HAL Id: jpa-00215204
https://hal.archives-ouvertes.fr/jpa-00215204
Submitted on 1 Jan 1973
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
N* AND Z* SPECTROSCOPY
P. Bareyre
To cite this version:
P. Bareyre. N* AND Z* SPECTROSCOPY. Journal de Physique Colloques, 1973, 34 (C1), pp.C1-
223-C1-226. �10.1051/jphyscol:1973124�. �jpa-00215204�
N* AND Z* SPECTROSCOPY P. BAREYRE D.Ph.P.E.
-
CEN-Saclay1.
-
NEW EXPERIMENTAL RESULTS ON X N + 2-BODY SCAT- TERING.-
1.1.- MEASUREMENT OF THE POLARIZATION PARAMETER FOR
-
0n p + x n
.-
Measurements of t h e p o l a r i z a t i o n parameter f o r t h e r e a c t i o n n-p $n have been performed w i t h t h e Berkeley Bevatron a t f i v e momenta between 1.Q3 and 1.79 GeV/c [ I ] . The experimental arrangement con- s i s t s i n 20 n e u t r o n c o u n t e r s ( f o r t i m e - o f - f l i g h t mea- surements and a n g u l a r i n f o r m a t i o n ) and t h i c k p l a t e s p a r k chambers t o d e t e c t t h e y r a y s from2
decay.The d e t e c t o r s surround a 7 cm l o n g propylene g l y c o l p o l a r i z e d t a r g e t ( 5 m p o l a r i z a t i o n ) . For each momen- tum, about 1 0 000 e v e n t s a r e d e t e c t e d i n a t y p i c a l l y a n g u l a r range : -.78 < c o s
eY<
.87.
The background due t o q u a s i - e l a s t i c e v e n t s i n t o t h e t a r g e t sample was e s t i m a t e d u s i n g a dummy t a r g e t . Those d a t a r e p r e - s e n t t h e f i r s t charge-exchange p o l a r i z a t i o n a n g u l a r d i s t r i b u t i o n e v e r made i n t h e energy domain covered by phase s h i f t a n a l y s e s .The prelimxnary r e s u l t s ( i n c l u d i n g s t a t i s t i c a l e r - r o r s o n l y ) a r e d i s p l a y e d on Fig.14 of B u t t e r w o r t h ' s r e - p o r t w i t h t h e predictions of CERN(1971)[2] and Saclay (1972)[3
1,
(1973)[4] phase s h i f t a n a l y s e s . The g e n e r a l agreement i s q u i t e good, s p e c i a l l y f o r t h e 1973 Saclay smoothed phases i f one remember t h a t s m a l l phase s h i f t changes can c o n s i d e r a b l y a l t e r t h e p o l a r i z a t i o n s . To show t h a t t h e agreement i s n o n - t r i v i a l we have compu- t e d , from I s o s p i n I n v a r i a n c e [ 5 ] , t h e bounds on charge exchange polarizations knowlng c r o s s - s e c t i o n s and po- l a r i z a t i o n s i n t h e C p e l a s t i c s c a t t e r i n g . Measure-+
ments a t momenta above 1.8 GeV/c would a l s o be p a r t i - c u l a r l y u s e f u l f o r c o n s t r a i n i n g phase s h i f t a n a l y s e s . 1.2.
-
BACKWARD CROSS SECTIONS FOR G p , xOn AND rlOn FINAL =ATE3 FRCM 0.6 113 1.05 GeV/c [6].-
A cusp is observed i n theFP
e l a s t i c cross-section a t exactly t;le q threshold ( F i g . 15 of B u t t e r w o r t h ' s r e p o r t ) . The noon c r o s s - s e c t i o n which peaks a t t h e q t h r e s h o l d r e p r e s e n t s a c o n s i d e r a - b l e improvement i n accuracy on t h e previous 22ta. T h i s c r o s s - s e c t i o n l i e s between t h e bounds given by I s o s p i n c o n s e r v a t i o n but n o t on t h e f r o n t i e r , a s was suggested p r e v i o u s l y [71.
