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MODELS FOR NON-DIFFRACTIVE TWO-BODY REACTIONS
G. Ringland
To cite this version:
G. Ringland. MODELS FOR NON-DIFFRACTIVE TWO-BODY REACTIONS. Journal de Physique
Colloques, 1973, 34 (C1), pp.C1-292-C1-295. �10.1051/jphyscol:1973136�. �jpa-00215216�
MODELS FOR NON-DIFFRACTIVE TWO-BODY REACTIONS
G.A. RINGLAND
R u t h e r f o r d High Energy Laboratory
1.- INTRODUCTION.- I n t h i s b r i e f review of reac- Pomeron c u t s , o p t i m i s t i c a l l y c a l c u l a t e d i n t h e t i o n mechanisms f o r ( q u a s i ) two-body s c a t t e r i n g we Absorption Model. On g e n e r a l grounds, t h e c u t ener- s h a l l l a r g e l y emphasize problems and d i f f i c u l t i e s gy dependence i s determined f o r l i n e a r t r a j e c t o r i e s , of Regge c u t models. The most r e c e n t exchange models by
w i l l be mentioned, and d e t a i l e d d i f f i c u l t i e s i n use- f u l e x t r a p o l a t i o n s t o low e n e r g i e s . Hence t h e pro- blem of s a t i s f y i n g FESR with t h e s e models w i l l be
For a
=
1 t . 3 t and aR= a(O)+t,
t h i s g i v e s emphasized. However t h e main c o n c l u s i o n of t h i s r e - Pa ( t ) = aR(0)
+
0 . 2 t,
s o t h a t t h e c u t s h o u l d domina- view ( i n9.)
w i l l be t o q u e s t i o n t h e a p p l i c a b i l i t y Ct e t h e p o l e a t l a r g e
-
t.
of any Mandelstam c u t - c o r r e c t e d Regge exchange model,
The Reggeized Absorption Model, w r i t t e n schema- on t h e grounds t h a t t h e d a t a appear f a r more Regge
t i c a l l y behaved t h a n any model w i t h s i g n i f i c a n t Mandelstam
c u t s . We t h e r e f o r e r e c a l l why some s o r t of c o r r e c - A ( s , t )
=
A R + i A p @ A R,
t i o n t o simple Regge p o l e exchange i s r e q u i r e d .
2.
-
THE BACKGROUND. - Regge pole exchange models a l l o w t h e c l a s s i f i c a t i o n of an enormous amount of d a t a . I n p a r t i c u l a r :i ) Prominent p e r i p h e r a l peaks a r e seen only where s i n g l e t r a j e c t o r i e s may be exchanged : t h e r e a r e no prominent e x o t i c peaks.
i i ) The energy dependence of 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 c a n l a r g e l y be i n f e r r e d from t h e l e a d i n g t r a j e c t o r i e s e x t r a p o l a t e d from t h e Chew-Frautschi
where @I d e n o t e s a c o n v o l u t i o n , g i v e s a d e s t r u c t i v e comparatively i s o t r o p i c conOribution which can move t h e wrong s i g n a t u r e z e r o of pure co exchange from t r 0 . 6 t o t h e cross-over p o s i t i o n i n e l a s t i c r e a c - t i o n s ; f u r t h e r m o r e t h e c u t c o n t r i b u t i o n need not f a c t o r i z e . The y p -t nin and np -t pn problem was given a s i m i l a r l y n a t u r a l e x p l a n a t i o n i n terms of t h e d e s t r u c t i v e c u t s of mixed p a r i t y , o r low par- t i a l wave s u p p r e s s i o n . T h i s a n c i e n t h i s t o r y i s sum- marized i n many p l a c e s [ I ].
p l o t of t h e allowed p a r t i c l e d a t e s i n t h e t-channel*:
3.- BASIC PROBLEMS OF THE OLD REGGEIZED ABSORPTION do- oc .2"It) - 2
-
d t M B .-
The g r e a t u t i l i t y of t h e Regge exchange model demands
m
t h a t s i g n i f i c a n t d i f f i c u l t i e s s h o u l d not f o r c e u s t o
d i s c o r d t h e model, but t o modify it. The s i g n i f i c a n t
-
5 50d i f f i c u l t i e s f o r pure Regge p o l e exchange a r e
-
1 ) f a c t o r i z a t i o n and t h e cross-over phenomenon : Z
0 0 t h e f a i l u r e of t h e z e r o i n t h e 61 c o n t r i b u t i o n t o NN I- Q.
k' and
FN
s c a t t e r i n g t o p r o p a g a t e i n t o o t h e r processes. a4 -h
2 ) t h e v a n i s h i n g of pure n exchange a t t = O i n 0 n.
y p -' ?t+n and np -t pn
.
