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Some remarks on the higher πN resonances
Volumt 12. pumber 2
P II Y S }C ~ lI[."~""r E l{ ~
SOME
REMARKS
ON
THE
G. H ( ) H L E R
15 September 1964
HIGHER
=N
RESONANCES
anc J. G I E S E C K E
l ~ s H f u : .tier 7"h~ n r e H s e h c K e r ~ p h y s * k ,
7ec
.t.~che I / o c h ~ r h u l e K n r l s v ~ , h c ,
h
Ger,~ary
Received 17 August 1964
In am e'4rller p a p e r 1) we have p r e s e n t e d a p r e dlctt:,n f o r the :rN c h a r g e exc "hange f o r w a r d cros,~ s e c t i o n , c a l c u l a t e d f r o m the d i s p e r s i o n r e l a t i o n and new data of the total , N c r o s s s e c t i o n s . N e a r T , ~ 2.6 C,eV otur re=mR Lho'#s a s t r u c t u r e , which a g r e e s with the s t r u c t u r e found In r e f . 2 and follows f r o m a peak in the d i f f e r e n c e <~_ - cy+ of the total c r o s s s e c t i o n s of Diddens et al. 3), which was not noticed b e f o r e . Above T w = 2.8 GeV t h e r e a r e d e v i a t i o n s and t h e r e f o r e it was of i n t e r e s t to r e c a / c u l a t e the p r e d i c t i o n w/th the new and v e r y a c c u r a t e total c r o s s s e c t i o n s of C i t r o n et at. 4). The method waJ the s a m e =us tn r e f . I. F r o m 5 GeV to infinity we have u s e d the e n e r g y d e p e n d e n c e (h =c : m w : I, k =plon lab. n~ome'Iblm}
~(.)
0.378 -..~ -
,
.,(+)
~.
1 . 0 9 2 , --~,-~-1.818.
(qFb)ex ~. -./2 q_u(')F,. : q F b r = ~.; [(J *
-~'-~-q ;) (_u a~- F
'=)[Olgrexpl1281j T -
1+~ 2)
1
'
°'il
T
I
tr
'
fl..
1
;!',
"
'!
i
,
Fig. !. Prediction for the chaxge exchange forward cross ~oction and experimental results ~ 5). At 10 GeV .'-ex(0~, 0.24 m b / s r with our interpol,~tinn (1) of :'(-).
X : IM q F b ( ' ) - 3.01 x 10 -2 ~
.
(3)
The m a x i m a and m i n i m a of Z (fig. 3) c o r r e s p o n d to possible T = .~ and ~ resonances, which are denoted by N(K') and ~fll,') r e s v e c t i v e l y , w h e r e F c~ i ~"qFb
(2)
7 . . . . '~---
/
/,.
|~)*I l ,
l,J w h e r e q. F b a r e m o m e n t u m and f o r w a r d axnplttude tn the c m. s y s t e m and ~>, 0 a r e the a b s o r p ti,,n p a r a m e t e r and the r e a l p a r t of the p h a s e shift. It is s e e n that at the e n e r g i e s of the m a x i m a of ~± the c u r v e d e s c r i b e s an a r c of a c i r c l e in a c o u n t e r clockwise d i r e c t i o n . T h i s f a v o u r s the a s s u m p t i o n that the m a x i m a a r e c a u s e d by r e s o n a n c e s . In o r d e r to d e t e r m i n e the r e s o n a n c e e n e r g i e s , we ~ubtract f r o m Im qJ~o( ' ) an e s t i m a t e d b a c k ground contribution (eq. (4.4) of r e / . I), o~2 =
. . . . . . . . . .
=~" !'" ~\~
o.~
F~
~
'T
(1)
which Ls sUghtly d i f f e r e n t f r o m the assuraptlon~ in r e f . 1. Since s o m e of the e x p e r i m e n t a l data are still p r e t L m t n a r y , the agreement in flg. I i s as good a s can be eR~ected. When the f~nal r e s u l t s axe a v a i l a b l e , they will be u s e d l o r an i m p r o v e d d e t e r m i n a t t o n 04 the d i s p e r s i o n integral over o . - o÷ f r o m t h r e s h o l d to Lnf/rLtty I). Fig. 2 shows the c o m p l e x d i a g r a m I) of the charge exchange forward anaplttude between 1.7
and 4 5 C~,V.
4 . . . . . . . o~,{0"}
J,
L,:.~o,,, _Z
/"
t',.
\~.
-2r
1
t
Fig. ~. Complex diagram for the forward amplitude qFb(-). The energy parameter gives Tn in MeV. The arrows show the position of the resonances proposed in ref. 7. Tim straight line corresponds to the asymptotic behavinur following from eq. (1).
149
PHYSIC8
Volume 12, number 2
~7 i s / h e m a s s in MeV. T a b l e 1 g i v e s o q r e s t i m a . :ions of t h e r e ~ . n a n e e e n e r g i e s a n d of t h e e n e r g i e s , w h e r e t h e r e a l p a r t s of t h e r e s o n a n t a m p l i t u d e s ~have t h e i r ma.xin~a a n d m i n i m a . ~ihts i n formation on the halI-wldths follows from our res u l t s f o r R e qFb T a n d d e p e n d s on a r a t h e r a r bitrary assumption about the background Isospm
15 8eptember 19~4
LE'~'T ER3 it "
o
...
._
,...