( F i e . 17 of B u t t e r w o r t h ' s r e p o r t ) .1.3.
-
PRELIMINARY VALUES FOR n-p-+-v
n FRCM 1600 TO 1740 MeV [8].- These good s t a t i s t i c s measurementsshow some pronounced s t r u c t u r e s f o r t h e Legendre po- lynomials c o e f f i c i e n t s aroung 1690 MeV. I n p a r t i - c u l a r , C i s 4 s t a n d a r d d e v i a t i o n s away from 0 .
4
1 . 4 . - MEASUREMENT OF x - ~ -, w n NEAR THRESHOLD [g].
The c r o s s - s e c t i o n dependence does not show t h e beha- v i o u r expected f o r a pure S wave p r o d u c t i o n , b u t t h e d a t a i s c o n s i s t e n t w i t h i s o t r o p i c c.m.s. a n g u l a r d i s - t r i b u t i o n s . F i n a l s t a t e i n t e r a c t i o n s could e x p l a i n t h e e f f e c t .
.2. PlIASE SNIFT ANALYSES OF ELASTIC (&IUD CdARGE EXCHANGE) r N and K+N SCATTERING.- Two a n a l y s e s
+
which t r e a t s i m u l t a n e o u s l y t h e d a t a i n t h e a v a i l a b l e c h a n n e l s have been submitted.
2 . 1
.-
xN SCATTERING.- The Saclay group [ 4 ] p r e s e n t s a n a n a l y s i s up t o 2.4 GeV t o t a l energy which d i f f e r s from t h e previous one [ 3 ] on two a s p e c t s :2.1.1.- New d a t a a r e included : a c c u r a t e r p d i f f e -
+
r e n t i a l e l a s t i c c r o s s - s e c t i o n s
[ l o ]
xn t h e low momex- tum r a n g e : 180 < p c 408 MeV/c and o h a r g e exchange a n g u l a r distributions from Berkeley [ 6 ] and S a c l a y [ l l ] f o r 1.0 < p < 2 . 4 GeV/c. I n t h e s e two energy domains a n independent-energy phase s h i f t a n a l y s i s has been f i r s t performed, u s i n g c o n v e n t i o n a l methods.A unique g e n e r a l s o l u t l o n has been o b t a i n e d a f t e r a p p l y i n g t h e c r i t e r i a of "minlmal path" i n t h e A r - gand p l o t .
2.1.2.- The p a r t i a l waves have been p a r a m e t r i z e d s e p a r a t e l y , a s f u n c t i o n s of energy u s i n g a g e n e r a l i - zed Breit-i'figner approximat ion : T
=
TRES+ T ~ ~ ~ ~ ~ *
The u n i t a r i z e d background a m p l i t u d e d i f f e r s from t h e previous a n a l y s i s i n o r d e r t o m a i n t a i n a c o r r e c t be- h a v i o u r a t t h r e s h o l d f o r t h e p a r t i a l amplitude. The main changes between t h e two a n a l y s e s a r e :
-
a b e t t e r d e t e r m i n a t i o n of Sll a t low e n e r g i e s ,-
a b e t t e r d e t e r m i n a t i o n of some s t r u c t u r e s above 1.9 GeV,e s p e c i a l l y on t h e low a n g u l a r momentum waves which
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973124
121-224 P. BAREYRE p e r m i t t e d t o i n c l u d e two more resonances of s m a l l
e l a s t i c i t y : S (2.0 GeV) and D13(2.029). These two 3 1
p a r t i a l waves a r e d i s p l a y e d on f i g u r e 1
,
with t h e i r r e s p e c t i v e speed p l o t s .3
Fig.1.- Sgl and D13 p a r t i a l waves obtained i n t h e 1973 S a c l a y phase s h i f t a n a l y s i s . S o l i d l i n e s correspond t o t h e f i t t e d p a r t i a l waves u s i n g a g e n e r a l i z e d B r e i t -
!Vigner approximation. New resonances a r e S31(2.0 GeV) and D13(2.029 GeV).