The escape r o u t e from t h e s e two problems was hoped t o be t h e a d d i t i o n of d e s t r u c t i v e Mandelstal Regge-
*
Wherever p o s s i b l e e x p e r i m e n t a l i s t s should d e r i v e F i g . 1 .-
The c u r v e i s a t y p i c a l Old Absorption Model a e f f ( t ) from t h e i r d a t a . The p r a c t i s e of c l a s s i f y i n g p r e d i c t i o n f o r n-p -t ?ton p o l a r i z a t i o n , compared r e a c t i o n s by n , where J ( d c / d t ) d t ocp-n,
throws away with r e c e n t d a t a .i n f o r m a t i o n , f a i l s t o r e v e a l r e g u l a r i t i e s , and h a s even suggested non-existent anomalies.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973136
MODELS FOR NON-DIFFRACT 'IVE TWO-BODY REACTIONS C1-293
A l l "old" a b s o r p t i o n models(reviewed i n [I
1)
pre- d i c t e d a deep n e g a t i v e spike i n t h e x-p -t 'KOn pola- r i z a t i o n a t t -.5,
i n v i o l e n t disagreement w i t h t h e d a t a ( s e e Fig.1 and r e f . [2]). T h i s disagreement was e x p r e s s e d i n terms of amplitudes 131 where i t was seen t h a t t h e d a t a r e q u i r e t h e n o n - f l i p amplitu- d e N t o have t h e p r o p e r t y t h a t I m N(p) changes s i g n b e f o r e Re N( p) whereas t h e o l d a b s o r p t i o n models demand t h e c o n v e r s e ( s e e Fig.2).T h i s p r o p e r t y of t h e o l d a b s o r p t i o n model c o u l d n o t be a l t e r e d by s i m p l e parameter v a r i a t i o n , d r a s t i c changes were r e q u i r e d . Three models, of v a r y i n g de- g r e e s of a r b i t r a r i n e s s , were proposed t o r e s o l v e t h e x p
-
+ $n p o l a r i z a t i o n problem and many o t h e r d i f - f i c u l t i e s , such a s l i n e r e v e r s a l i n e q u a l i t i e s and t h e apparent n o n - p e r i p h e r a l i t y of t e n s o r exchanges[ 4 ] (implying a non-dual s t r u c t u r e of t h e f u l l am- p l i t u d e s ) .
4.- MODIFIED ABSORPTION MODELS AND THEIR PROBLEMS.- The t h r e e models were :
i ) " ~ e ~ ~ e - ~ o r n e r o n - ~ e g g e " , model of t h e S a c l a y group [5]. T h i s model keeps t h e o l d a b s o r p t i o n model w i t h d u a l Regge p o l e i n p u t and adds lower l y i n g s i n g u l a - r i t i e s , Regge-Pomeron-Regge c u t s . (The i n s e r t i o n of t h e Pomeron i s r e q u i r e d t o prevent t h e s e s i n g u l a r i - t i e s decoupling where t h e y a r e most needed.)
i i ) Hartley-Kane model ( r e c o n s t i t u t e d Michigan mo- d e l ) [6]. Here t h e a b s o r p t i o n model i s modified by r e q u i r i n g a l a r g e n e g a t i v e r e a l p a r t f o r Ap ( t $ O ) , and a non-dual Regge i n p u t ( w i t h o u t WS'3 i s used.
i i i ) The "i-f a c t o r model" [7
1.
Here t h e s t a n d a r d c u t c o n v o l u t i o n i s a p p l i e d t o t h e p l a n a r ( r o t a t i n g - phase o r e-ixa) p a r t of t h e Regge p o l e i n p u t , b u t t h e a b s o r p t i v e c u t c o n t r i b u t i o n from t h e non-planar p a r t i s p h a s e - r o t a t e d by d 2.
The main j u s t i f i c a t i o n f o r t h e above models i s t h e remarkable amount of d a t a
-
mainly f o r pL > 4 GeV/c-
t h a t was economically f i t t e d , and even p r e d i c t e d . Thus a t l e a s t o p e r a t i o n a l l y t h e y can be claimed t o be a n advance over p r e v i o u s phenomenological models.
