SOME THEORETICAL PROBLEMS RELATED WITH NON RESONANT ENHANCEMENTS

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SOME THEORETICAL PROBLEMS RELATED WITH NON RESONANT ENHANCEMENTS

G. Cohen-Tannoudji

To cite this version:

G. Cohen-Tannoudji. SOME THEORETICAL PROBLEMS RELATED WITH NON RESO- NANT ENHANCEMENTS. Journal de Physique Colloques, 1973, 34 (C1), pp.C1-235-C1-238.

�10.1051/jphyscol:1973127�. �jpa-00215207�

SOME THEORETICAL PROBLEMS RELATED

WITH

SOME THEORETICAL PROBLEMS RELATED WITH NON RESONANT ENHANCEMENTS

G. COHEN-TANNOUDJI

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CEN SACLAY

1 .- INTRODUCTION.- Knowing w h a t i s n o t a r e s o n a n c e - i s o b v i o u s l y n e c e s s a r y t o know w h a t i s a r e s o n a r l c p . The w h o l e h a d r o n i c s p e c t r o s c o p y i s t h u s a f f e c t e d by t h e p o s s i b i l i t y o f e x i s t e n c e o f non r e s o n m t m h a n c e - m e n t s . As a c o n s e q u e n c e t h e w h o l e m d e r s t a n d i n g o f h a d r o d y n a m i c s i s a l s o a f f e c t e d b y t h i s p o s s i b i l i t y . F o r i n s t m c e , t h e c l a s s i f i c a t i o n o f s t a t e s a c c o r d i n g t o symmetry s c h m e s r e l i e s on t h e d e c i s i o n o f g i v i n g s u c h o r s u c h s t a t e t h e d i g n i t y o f b e i n g a r e s m a n - c e . T h i s i s o b v i o u s l y t r u e f o r SU[3) b u t a l s o f o r i n s t a n c e f o r c h i r a l symmetry: i n t h i s r e s p e c t t h e p o s s i b i l i t y t h a t A1 i s n o t a r e s o n a n c e p u t s a l o t o f t r o u b l e s f o r t h e t e n a n t s o f s u c h a symmetry s c h e m e . T h e s e p a r a t i o n o f r e s o n a n c e s f r o m p s e u d o r e s o n a n c e s i s a l s o c r u c i a l f o r t e s t i n q some d y n a m i c a l s c h e m e s l i k e , s a y , d u a l i t y . As we s h a l l s e e a t t h e e n d o f t h i s t a l k o n e d o e s n o t know y e t w e t h e r t h e t w o compo- n m t d u a l i t y c o n j e c t u r e d by H a r a r i a n d F r e m d i n t w o body s c a t t e r i n g i s v a l i d o r n o t i n d i f f r a c t i v e p r o d u c - t i o n s .

I t i s r a t h e r d i f f i c u l t t o d e c i d e i n a v e r y c l e a r way w h a t i s a r e s o n a n c e . T h e f r e n c h summer s c h o o l o f GIF s u r YVETTE d e v o t e d a c o m p l e t e s e s s i o n i n 1971 t o t h i s q u e s t i o n . One o f t h e p r o p o s e d a n s w e r s w a s t h a t a r e s o n a n c e i s a s i q a l a p p e a r i n g i n a g i v e n s t a t e i n d e p e n d e n t l y o f t h e o r o d u c t i o n mechanism.

c o n t r a - r i o a non r e s o n a n t e n h a n c e m e n t d e p e n d s o f t h e p r o d u c - t i o n a m p l i t u d e . S o , s t u d y i n g t h e s e p s e u d o r e s o n a n c e s i s n o t o n l y i m p o r t a n t f o r h a d r o n s p e c t r o s c o o y b u t a l s o f o r t h e m d e r s t a n d i n g o f t h e p r o d u c t i o n p r o c e s s i t s e l f . I n t h i s r e s o e c t t h e e x p l a n a t i o n o f t h e s o c a l l e d ABC e f f e c t , p r o p o s e d i n t h i s c o n f e r e n c e i s p a r t i c u l a r l y i n t e r e s t i n g .