I t should be n o t i c e d t h a t t h e spacing between 2 e n e r g i e s a t which phase s h i f t s e x i s t i n c r e a s e s w i t h energy. Above 2 GeV mass, t h e c o n d i t i o n of 4 p o i n t s a l o n g h a l f a c i r c l e on t h e Argand p l o t t o d e f i n e a resonance p u t s
rtot
> 150 t o 200 MeV.
New d a t a ( c r o s s s e c t i o n s and p o l a r i z a t i o n s ) a r e needed t o be s u r e t h a t s t a t e s of small e l a s t i c i t y and width have s o t been missed.The u s e of a d i s p e r s i o n r e l a t i o n f o r t h e B + ( v , t = O )
-
i n v a r i a n t amplitude computed from t h e phase s h i f t s h a s given a n a c c u r a t e d e t e r m i n a t i o n of t h e pion-nu- c l e o n c o u p l i n g c o n s t a n t : f L
=
0.0742+
0.0013 ( F i g . 1 1 of B u t t e r w o r t h ' s r e p o r t ) .2.2.
-
K+N SCATTERING.-
The BGRT c o l l a b o r a t i o n has s u b m i t t e d t h e f i n a l v e r s i o n [ 1 2 ] of phase s h i f t ana- l y s e s i n c l u d i n g both I = l and 0 i s o s p i n s t a t e s and performed up t o 2.02 mass. The experimental d a t a a- v a i l a b l e c o n t a i n s t h e t o t a l , i n 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 s and p o l a r i z a t i o n s f o r t h e Kf p ( I=
1channel: I t i n c l u d e s Ktn -t K O ~charge-exchange and K+n + ~ + n 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 , most of which were measured by t h i s c o l l a b o r a t i o n . I t u s e s a l s o t o - t a l and t o t a l i n e l a s t i c c r o s s - s e c t i o n s f o r t h e I = O
s t a t e but not t h e
new
t o t a l c r o s s - s e c t i o n s from Brookhaven [13].Three t y p e s of phase s h i f t a n a l y s e s have been per- formed : an energy-dependent analysis (5 parameters p e r wave) and two energy-dependent a n a l y s e s . I n one of them, t h e I = 1 p a r t i a l waves were kept f i x e d a t a s o l u t i o n coming from t h e a n a l y s i s of t h e I = l chan- n e l a l o n e [14].
These t h r e e methods y i e l d s i m i l a r r e s u l t s . I n par- t i c u l a r , 3 common f a m i l i e s of s o l u t i o n s were found.
Some checks w i t h p a r t i c u l a r f e a t u r e s of t h e d a t a (new I
=
0 t o t a l c r o s s - s e c t i o n s and c h a r g e exchange p o l a r i z a t i o n a t 0.6 GeV/c) may be c o n s i d e r e d t o f a - vour t h e s o l u t i o n s which g i v e t h e b e s t Z: c a n d i d a t e w i t h t h e Pol wave. F i g . 2 shows t h e corresponding Argand 'plots together with the ones of the b e s t :2 c a n d i d a t e (P ) 13Fig.2.- Argand p l o t s of : P13, d o t t e d l i n e c o r r e s - ponds t o t h e a n a l y s i s of ~ + p e l a s t i c channel a l o n e and o t h e r l i n e s come from t h e energy-independent ana- l y s i s of Iz0.1 s t a t e s . P energy-dependent ( s o l i d l i n e s ) and energy-indepen8ent s o l u t i o n s of t h e D
c l a s s . (Numbers correspond t o i n c i d e n t momenta (hkV/c))
.
T h e r e f o r e a unique g e n e r a l s o l u t i o n i s not o b t a i n e d i n K'N a n a l y s e s and no d e f i n i t e c o n c l u s i o n can be drawn on t h e e x i s t e n c e of a 2". C l e a r l y , more pola- r i z a t i o n s a r e needed t o c o n s t r a i n t h e K+N phase s h i f t a n a l y s e s . I n p a r t i c u l a r , new d e u t e r a t e d p o l a r i z e d t a r g e t s [IS] open t h e p o s s i b i l i t y t o measure p o l a r i - z a t i o n s i n e l a s t i c and c h a r g e exchange ~ + n s c a t t e - r i n g , which seems e a s i e r than t h e d e t e r m i n a t i o n of A and R parameters i n K+p s c a t t e r i n g .
