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pp AND p[MATH] DIFFRACTIVE SCATTERING
A. Martin
To cite this version:
A. Martin. pp AND p[MATH] DIFFRACTIVE SCATTERING. Journal de Physique Colloques, 1982,
43 (C3), pp.C3-164-C3-167. �10.1051/jphyscol:1982337�. �jpa-00221890�
JOURNAL DE PHYSIQUE
ColZoque C3, suppZdment au n o 12, Tome 43, ddcembre 1982 page C3-164
PP
A N D
P@D I F F R A C T I V E
SCATTERINGA. Martin
TH Division, CERN, CH-1211, Geneva 23, Switzerland
1. Introduction.- The CERN colliders offer a unique opportunity to test general consequences of analyticity and unitarity of scattering amplitudes. The ISR, al- lowing a comparison of pp and p; amplitudes and total cross-sections at energies from 15 + 15 to 31 + 31 GeV makes it possible to test the Pomeranchuck theorem and its generalizations. The S P S collider makes it possible to explore a new range of energies (equivalent to 150 000 GeV lab energy) and test asymptotic bounds and high energy models.
2. Pomeranchuck theorems and ISR experiments.- Notations:
E = lab energy = s/2M (in GeV) FC = F + F F - = F - - F
PP_
PE
PP PP'The Pomeranchuck theorem says: o~,t PP
-
+ 0, if F-/E logE + 0 for E + l) or R~F-/(IrnF-logE) + 0 2), or ReF ImF- > 0 for E > E , 3 ) .F-, up to recently, was not directly accessible to experiment and one could prefer to the weaker statementq1:
,pis
/,pp + 1 if either oTOtPP
-+
"
0r oyt't-+rnTot Tot
Analysis of previous experiments5), with the best fit ,P!/PP = 42
E-0.37
T
+
24E - ~ ' ~ ~ +
27+
0.17 (log 2~)'" mb,
suggest that indeed
oT
+Finally, there is a version of the Pomeranchuck theorem for elastic scattering5):
(do~P/dt)/(doPP/dt) + 1 inside the diffraction peak. In particular bpp/bpp + 1, if b(s,t) = d/dt[log(do/dw) (s, t)].
Two experiments at the I S R test these properties, R 210 and R 211, R 210~) measures o~ and b(s,t) for 0.02 < It1 < 0.7 (G~v)'. They find that cP$ > oFP. Their best fit is
2
E oyP
= 38.3+
0.5 log(n)
mbIn particular
Ao = 1.85
+
0.8 atplab
= 500 GeV 1.5+
0.55 at plab = 1500 GeV0.85 k0.45 at
ptab
= 2000GeVArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982337
A . M a r t i n C3- 165
- -
So n o t o n l y oFP/ofP + 1 b u t oPP
-
oFP + 0 . Concerning s l o p e s t h e y g e t , a t ECM == 5 3 GeV, b
-
- 1 4 r 2 . 6 GeV-T, b = 12.6 f 1 . 4 G ~ V - ' f o r t < 0 . 1 ( G ~ v ) ' c o n s i s t e n t w i t h b - / b pp PP "=-1, bpp = 1 0 . 4 ko.!,
bpp = 1 0 . 4+
0 . 4 f o r t > 0 . 1 Gev2. The theorem on t h e s l o p e s i s t h e r e f o r e s a t i s f i e d . I n f a c t , f o r < I tI>
% 0 . 2 Gev2, we h a v e ,b -/b = 1.12
PP PP
a t Elab = 30 GeV1.05 a t Elab = 100 GeV
1.00'0.06 a t Elab = 1500GeV
which shows t h e r i g h t t r e n d .
R 2117) measures 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 a t v e r y s m a l l t , < It
1
<< 6 0 x Gev2, and s e e s t h e Coulomb peak and t h e Coulomb n u c l e a r i n t e r f e r e n c e . Hence t h e y measure p = ReF/ImF,
oT
and b ( s , t S 0 1 , b o t h f o r pp and pp s c a t t e r i n g . T h e i r r e s u l t s a r e a tEC,{ = 30.4 GeV
ECM
= 52.3 SeVo y
= 4 1 . 7 k 0 . 5 1 n b-
oyP
= 43.68 + 0.2 mbb = 1 2 . 8 5 * 0 . 1 2 ~ e ~ - ~ (Here b i s p o s t u l a t e d t o be
P P
1 2 . 2 G e T 2 f o r pp and 12.6 G ~ v - ~ b
-
= 13.36+
0.53 Gevm2f o r p i j ) . PP
It i s remarkable t h a t h e r e , f o r t h e f i r s t t i m e , b o t h t h e r e a l and imaginary p a r t s o f FPP and FPP, and t h e r e f o r e o f F+ and F- a r e o b t a i n e d . These measurements:
1) f a v o u r , l i k e R 210,-Ao + 0 ;
2 ) show t h a t IReF-/ImF ( i s n o t l a r g e and a l s o t h a t R ~ F - x I ~ F - > 0 and h i n t t h a t two s u f f i c i e n t c o n d i t i o n s f o r t h e v a l i d i t y o f t h e Pomeranchuck theorem might be s a t i s f i e d ;
3 ) make v e r y u n l i k e l y unorthodox p o s s i b i l i t i e s s u c h a s t h e p r e s e n c e o f 110dderons7f.