2.- THE DECK MECHANISM.- We s h a l l f i r s t r e c a l l b r i e - f l y how t h e s o c a l l e d Deck mechanism w o r k s in p r o d u - c i n g p s e u d o r e s o n m c e s . C o n s i d e r t h e p r o d u c t i o n am- p l i t u d e a

b

c

d

e s y m b o l y s e d i n f i g . 1 on w h i c h t h e k i n e m a t i c s i s d e f i n e d .

t a c

F i g . 1

O r i g i n a l l y t h e Oeck e f f e c t i s a k i n e m a t i c a l e n h a n c e - m m t p r o d u c e d b y t h e p r e s e n c e o f a p o l e i n t h e t

a c v a r i a b l e , c l o s e t o t h e p h y s i c a l r e g i o n . Even i f t h e r e i s n o r a p i d v a r i a t i m i n t h e scd v a r i a b l e , t h e p r e - s e n c e o f n e a r b y p o l e i n tac f a v o r s t h e low c d i n v a r i - a n t m a s s e s , a s shown i n f i g . 2.

-- ccumulat ion

low scd events

physical.

region

F i g . 2

One m d e r s t i n d s e a s i l y t h a t t h e Oeck e f f e c t d i s a g - p e a r s . r a p i d l y w i t h i n c r e a s i n g i n i t i a l e n e r g y s . I n f a c t when s i n c r e a s e s t h e p h y s i c a l domain b r o a d e n s a n d f l a t t e n s n e a r t

0 i n s u c h

way t h a t t h e low

a c

m a s s e n h a n c e m e n t v a n i s h e s . C u r i o u s l y i t is t h e d e v e - l o p m e n t o f Regg.e f o r m a l i s m i n i n c l u s i v e p r o c e s s e s w h i c h h a s a l l o w e d t o u n d e r s t a n d why t h e Deck mecha- n i s m may p e r s i s t w i t h i n c r e a s i n g m e r g y . Assume t h a t p a r t i c l e s c m d

a r e a p a r t o f t h e m i s s i n g m a s s in

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973127

t h e i n c l u s i v e p r o c e s s a

b

e . + x. I n t h e f r a g m e n - t a t i o n r e g i o n [ s l a r g e , tbe s m a l l ) t* Regge b e h a v i o u r i s g i v e n by

w h e r e a i s t h e t r a j e c t o r y e x c h a n g e d between b m d e . The h i g h e r i s t h i s t r a j e c t o r y , t h e s t r o n a e r i s t h e c u t o f f i n s

c d '

T h i s e x p l a i n s why Deck e n h a n c e m e n t s a r e l i k e l y t o o c c u r when

- p i o n c a n b e e x c h a ? q e d between a a n d c ( n e a r b y p o l e 1

- Pomeron can b e e x c h a n g e d b e t w e e n b

e (scd -2 c u t o f f 1 .

3 . -

THE Q CROSS OVER PUZZLE.- T h e d i f f r a c t i v e l y p r o d u c e d Q e n h a n c e m e n t i s c o n s i d e r e d a s o n e o f t h e b e s t i l l u s t r a t i o n o f t h e Deck mechanism. The Deck d i a g r a m shown i n f i e . 3 a l l o w s t o e x o l a i n m o s t of t h e o b s e r v e d f e a t u r e s

K

I

x

N

- t h e s h a p e o f t h e 61 e n h a n c e m w t

- t h e e n e r g y d e p e n d e n c e o f i t s p r o d u c t i o n c r o s s s e c t i o n

- t h e d e n s i t y m a t r i x o f K*.

L h f o r t m a t e l y t h i s mechanism d o e s n o t e x p l a i n t h e o b s e r v e d c r o s s o v e r o f

a n d 5 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

d u e t o a i o n e x c h a n g e o n e e x p e c t s a .rr-Nucleon t y p e c r o s s o v e r w h e r e a s o n e o b s e r v e s

K-Nucleon l i k e o n e . The s i t u a t i o n i s even w o r s e i n n e u t r a l Q0 m d

Go p r o d u c t i o n s w h e r e t h e o b s e r v e d e f f e c t i s t h e i n - v e r s e o f t h e o n e e x p e c t e d f r o m n a i v e p i o n e x c h m g e .

( s e e f i g .