3.- PARTIAL WAW ANALYSES OF THE 3-BODY INELASTIC CHANNELS.- Three-body i n e l a s t i c channels i n $p and K+N s c a t t e r i n g account f o r n e a r l y a l l t h e t o t a l i n - e l a s t i c c r o s s - s e c t i o n (about h a l f of t h e t o t a l c r o s s - s e c t i o n ) below 2.0 GeV mass.
Two methods of a n a l y s i s have been followed :
-
a n a l y s i s of quasi-two-body r e a c t i o n s , w h i c h have been i s o l a t e d by c u t s i n D a l i t z p l o t s :by a CERN-Saclay c o l l a b o r a t i o n [16] : 70 000 e v e n t s f o r 1.89 < & < 2.1 GeV
.
- G e n e r a l i z e d i s o b a r model a n a l y s e s o f t h e whole f i n a l s t a t e , u s i n g t h e Deler-Valladas formalism :
N* AND Z* SPECTROSCOPY C1-225
$p -, XXN-,
d ,
N p,
N ~ ( x x ) ~= J =
Two p a r t i a l wave a n a l y s e s u s i n g t h i s t e c h n i q u e ha- ve been s u b m i t t e d :
-
LBL-SLAC c o l l a b o r a t i o n (17 ] : 200 000 e v e n t s f o r1.3 <
&<
2.0 GeV ( e x c e p t f o r a 0.11 GeV gap1 . 5 4 <
5
C 1.65).-
Saclay [18] : 30 000 e v e n t s f o r 1 . 4 <,&
< 1.54 GeV.We s h a l l summarize t h e s e 3-energy-independent par- t i a l wave a n a l y s i s , t h e p a r t i a l waves b e i n g l a b e l l e d
,2J where L i s t h e incoming ( x , K-N) a n g u l a r momentum, L ' t h e outgoing a n g u l a r momentum between t h e resonance R : A
, p ,
~ ( ? n c ) ~= J = ,
K*(890) and t h e remaining p a r t i c l e (x,K o r N). I and J a r e t h e i s o s p i n and t o t a l s p i n , S i s t h e t o t a l i n t r i n s i c spin.3.1.- SIMULTANEOUS PARTIAL WAVE ANALYSIS OF THE 3 FINAL STATES : ~ + p
,
1 ~ * ( 8 9 0 ) ~,
~ A ( 1 2 3 0 ) . - Data have been measured a t 4 e n e r g i e s c o v e r i n g t h e wide bump of t h e I=
1 t o t a l i n e l a s t i c c r o s s - s e c t i o n .The p r o d u c t i o n a n g u l a r d i s t r i b u t i o n s (expanded i n Legendre polynomials) and t h e d e n s i t y m a t r i x elements
of the A++KO and ~ * ( 8 9 0 ) p have been used t o g e t h e r w i t h t h e d a t a ( c r o s s - s e c t i o n s and p o l a r i z a t i o n s ) from K+p e l a s t i c s c a t t e r i n g . T h i s a n a l y s i s does n o t make u s e of t h e i n t e r f e r e n c e e f f e c t s a s s o c i a t e d with t h e o v e r l a p of t h e K* and A bands, i . e . i t cannot r e l a t e i n phase t h e two channels.
At each energy, s e v e r a l a c c e p t a b l e s o l u t i o n s were found, showing t h e f o l l o w i n g f e a t u r e : t h e A K channel which i s t h e o n l y one f o r which r e l i a b l e amplitudes c a n b e o b t a i n e d does n o t seem t o be dominated by a s i n g l e p a r t i a l wave. Four waves were found important ; A s D ~ ~
,
APP33,
ADD35 and AFF37.