However, a l l t h r e e models have a common f e a t u r e : t h e i n t r o d u c t i o n of lower-lying j-plane s i n g u l a r i - t i e s . These s i n g u l a r i t i e s p l a y a s i g n i f i c a n t r o l e i n c o r r e c t i n g t h e phase of t h e a m p l i t u d e a t pL 5 GeV/c
,
but a s energy d e c r e a s e s become e x t r e - mely important.Worden [ 8 ] has a n a l y s e d t h e c o n s i s t e n c y of t h e above models u s i n g FESR, and h a s found a t s m a l l t , a v i o l e n t disagreement between t h e low energy i n t e - g r a l s o v e r t h e d a t a and t h e model a m p l i t u d e s , whL&
i s a t t r i b u t e d t o t h e low-lying s i n g u l a r i t i e s . T h i s d i f f i c u l t y i s i l l u s t r a t e d i n f i g u r e 3 f o r t h e RPR model ; t h e disagreement i s s i m i l a r f o r t h e o t h e r two models.
I I I I
I
I I I0 0.5
- t GeV 2
F i g . 3 . - A comparison of FESR i n t e g r a l s , f o r t h e odd-signature n o n - f l i p 7CN s c a t t e r i n g a m p l i t u d e , from r e f . [8
1.
The s o l i d curve i s f o r experimental i n p u t . The dashed c u r v e i s f o r t h e f u l l RPR model, and t h e d o t t e d c u r v e i s f o r t h e RPR c u t term alone.One t h e n must d e c i d e whether t h i s i s a s e r i o u s d e f e c t of t h e models, o r whether t h e s u c c e s s e s of FESR a r e f o r t u i t o u s . Now FESR i n t e g r a l s over t h e low energy d a t a have i n d i c a t e d :
i ) t h e z e r o of I m N(p)
i i ) t h e change of s i g n of Re N(p)
after
I m N(p)*
i i i ) s-channel h e l i c i t y c o n s e r v a t i o n f o r t h e Pome- r o n .
"1t should be remembered t h a t B a r g e r and P h i l l i p s [9
]
u s i n g a n e f f e c t i v e ( i . e. non-f a c t o r i z i n g ) Regge p o l e d e s c r i p t i o n of x-p + f i n,
c o n s t r a i n e d by FESR, p r e d i c t e d p o l a r i z a t i o n w i t h o u t a n e g a t i v e s p i - ke a s l o n g ago a s 1968.T h i s makes a grave d i f f i c u l t y f o r t h e s e modified models a t small t. We n o t e f u r t h e r t h a t optimized FESR have been used t o determine t h e Regge parame- t e r s f o r t h e ~3 amplitude A ( - ) o u t t o t - v a l u e s of almost -3.0
[lo].
T h i s a n a l y s i s showed a remarkable d e g r e e of Regge behaviour and l o c q l d u a l i t y , f i t t i n g w e l l t h e amplitudes r e c o n s t r u c t e d from t h e 1972 S a c l a y phase s h i f t a n a l y s i s down t o pL= 1.74 GeV/c.I n p a r t i c u l a r t h e e x i s t e n c e of a r i g h t s i g n a t u r e z e r o i n Im A ( - ) a t t -1.5 is i n c o n s i s t e n t w i t h t h e Hartley-Kane model which h a s no z e r o f o r .6 < -t < 3 . 5
.
5. GENERAL DIFFICULTIES OF REGGE-CUT MODELS : s h r r n k a g e and z e r o s t r u c t u r e . - A s noted i n 52.
,
t h et r a j e c t o r y f o r a Regge-Pomeron c u t should be r a t h e r f l a t , aAw.2 f o r a p l e u s i b l e Pomeron s l o p e (aicv.3).
T h i s demands t h a t amplitudes with Regge c u t c o r r e c - t i o n s should be dominated a t l a r g e energy by t h e c u t , p a r t i c u l a r l y f o r l a r g e -t, and s h r i n k slowly. There i s i n c r e a s i n g evidence t h a t t h o s e Regge exchange am- p l i t u d e s whlch r e q u i r e c o r r e c t i o n s show t h e s t r o n g s h r i n k a g e 1 ) expected from simple p o l e exchan- ge r a t h e r t h a n t h e weak s h r i n k a g e ( a i f f = 0 . 2 ) expec- t e d f o r c u t s . T h i s was f i r s t noted by Schmid 111
1,
i n a d i s c u s s i o n of Im N(w) i n K-p
+
s c a t t e r i n g , butwas a p p a r e n t l y overlooked. T h i s p o i n t i s i l l u s t r a t e d i n f i g u r e 4 ; t h e wP c u t i s of c o u r s e r e q u i r e d f o r t h e cross-over. An a n a l y s i s of Im N ( p ) a t l a r g e t a l s o shows Regge-like behaviour compared w i t h slow c u t s h r i n k a g e [13] ( s e e Fig.5).
