t i a l l y w i t h T. In e q . ( 2 ) a m i s t h e t o t a l c r o s s s e c t i o n of m ~ p r o d u c t i o n , Tm i s t h e b o u n d a r y m o m e n t u m t r a n s f e r : Tm = = [ ( m ~ 1 ) 2 - 1 1 2 / x 2 / 4 E 2, E i s t h e l a b . e n e r g y , p is the pion mass. Only data on reactions without n e u t r a l p a r t i c l e s (m e v e n ) , o r w i t h o n e n ° (m odd) a r e a v a i l a b l e . In o r d e r to f i n d crm w e a s s u m e t h a t t h e t r a n s i t i o n ~ - ~ n - + mTr p r o c e e d s w i t h o u t c h a n g e of t h e i s o s p i n , a n d a p p l y t h e s t a t i s t i c a l m o d e l [5]. T h e n a t m = 1 , 2 , 3 , 4 , 5 , 6 w e g e t f o r b r a n c h i n g r a t i o s of t h e c h a r g e d p i o n s 1, 3 / 5 , 4 / 5 , 2/7, 15/28 and 5/39, respectively. F o r t h e d e u t e r o n f o r m f a c t o r p u t cr(~-) = = exp(-a~) with the parameter a in accordance w i t h t h e nd d a t a i n t h e G e V r e g i o n : a = 3 5 ( G e V ) -2 ( n u c l e a r p h y s i c s p r e d i c t s a n e a r v a l u e [6]). F r o m e q s . (1) a n d (2) we g e t
a =2~m~mAm(a+Am)-lexp(-a-rm ).
(3)
T e r m s w i t h m > 6 a r e s u p p r e s s e d h e r e by t h e e x p o n e n t . T h e r e s u l t * i s A ~ 1.6 5 = 2.3 m b . * Note that with account of the inelastic s c r e e n i n g the ~'-n c r o s s section at 20 GeV extracted from the Serpukhov data is in perfect a g r e e m e n t with the ~+p c r o s s section m e a s u r e d at Brookhaven. 55
Volume 32B, number ]
PHYSICS
T h e p r i n c i p a l a s s u m p t i o n f o r eq.(1) i s t h a t t h e ~N i n t e r a c t i o n a m p l i t u d e i s p u r e i m a g i n a r y . It i s v a l i d , in p a r t i c u l a r , if t h e i n t e r a c t i o n i s d u e to t h e v a c u u m R e g g e p o l e . Such a m e c h a n i s m m a y w e l l d o m i n a t e the p r o c e s s e s w i t h e v e n m, low T a n d h i g h E . A s f o r odd m , t h e w p o l e i s e v i d e n t l y t h e d o m i n a t i n g one a n d the r a t i o R e / I m i s not s m a l l . T h i s r e s u l t s in s u p p r e s s i n g t h e c o n t r i b u t i o n f r o m p r o c e s s e s w i t h odd m . N o t e , h o w e v e r , t h a t t h e c o n t r i b u t i o n i s s m a l l : if it v a n i s h e s t h e r e s u l t would be A ~ 1.4 5 = 2 rob. Now t r y to s p e c u l a t e on t h e i n e l a s t i c s c r e e n i n g at Serpukhov energies. Neglect the K-meson and n u c l e o n p a i r p r o d u c t i o n (the l a s t i s c o r r e c t i n v i e w of t h e d e u t e r o n f o r m f a c t o r up to 70 GeV). T h e c r o s s s e c t i o n of the ~ - p - - p ~ - ~ - ~ + r e a c t i o n t h a t c o n t r i b u t e s t h e m a i n p a r t of the i n e l a s t i c s c r e e n i n g a t 16 GeV f a l l s , e v i d e n t l y , to o n e h a l f of i t s v a l u e w h e n e n e r g y r i s e s f r o m 16 up to 65 GeV (the r e s u l t d e d u c e d e x t r a p o l a t i n g t h e c u r v e s i n r e f . [4]). M e a n w h i l e , t h e e l a s t i c c r o s s s e c t i o n d o e s not v a r y e s s e n t i a l l y . In t h e f r a m e w o r k of the Regge pole model, the slopeA 2 may increase f r o m 7 up to 8.5 GeV - 2 , but A o a l s o i n c r e a s e s and the ratio is likely constant. The result is t h a t t h e c o n t r i b u t i o n f r o m (~2 f a l l s f r o m 0.3 up to 0.15 5. As f o r o t h e r p r o c e s s e s , no i n f o r m a t i o n on t h e i r h i g h e n e r g y b e h a v i o u r i s n o w a v a i l a b l e . T h e p e r i p h e r a l p r o d u c t i o n w i t h odd m i s e x p e c t e d to d e c r e a s e due to t h e a b s e n c e of t h e v a c u u m
56
LETTERS
2 5 M a y 1970
p o l e . T h e c r o s s s e c t i o n f o r e v e n m d o e s not i n c r e a s e l a s t l y a s no e s s e n t i a l r i s e of t h e m e a n p i o n multiplicity is observed: production processes a r i s i n g at t h r e s h o l d e n e r g i e s a m o u n t to r a t h e r low p r o b a b i l i t i e s a n d t h e n f a l l . E s t i m a t i n g t h e c o n t r i b u t i o n f r o m p i o n i z a t i o n w i t h e v e n m by m e a n s of t h e P o i s s o n d i s t r i b u t i o n we g e t a r e s u l t of few p e r c e n t . In c o n c l u s i o n n o t e t h a t w i t h a c c o u n t of i n e l a s t i c s c r e e n i n g t h e d i f f e r e n c e cr(~-p) - ~(~-n) a t E = = 16 GeV e q u a l s to 1.4 m b a n d f a l l s by ~ 3 0 % a t E = 65 G e V ( i n s t e a d of 2.1 m b a n d f a l l to i t s h a l f w h e n c a l c u l a t e d by m e a n s of t h e s i m p l e s h a d o w f o r m u l a [1]. D i s c u s s i o n s w i t h D r . A. B. K a y d a l o v a n d P r o f . K. A. T e r - M a r t i r o s y a n are greatly acknowledged.
References [1] A[labi et al. (IHEP-CERN Collaboration) Phys. L e t t e r s 30B (1969) 500. [2] A b r a m s et al. Phys. Rev. L e t t e r s 18 (1967) 1209. [3] V.N.Gribov, J Expl. Theor. Physics (USSR), 56 (1969) 892. ['41 Honeeker et al. (Aaehen-Berlin-CERN-CrakowHeidelberg-Warsaw Co[tab.). NucL Phys. B13 (1969) 571. [5] F. Ceru[us, Nuovo Cimento 19 {1961) 528. [6] M. Verde, He[v. Phys. Acta 22 (1949) 339.