The d a t a were found a l s o compatible w i t h t h e d u a l i - t y h y p o t h e s i s ( a l l p a r t i a l waves i n phase) and w i t h l i n e a r dependent energy p a r a m e t r i z a t i o n s of t h e par- t i a l waves. These c o n c l u s i o n s d i s a g r e e w i t h t h e ana- l y s i s of t h e KN + KIN s c a t t e r i n g f o r which t h e I
=
0 , l I s o s p i n s t a t e s have been s e p a r a t e d [ 2 2 ] . A peak s t a - t i s t i c a l l y marginal i s found on r1 = 0 n e a r 2 GeV mass. Moreover, t h e I = 0 , 1 i n t e r f e r e n c e term shows t h a t non n e g l i g i b l e imaginary p a r t s of t h e amplitudes a r e p r e s e n t .
C l e a r l y , a more s o p h i s t i c a t e d a n a l y s i s based on t h e Isobar-model (which i s i n p r o g r e s s ) i s needed t o g i v e more p r e c i s e r e s u l t s . I n t h e p r e s e n t s i t u a t i o n , t h e a n a l y s i s i s c o n s i s t e n t w i t h t h e non-resonant i n t e r p r e - t a t i o n of t h e c r o s s - s e c t ion bump.
3.2.- ISOBAR MODEL ANALYSIS OF xN
*
XXN.-
The Sa-c l a y group and t h e LBL-SLAC c o l l a b o r a t i o n a r e p u r s u i n g
t h e i r own a n a l y s i s . A s n o t i c e d by C. Lovelace [19]
s e v e r a l y e a r s ago, " p h a s e - s h i f t a n a l y s i s i s one a r e a where t h i s d u p b i c a t i o n i s u s e f u l . To have M v e groups t r y i n g t o c u t each o t h e r s ' t h r o a t s i s much more e f f i - c i e n t t h a n random s e a r c h i n i t .
The S a c l a y group [ 1 8 ] r e p o r t p r e l i m i n a r y r e s u l t s of a n energy-independent p a r t i a l wave a n a l y s i s a t f o u r e n e r g i e s , i n which t h e y f i t s i m u l t a n e o u s l y t h e 3 r e a c t i o n s :
S e v e r a l improvements a r e i n t r o d u c e d i n t h e f i t s w i t h r e s p e c t t o t h e i r p r e v i o u s a n a l y s i s [ 1 8 ] :
-
t h e f i t of t h e c h a n n e l nCp -+ p nixo ;-
t h e i n c l u s i o n of u n i t a r i t y l i m i t s ;-
a b e t t e r p a r a m e t r i z a t i o n of t h e r a n d of c e n t r i - f u g a l b a r r i e r f a c t o r s .The o v e r a l l a r b i t r a r y phase i s chosen by a s s i g n i n g t o t h e APPll p a r t i a l wave amplitude t h e phase of t h e e l a s t i c p a r t i a l wave.
The LBL-SLAC a n a l y s i s h a s been r e p o r t e d p r e v i o u s l y [20]. I t u t i l i z e s t h e d a t a i n a very e f f i c i e n t way making a simultaneous maximum l i k e l i h o o d f i t t o a l l t h e e v e n t s f o r t h e t h r e e c h a n n e l s mentionned above.
The a n a l y s i s i s c o n f i n e d t o F waves o r l e s s (L, L'
5
3 ) which a l l o w s i n p r i n c i p l e by s p i n - p a r i t y c o n s e r v a t i o n 60 i n e l a s t i c a a p l i t u d e s . I n f a c t , a q u a r t e r of them below 1520 MeV and about h a l f of them above have been determined.The a b s o l u t e phase i s s p e c i f i e d by smoothing t h e s o l u t i o n s u s i n g a multichannel K-matrix f i t of t h e dominant waves i n t h r e e s e p a r a t e energy r e g i o n s P11(1310-1540 MeV), D15, F15(1650-1810), F35(1810-
1970). The o v e r a l l i n e l a s t i c phase i s t h u s t i e d t o t h e e l a s t i c phase.
COMPARISON OF THE RESULTS.