I n a p a p e r s u b m i t t e d t o t h i s c o n f e r e n c e

G. Cohen Tannoudj

C. G i l a i n a n d A. S a n t o r o p r o p o s e a s o l u - t i o n b a s e d on d u a l i t y a r g u m e n t s t o t h i s p u z z l e . It i s known t h a t t h e c r o s s o v e r e f f e c t i n K-Nucleon s c a t - t e r i n g i s d u e t o t h e i n t e r f e r e n c e b e t w e e n t h e Pomeron a n d t h e o c o n t r i b u t i o n s . T h e c r o s s o v e r e f f e c t i n n-Nucleon s c a t t e r i n g i s much w e a k e r b e c a u s e t h e w i s n o t c o u p l e d t o

I n o r d e r t o h a v e a K-Nucleon l i k e c r o s s o v e r i n Q p r o d u c t i o n o n e t h u s n e e d s t h e e x c h a n g e o f t h e w . T h e a b o v e m e n t i o n e d a u t h o r s show t h a t t h i s

e x c h a n g e i s p o s s i b l e p r o v i d e d t h a t t h e p i o n i s n o t e x c h a n g e d a l o n e b u t i n company w i t h i t s e x c h a n g e d e k e n e r a t e p a r t n e r ( w h i c h c o u l d b e t h e

meson I . F i g .

shows t h e d u a l i t y d i a g r a m s c o n t r i b u t i n g t o w e x c h a n q e i n

p r o d u o t i o n

F i g . 5

I n d e e d t h i s e x p l a n a t i o n o f t h e Q c r o s s o v e r p u z z l e a p p l i e s o n l y t o t h e

p r o d u c t i o n .

When t h e O bump i s o b s e r v e d i n t h e K

s y s t e m , t h e r e i s n o o u z z l e s i n c e it i s t h e K w h i c h i s e x c h a n - g e d . Rut t h e O i s m a i n l y o b s e r v e d i n t h e K% s y s t e m .

4 . -

DUALITY I N DIFFRACTIVE PRODUCTIONS.- As we h a v e s e e n a b o v e t h e Deck e f f e c t i s l i k e l y t o o c c u r i n d i f - f r a c t i v e o r o d u c t i o n s . I n an i n c l u v e p o i n t o f v i e w a d i f f r a c t i v e p r o c e s s i s o f t h e t y p e a

b

x. I n t e r m s o f t h e R e g g e - M u e l l e r a n a l y s i s t h e i n c l u s i v e d i f f r a c t i v e c r o s s s e c t i o n i s , i n t h e f r a g m e n t a t i o n r e g i o n r e l a t e d t o t h e t o t a l c r o s s s e c t i o n o f t h e s c a t t e r i n g o f a v i r t u a l Pomeron on p a r t i c l e a

see f i g . 6 .

F o r l a r g e m i s s i n g m a s s e s o n e e x p e c t s t h i s v i r t u a l

r e a c t i o n t o b e d o m i n a t e d b y Pomeron a n d s e c l n d a r y

Regge e x c h a n g e s . F o r low m i s s i n g m a s s e s o n e e x p e c t s

t h e o c c u r e n c e o f d i f f r a c t i v e r e s o n a n c e s a n d d i f f r a c -

SOME

THEORETICAL PROBLEMS RELATED

F i g . 6

t i v e b a c k g r o m d . It i s o f g r e a t t h e o r e t i c a l i n t e r e s t t o know whether t h e two component conj o n c t u r e o f H a r a r i and F r e m d a c c o r d i n g t o which r e s o n a n c e s a r e d u a l t o Regge p o l e s and background t o Pomeron i s a l s o v a l i d i n d i f f r a c t i v e r e a c t i o n s . In p a r t i c u l a r . i f one was a b l e t o s e p a r a t e d i f f r a c t i v e r e s o n m c e s from d i f - f r a c t i v e b a c k r o m d , one s h o u l d be a b l e t o g e t t h r o u g h F i n i t e Mass Sum R u l e s

t h e i n c l u s i v e v e r s i o n of F i n i t e Energy Sum R u l e s ) m i d e a o f t h e r e l a t i v e s t r e n g t h of Pomeron -Pomeron -Reme and Pomerm -Pornarm- Pomerm c o u p l i n g s . U l f o r t m a t e l y , a s we have s e e n , t h e Deck mechanism i s a b l e t o t e r r i b l y c o m p l i c a t e t h e s i t u a t i o n i n p r o d u c i n g non r e s o n a n c e b u t r e s o n a n c e l i k e e n h m c e m e n t s . In o t h e r words t h e d i f f r a c t i v e b a c k g r o m d s h a r e s w i t h d i f f r a c t i v e r e s o n a n c e s many o f t h e i r f e a t u r e s . Due t o t h e i m p o r t a n c e of y e s t i o n ' s r e l a t e d w i t h t r i p l e Pomeron c o u p l i n g , we t h i n k it would be i n t e r e s t i n g t o improve d e t a i l & a n a l y s e s o f t h e d i f f r a c t i v e l y produced m i s s i n g m a s s - ( p h a s e s h i f t m a l y s i s , d e n s i t y m a t r i x , p h a s e v a r i a t i o n . . . ) i n o r d e r t o w e l l s e p a r a t e r e s o n a n c e s from b a c k g r o m d . L e t u s c o n c l u d e t h i s s e c t i o n by m e n t i o n i n g t h e p a p e r submit- t e d by L u b a t t i m d Moriyasu ( 2 1 which c o u l d a l l o w s y s t e m a t i c s t u d i e s o f t h e i m p l i c a t i o n s o f d u a l i t y m d q u a r k model i n d i f f r a c t i v e d i s s o c i a t i o n s .

