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DISCRETE AMBIGUITIES AND SOME PECULIARITIES OF N-N AMPLITUDES
A. Gersten
To cite this version:
A. Gersten. DISCRETE AMBIGUITIES AND SOME PECULIARITIES OF N-N AMPLITUDES.
Journal de Physique Colloques, 1985, 46 (C2), pp.C2-471-C2-473. �10.1051/jphyscol:1985258�. �jpa-
00224574�
JOURNAL DE PHYSIQUE
Colloque C2, supplement au n°2, Tome 46, fevrier 1985 page C2-471
DISCRETE AMBIGUITIES AND SOME PECULIARITIES OF N~N AMPLITUDES A. Gersten
Department of Physios, Ben-Gurion University of the Negev, Beer-Sheva 84120, Israel
Abstract - The applications of the zeros method are reviewed. The reconstruc- tion of the n-p amplitudes and amplitude regularities are discussed.
* 1 2
The method of zeros ' is a useful tool of studying ambiguities of phase shift analyses. It had direct applications in the case of scattering of spin zero particles , spin •=• on spin zero particles and in NN + irn scattering ' .
The case of elastic N-N scattering was studied by Manolessou-Grammaticou and by
Q
Grebenyuk, Komarov and Shklyarevskii who had done a detailed analysis of elastic p-p scattering. The relation of the ambiguities to the transversity amplitudes was pointed out in Ref. 9. In the above papers the ambiguities are based on the 5 observables oEdo/dn, PsA„„, D„„, C„„, K„„ and on 3 total cross sections. The
NN NN NN NN
application of the method of zeros to the above set of observables is rather limited because usually other observables are measured (Wolfenstein parameters) and there are constraints on the residues at the pion and photon poles. In ref. 8 are presented two ambiguous sets of p-p phase shifts at energies approaching 1 GeV.
The application to the study of the existence of the dibaryon resonances is also limited because of the very large background and because of a lack of an evidence of Regge trajectories passing through the suspected dibaryon resonances and through states of lower angular momenta as well (3P before 3F, and *S before *D-, although the antibound JS state can be considered as a Regge pole).
I would like to present here a formula which greatly facilitates the computation of zeros and ambiguities for any spin using the variable <i)=e . Let a helicity amplitude 1 9 (j>(6) be given in the form
Résumé - Un résumé de la méthodede zéros sera présenté, ainsi que la
reconstruction des amplitudes n-p et la régularité des amplitudes N-N
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985258
JOURNAL DE PHYSIQUE
then
Usually the ambiguities are obtained by complex conjugation of the zeros of transversity amplitudes in the w plane. The transversity amplitudes are linear combinations of the helicity amplitudes and in this case the use of formula ( 2 ) simplifies greatly the computations.
At present there are not enough experiments available for a unique determination of the n-p amplitudes above 500 MeV. It is of interest to point out that with the knowledge of isospin 1 amplitudes (from p-p scattering) and the 5 mentioned
observables for n-p scattering,it would be possible (within some sign ambiguities)to determine the n-p amplitudes.
We shall present the results for the transversity amplitudes using the notation of ref. 10. We shall also use the notation Tj(8)2T;; J j=l,..S; I=O,l (isospin), AIEo,
I I I
A "UP, A3PoDNN, A4ZoKNN, A5=aCNN (for n-p observables) and T (e)=(~
.(
exp [iaj(8)].2- j J
The results for the- transversity amplitudes :T are:
ZIT;((T~(COS
[a;(8)-
a:(8)] =1
BjkAk(8)-1
CjkAk(n-8) (4)k where
The amplitude ambiguities could be further reduced if regularities or constraints can be found 11s12p13'14. It seems to me that the N-N repulsive core should be better understood and explored in phenomenological and high energy models. An attempt in this direction is the no-exchange model 13 (NEM). I will present here a
generalization of the model for any spin, starting from the representation
where j and k are spherical Bessel functions, q = J-t, t is the 4-momentum
v v
transfer squared, = ( A ~ - ) - ( are initial hellcities and A3A4 are
f i n a l h e l i c i t i e s . The NEM c o n s i s t s o f r e p l a c i n g t h e o n e p a r t i c l e e x c h a n g e t e r m of eq ( 5 ) by
NEM, 2 y 1
n j v ( q r ) k v ( p r ) r 2 d v ( 6 )
v+l R
= [ u ~ j ~ ( q ~ E , , + ~ ( Y R )
-
q R j y t l ( ~ R ) ~ ~ ( Y R )1.
The p h y s i c a l meaning of eq ( 6 ) i s t h a t p a r t i c l e s a r e exchanged o n l y o u t s i d e t h e r a d i u s R. The r e a l p a r t s of t h e d o u b l e s p i n f l i p N-N h e l i c i t y a m p l i t u d e s a r e d e s c r i b e d q u i t e w e l l w i t h t h i s model w i t h R = l . l fm a s s u m i n g t h e p i o n e x c h a n g e f o r l a b e n e r g i e s a b o v e 100 MeV up t o e n e r g i e s where p h a s e s h i f t a n a l y s i s i s b e i n g done.
Very f r u i t f u l d i s c u s s i o n s w i t h D. V. Bugg a r e h i g h l y a p p r e c i a t e d .
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