A comparison
[lo]
of I m ~ ( p ) r e c o n s t r u c t e d from t h e h i g h e r energy end of t h e Saclay 1972 x N a n a l y s i s shows a l s o a l a r g e l y Regge-like z e r o s t r u c t u r e o u t t o t -3,
i n marked disagreement w i t h c u t models, and a magnitude d i s c r e p a n c y f o r - t > . 5 r e l a t e d t o t h e s h r i n k a g e mismatch.Evidence a l s o e x i s t s f o r p o l e - l i k e s h r i n k a g e i n t h e u n n a t u r a l - p a r i t y n o n - f l i p amplitude of xN - t p N
[14]. T h i s amplitude i s l a r g e and completely given by 'KP c u t a t t = O
,
s o i t s s h r i n k a g e f o r -t < .5 i s f u r t h e r evidence a g a i n s t t h e Regge-Pomeron c u t .I n c o n c l u s i o n :
1 ) F a c t o r i z a t i o n and pion e v a s i o n demand s i g n i f i - c a n t c o r r e c t i o n s t o t-channel Regge exchange, and q u a l i t a t i v e l y t h e a b s o r p t i v e Regge c u t s appeared t o s u f f i c e a t s m a l l t
.
2 ) The amplitudes r e q u i r i n g c o r r e c t i o n have a pole- l i k e s h r i n k a g e , and some evidence f o r a p o l e - l i k e z e r o s t r u c t u r e , i n c o n t r a d i c t i o n with Regge-Pomeron c u t c o r r e c t i o n s .
3 ) Models must be sought i n which t h e c o r r e c t i o n s have p o l e - l i k e s h r i n k a g e ( t h e c u t d i s c o n t i n u i t y pea- k i n g n e a r t h e p o l e ) and/or i n which t h e c u t d i s a p - p e a r s r a p i d l y i n t. ( T h i s l a t t e r p o s s i b i l i t y seems c o u n t e r - i n t u i t i v e f o r double exchange which i s ex- p e c t e d t o h e l e s s important i n h i g h p a r t i a l waves t h a n s l n g l e exchange.)
4 ) T h e r e a r e h i n t s t h a t c u t models may be cons- t r u c t e d , where t h e c u t c o u p l e s through t h e p o l e and s h r i n k s a t s m a l l t. However one w i l l s t i l l have t o u n d e r s t a n d t h e l a r g e r - t problem, and a l s o t h e s e
Fig.4.
-
E f f e c t i v e W ~ r a j e c t o r i e s deduced i n r e f . C121 Fig.5.-
E f f e c t i v e t r a j e c t o r y f o r t h e nN charge- from Kn, KN andNN, NN d i f f e r e n c e s ( d a t a p o i n t s ) , exchange non-f l i p amplitude from r e f . 1131,
compared compared with t h e expected w t r a j e c t o r y ( s o l i d l i n e ) w i t h t h e expected t r a j e c t o r i e s of t h ep
p o l e ( s o l i d and wP c u t t r a j e c t o r y (dashed l i n e ) r e q u i r e d f o r t h e l i n e ) and pP c u t (dashed l i n e ) .cross-over.
MODELS FOR NON-DIFFRACTIVE TWO-BODY REACTIONS C1-295
a m p l i t u d e s ( r e q u i r e d i n 'fp + n+n
,
np -t pn and i i i ) S t r u c t u r e s a r e e q u a l l y spaced i nfi,
compa- n p + p n ) where t h e n P c u t i s s t r o n g h u t t h e n p o l edecouples a t s m a l l t.
6.- THE DIRECT CHANNEL OR GEOMETRICAL APPROACH.- Schrempp and S c h r e m p ~ [15] have proposed a n e x t e n - s i o n t o t h e d u a l a b s o r p t i o n model of H a r a r i , and now p r e s c r i b e r e a l p a r t s , s h r i n k a g e and d i p s y s t e m a t i c s i n terms of a s i n g l e complex s-channel t r a j e c t o r y of p e r i p h e r a l resonances. The i n p u t i s d u a l i n t h e s e n s e of c o n s i d e r i n g V ( s , t ) and V ( u , t ) t y p e terms.