5.-

THE ABC EFFECT AND ITS EXPLANATION.- We c o n c l u d e t h i s b r i e f s u r v e y o f t h e o r e t i c a l i n t e r p r e t a t i a n s of

r e s o n m t e n h m c e m e n t s by m e n t i o n i n g t h e e l e g m t e x p l a n a t i o n o f t h e s o c a l l e d ABC e f f e c t propoded i n a s u b m i t t e d p a p e r by J. h j o s ,D. Levy m d A. S m t o r o [ S ) .

The ABC e f f e c t i s a n e a r t h r e s h o l d e n h m c e m m t o b s e r v e d i n t h e m i s s i n g mass s p e c t r u m i n t h e r e a c t i m d

p

He3

T h i s e f f e c t was f i r s t o b s e r v e d a l o n g t i m e ago and d i d n o t r e c e i v e m y s a t i s f a c t o r y e x p l m a t i o n .

^series o f e x p e r i m e n t s

, u s i n g t h e e x t r a c t e d d e u t e r o n beam from t h e s y n c h r o t r o n S a t u m e a t S a c l a y h a s been r e c w t l y performed by a S a c l a y , Cam m d F r a s c a t i c o l l a b o r a t i o n . L. G o l d z a h l h a s r e p o r t e d h e r e t h e main f e a t u r e s o f t h e e x p e r i m e n t a l d a t a . I n f i g . 7 we show t h e a p p r o x i m a t e s h a p e o f t h e o b s e r v e d spectrum p l o t t e d v e r s u s t h e l a b o r a t o r y mo- mentum o f t h e o u t g o i n g He3. The t h r e e bumps a r e

c a l l e d from l e f t t o r i g h t ( i n c r e a s i n g He3 momentum1

"forward ARC", "middle bump", "backward ABC".

P Lab (lie31

F i g . 7

The proposed t h e o r e t i c a l e x p l a n a t i o n r e l i e s on t h e t r e a t m e n t of t h e r e a c t i o n a s a r e a l t h r e e body p r o - blem

two p i m s a r e produced i n a two s t e p r e a c t i o n N1

p

d

nl f o l l o w e d by di

n,

where

i e'

N m d N a r e t h e c m s t i t u a n t s o f t h e d e u t e r m and

1

d an i n t e r m e d i a t e d e u t e r m . The k i n e m a t i c a l c m f i g u -

r a t i o n i s s u c h t h a t t h e i n t e r m e d i a t e d e u t e r o n i s a l - most on i t s mass s h e l l , s o t h e diagram of f i g .

i s

dominant .

F i g . 8

The two p r o c e s s e s I and 11, w i t h r e a l d e u t e r m

have been e x p e r i m e n t a l l y s t u d i e d . 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 s show s t r o n g f o r w a r d m d backward p e a k s .

Q u a l i t a t i v e l y m e c m m d e r s t e n d t h a t when b o t h

r e a c t i o n s t a k e p l a c e i n t h e f o r w a r d d i r e c t i o n m e

g e t s t h e f o r w a r d ABC, when t h e y t a k e p l a c e i n t h e

backward d i r e c t i o n m e g e t s t h e backward ARC, m d

when m e t a k e s p l a c e i n t h e f o r w a r d d i r e c t i o n and

t h e o t h e r i n t h e backward d i r e c t i o n m e g e t s t h e

m i d d l e bump; Nore q u m t i t a t i v e c a l c u l a t i o n s t a k i n g

i n t o a c c o m t t h e Fermi motion i n s i d e t h e d e u t e r m

l e a d t o a s a t i s f e c t o r y , a g r e e m e n t w i t h t h e d a t a .

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I1 1 COHEN-TANNOUDJI ( G I

.

Papar No 407. No 114.

I 2 1 LUBATTI I H . J l md WORIYASU I K I . Paper No 377. I 4 1 BANAIGS [ J 1

et

. ^,

BANAIGS

(J1

. ,

.