-
The S a c l a y group h a s k e p t more p a r t i a l waves i n h i s a n a l y s i s t h a n LBL- SLAC (24 i n s t e a d of 15 around 1 . 5 GeV) and two of t h o s e a d d i t i o n a l waves a r e found t o be important plPPll andADD15.
I n o r d e r t o show t h e r e l i a b i l i t y of t h e s e a n a l y s e s , we show on f i g u r e 19 of
utterw worth's
r e p o r t t h e A r -gand p l o t s of t h e 3 dominant waves f o r both a n a l y s e s i n t h e same energy r a n g e (1.38-1.54 GeV). There i s a g e n e r a l agreement e x c e p t f o r t h e
P
PP1 11 wave men- t i o n n e d above. The d i f f e r e n c e s observed i n d i c a t e t h a t t h e s e a n a l y s e s have t o be pursued.
Above 1500 MeV, t h e LBL-SLAC c o l l a b o r a t i o n h a s r e c e n t l y found a second s o l u t i o n ( s t i l l b e i n g explo- r e d [21] which c o n t a i n s t h r e e more waves t h a n t h e one p r e s e n t e d a t t h e B a t a v i a Conference. Those a r e
C1-226 P. BAREYRE
plPPll
,
Aspll and A F F ~ ~.
The APP h a s a d i f f e r e n t ges t h e c o u p l i n g s i g n s of a l l t h e resonances above 11behaviour a c r o s s t h e gap ( s e e f i g u r e 22 of B u t t e r - 1620 M e w r e l a t i v e t o t h e low energy ones (P 11 'D13) w o r t h ' s r e p o r t ) . As a r e s u l t , o t h e r waves under- g i v i n g a good agreement between t h e r e l a t i v e s i g n s
go a n almost 180° r o t a t i o n . Consequently, t h i s chan- of t h e Ax and C(1385)x a m p l i t u d e s , a s w e l l a s w i t h t h e p r e d i c t i o n s of SU6 and t h e quark model.
REFERENCES
[ I ] SHANNON (S.R.) e t a l . LBL-2114 (1973).
[2
]
ALMMED (S. ) and LOVELACE (C. 1, Nucl. Phys.B40
(1972) 157.
[3
]
AYED (R. ), BAREYRE (P. ) and LEMOIGNE (Y. ),
Bata- v i a 1972 Conference (paper 990).141 AYED (R.) and BAREYRE ( P . ) , submitted t o t h e Aix Conference (paper 311 ).
[5] DASS (G.V.) e t a l . , Phys. L e t t . (1971) 339.
[ 6 ] BINNIE (D.M.) e t a l . , Aix, paper 302.
[ 7 ] AYED (R. ) e t a l . submitted t o t h e Amsterdam Conference (1971 ).
[ 8 ] CHAFFEE e t a l . , t o be published.
[ 9 ] BINNIE (D.M.) e t a l . , Aix, paper 273.
[lo]
BUSSEY (P.J. ) e t a l . , p r e p r i n t RPPLH/107 (1973).[ l l
]
FELTESSE (J. ) e t a l . , t o be published.[12] GIACCMELLI (G. ) e t a l . , t o he published.
[13] ABRAMS (R.J.) e t a l . , B a t a v i a Conference (1972).
[14] ALBROW (M.G.) e t a l . , Nucl. Phys.
-
B30 (1971) 273.DAUM(C.) e t ax., CERN p r e p r i n t , A p r i l 2 (1973).
16 BERTHON (A.) e t a l . , Aix, paper 315
.
P5 I
[17] LONGACRE (R.) e t a l . , Aix, paper 309.
[18] DOLBEAU (J.) and 'IRIANTIS (F.A.), A i x , paper 308.
[19] LOVELACE (C. ), I n v i t e d t a l k , Berkeley Conferen- c e (1966).
[20] HERNDON (D.J.) e t a l . , LBL-1065 (1972).
[21] ROSENFELD (A. ), p r i v a t e communication.
[22] ALEXANDER e t a l . , Aix, paper 77.