P e r i p h e r a l i t y i s e n f o r c e d by demanding t h e l a r g e s- dominance of one complex s-channel t r a j e c t o r y
a s ) r
@
I n ( ' f o r l a r g e I s \a s
= +
i('I
f o r s > 0.
The e s s e n t i a l f e a t u r e s which d i s t i n g u i s h t h i s model from t h e exchange of t r a j e c t o r i e s l i n e a r i n t a r e :
i ) Im a c o n t r o l s s h r i n k a g e , implying A N s
-RG/
Xcompared w i t h A s - I t ' f o r t-channel Regge p o l e s . i i ) Re a c o n t r o l s t h e phase f a c t o r , which i s eiRG f o r p l a n a r p a r t s and 1 f o r non-planar p a r t s ,
- i n a o - i x t
compared w i t h e
.
e and 1 f o r t h e correspon- d i n g t-channel Regge c a s e s .r e d with t f o r t-channel poles.
i v ) The phase d i f f e r e n c e of t h e p l a n a r p a r t s of s-channel f l i p and n o n - f l i p h e l i c i t y amplitudes i s
-a =
7d2.
T h i s would be a d i f f i c u l t y , a t l e a s t N Fa t h i g h energy, i f f l i p and n o n - f l i p amplitudes of d e f i n i t e c r o s s i n g symmetry have t h e same energy de- pendence.
I n c o n c l u s i o n :
1 ) The model a p p e a r s f i r m l y p r e d i c t i v e and s h o u l d he d e f i n i t i v e l y t e s t e d . S u r p r i s i n g l y , t h e aeff f o r x-p -+ nOn (6 < pL < 5 0 ) t h a t i s w e l l f i t t e d by a li- n e a r t r a j e c t o r y can a l s o b e accommodated i n a
f i
f i t ( f o r t h e range -t >0.25).
2 ) The s-channel resonance spectrum a l s o t e s t s t h e model : e . g. a n assignment J' 19/2+ f o r A(3230)
would be a major d i f f i c u l t y f o r it.
3 ) S l o p e r e g u l a r i t y i n a p p e a r s q u i t e good, but r e g u l a r i t y of s t r u c t u r e i n
f i
would be c o n t r a d i c t e d by c o n f i r m a t i o n of p-Regge z e r o e s i n ImF a t -t z 1.5 and 2.5 a t h i g h e r e n e r g i e s .4 ) The model can o n l y be a p p l i e d f o r \ t
1
> 0.25 ) P r e d i c t i v e power i s l a c k i n g f o r s-dependence, t h e t-channel approach's main v i r t u e .
R e f e r e n c e s
[ I ] PHILLIPS (R. J.N. ), Proc. of Amsterdam I n t . Conf. [ 7 ] RINGLAND (G.A. ), ROBERTS (R.G. 1, ROY (D.P. ) and on Elementary P a r t i c l e s (North-Holland, TRAN THANH VAN ( J . ) , Nucl. Phys.
B44
(1972)Amsterdam, 1971) ; CHIU (C.B.), Ann. Rev. 395.
Nucl. S c i . 22 (1972) 255. [ 8 ] WORDEN (R.P. ) , Nucl. Phys.
B58
(1973) 205.[ 2 ] CERN d a t a ,
BONE
( P . ) e t a l . , Nucl. Phys.B52
[ 9 ] BARGER (V. ) and PHILLIPS (R. J . N . 1, Phys. Rev.(1973) 392 ; ANL d a t a , HILL (D.) e t a l . , L e t t . (1968).
Phys. Rev. L e t t .
30
(1973) 239. [ l o ] ELVEKJAER (F. ),
I N A M I (T. ) and RINGLAND (G.A. ),
[3] RINGLAND (G.A.) and ROY (D.P.), Phys. L e t t . 36B Phys. L e t t .
44B
(1973) 91.(1971) 110 ; HALZEN (F.) and MICHAEL (C.), [ l l
]
SCHMID (C. 1, Phenomenology i n P a r t i c l e P h y s i c s~ h y s . ~ e t t . 36B (1971) 367. (1971 ).
[ 4 ] BARGER (V. )
~ ~ ~ H A L Z E N
(F. 1, Nucl. Phys.B43
[12] BAilGER (V. ),
GEER (K. ) and HALZEN (F. 1, Nucl.(1972) 62 ; BARGER (V. and MARTIN (A.D. ), Phys. B44 (1972) 475.
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