On t h e o t h e r hand, t h e r a t i o o f t h e s l o p e s , a t ECM = 5 3 GeV, i s c o m p a t i b l e w i t h u n i t y i n agreement w i t h o u r theorem.
The d a t a a t ECM = 62 GeV a r e n o t y e t a n a l y z e d .
From t h e e x i s t i n g d a t a a f i t o f o T h a s been p r o p o s e d , c o m p a t i b l e w i t h a ( 1 0 ~ s ) ~ i n c r e a s e , which p r e d i c t s 8 ) 0~ = 7 1 mb a t EiM = 540 GeV o r 66mb i f o T ( a ) = 1 3 0 mb
w h i l e R 210 p r e d i c t s oT = 69 mb a t ECM = 5 0 GeV and Ref. 5 ) p r e d i c t s uT = 6 3 mb a t ECM = 540 GeV.
A f i t o f t h e s l o p e 9 ) based on R 211 i n d i c a t e s t h a t a l i n e a r f i t i n l o g E i s u n a c c e p t a b l e and t h a t a q u a d r a t i c f i t b = A = B logE + ( l o g E )
'
i s needed.~ 3 - 166 JOURNAL DE PHYSIQUE
3. Asymptotic bounds and behaviour, and SPS collider experiments.- The fastest growth of the total cross-section allowed by field theorylo) is given by the "Froissart boundn first derived from Mandelstam representationl1)
aTot
<Const ( l o g
E ) ~.
~f
oTot/(log
E)' +c o n s t
#o ,
a situation which, to the best of our knowledge, is co~npatible with analyticity and unitarity in all channels12) we have13)
'e1astic"~ot
-tConst
# 0,
b ( s , t
= 0 )-- ( l o g
E ) ~ YF ( z ) = entire function of order 1/2 = analytic function of z, bounded by exp
~m
in the whole complex plane.
Another possible asymptotic behaviour is that of the critical ~ o m e r o n l ~ ) , for which
o
- ( l o g 9
o e l / a ~
- ( l o g E ) - O - ~ ~ ,
b
- ( l o g E)'.l3 ,
and
Data at energy 5 ISR energies are compatible with a qualitative saturation of the Froissart bound [the best fit of Ref. 5) gives 5 T z (log~)~.~~O.l], but this is based on a 10% increase of
oT.,
The great interest of the SPS collider is that it allows to observe a much more impressive effect. The UA4 collaboration has measured at 540 GeV cm the slope of the diffraction peak for 0.05 < It1 < 0.18 G ~ l5); it is V ~By extrapolating to t = 0, they get L x do/dt (0) = const x L x ( ~ ~ ~ ~ ( l + p ~ ) . L luminosity can be eliminated by measuring the total rate of events, L 5 ~ and one 7 gets (with p = O ; remember that p 5 0.15)
A . Martin C3-167
T h i s measurement i s compatible w i t h t h e v a r i o u s e x t r a p o l a t i o n s from ISR and s l i g h t l y f a v o u r s a model s a t u r a t i n g t h e F r o i s s a r t bound.
The s l o p e , thought f i r s t t o be anomalously l a r g e , i s i n f a c t compatible w i t h a model s a t u r a t i n g t h e F r o i s s a r t bound b u t a l s o w i t h t h e c r i t i c a l Pomeron.
The U A 1 g r o u p , on t h e o t h e r hand, h a s made measurements o f b a t l a r g e r t 0.15 <
I
t1
< 0.26 G ~ and found a much s m a l l e r v a l u e l 6 ) V ~The tendency o f t h e s l o p e t o d e c r e a s e w i t h It1 i s s e e n a t lower e n e r g i e s b u t seems t o be more marked h e r e . T h i s i s n o t i n c o m p a t i b l e w i t h t h e o r y because, i f
OT 'L ( l o g E I 2 we e x p e c t a non uniform behaviour o f b ( E , t ) a s a f u n c t i o n o f t:
b ( s , t = O ) % ( 1 0 ~ s ) ~ while b ( s , t ) t , fixed ( 0 % l o g s .
I n t h i s s h o r t review17) we have t r i e d t o show t h e g r e a t p o t e n t i a l o f t h e SPS c o l l i d e r e l a s t i c s c a t t e r i n g experiments. It i s o n l y i n one o r two y e a r s t i m e t h a t , w i t h I n c r e a s e d a c c u r a c y , we s h a l l be a b l e t o draw f i r m e r c o n c l u s i o n s . I f r e a l p a r t measurements were a l s o made a t t h e s e e n e r g i e s t h e y would a l l o w t o g u e s s what happens t o o t o t a l a t much h i g h e r e n e r g i e s ( a s was done a t t h e ISR) and t h i s would be a most v a l u a b l e i n f o r m a t i o n .
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