Table 1 3-"
W
Real p a r t h a s E a r l i e r u t l n m t e s T~ (GeV) Max Mtn ~1 ref. (W in MeV)
~(1920) N(2210) A(2440) N(2660) L(2870)
N(3080~
1.34 1.98 2.55 3.15 3.78 4.44
1830 2100 2295 2560
2000 2300 2540 2760
"01 2190 2360 2645 + l 0 2825 ± 15
3) 3~ 4) 4)
It is remarkable that abgve N{2210) th_~re s e e m s to be an CClUal spacing of the resonance energies in'the W-scale. The ratio of the heights of two adjacent rt onances with the s a m e isospin is about 4.5 (fig. 3), so this series of resonances probably extends not further than 6 GeV. W h e n the results of future experiments are presented, one should include (~_ - ~+, because this quantity is very sensltlw: to a possible structure. For instance the data of Baker et al. 6) already show evidence for the structures at 7'= = 3.8 and 4.5 GeV. Also the structure above A~2870) in ]is. 3 was not mentioned in rd. 4. It will be interesting to see, i f it i s c o n f i r m e d w i t h the f i n a l data. Evidence for two new r( son,nee, in pl,m photoproduction has been reported by Osborne ':t al. 7). In our opinion the sim vlest interprctatlon is to assume the same situatio[~ ~s for the low energy resonances: There is a large and ~redominantly real background amplitude and the peaks are caused by its inte£ference with the real parts of the resonant multipoles, which have t h e i r m a x i m a o r m i n i m a at a b o u t t h e ~ n e e n e r gy ~ s t h e r v a l p a r t s of t h e r e s o n a n t s c ~ t e r i n g p a x t m l w a v e s . T h e n a c c o r d i n g to fig. 2 t h e s t r u c t u r e a t E~ ~ 2.9 = 0 . I GeV i s n o t a n e w r e s o n a n c e b u t a n e f f e c t of ~ ( 2 4 4 0 ) , t h e r e a l p~trt of w h i c h i s l a r g e a t t h i s e n e r g y . T h e s t r u c t u r e a t E y = F..5
Fig. 3. The qutmttty Z (eq. ,t3}) s~ a fi,ttcttr~n of e ~ r l l y . The ,~etltls above 4 C~V a r e wA reliable, bectmtm took the c-eros section, f r ~ the g r a p h s L~ t e l . 4 only. GeV b e l o n g s to N(2660). T a b l e I i s u s e f u l f o r f u r t h e r d i s c u s s l o n s. W e a r e g r a t e f u l to P r o f . O s b o r n e , D r . Sond , r egger and Dr. Wahlig for sending us preprtnts and p r i v a t e c o m m u n i c a t i o n s a n d to P r o f . S c h o p p e r f o r m a k i n g a p r e p r t n t of r e L 4 a v a i l a b l e to tin. A f t nanc/al support by the "Deutsche Forschungsgem e t n s c h ~ t ' Is g r a t e f u l l y a c k n o w l e d g e d ,
l) O. Ii~hler, G.Ebel and J.Gtes0cke, fubmltt*d t,~ Z. Phystk. z) M.A.Wahllg, ] . M a n . s i l l , L.~.dlck~cm, O Faclder. C.W:trd, T Kan ;~nd E..Cglll~ in. |'hy=. R,w. L~tt~.rs ]3 (l'Jf~l) ]03. 3) A.N Dlddom=, E.W.Jenklna, T. F . K y c l a and K. F. [¢tloy, PhyB. Rev. LetterB I0 (1963) 262. 4) A . C i t r o n , W.C,eJbralth, T . F . K y c f ~ , B.A. Leontie, R . H . P h l H i p 6 and A . R o u s s e t , P h y s . Rev. L e t t e r s 13 (1964) 205. 5) P. BorKeaud. C. B~L~,ton, Y.Ducroa. P. F a l k - V l l rant, O.Gulsan0 J. Movchm,, P . h ~ o n d o r ~ r . A . ~ . l r lin~, M . Y v e r t , A . T r a n Ill and S.D. Warshaw, lthlyM ic~ Letters l0 (I~64} 134. G) W. F. Iktkor, E . W . J e n k l n s . T . F . Kycta, R.H.Pht]Hpe, A . L . R o s d , K. F. Rlley and H . R u d e r m a n n , P r o c . ~ e n na Int. Conf. o~ e l e m e n t a r y pxrticleso Vol. I, p. 634. 7) R.Alva.rez, Z . B a r - Y a m , W . K e r n , D. Luckoy, L.S. Osoorne, 3 . T a z z a r l and R. Fes~el, P h y s . Rev. l,cttors 12 (1964) 7{(}.
150
P II Y S }C ~ lI[."~""r E l{ ~
SOME
REMARKS
ON
THE
G. H ( ) H L E R
15 September 1964
HIGHER
=N
RESONANCES
anc J. G I E S E C K E
l ~ s H f u : .tier 7"h~ n r e H s e h c K e r ~ p h y s * k ,
7ec
.t.~che I / o c h ~ r h u l e K n r l s v ~ , h c ,
h
Ger,~ary
Received 17 August 1964
In am e'4rller p a p e r 1) we have p r e s e n t e d a p r e dlctt:,n f o r the :rN c h a r g e exc "hange f o r w a r d cros,~ s e c t i o n , c a l c u l a t e d f r o m the d i s p e r s i o n r e l a t i o n and new data of the total , N c r o s s s e c t i o n s . N e a r T , ~ 2.6 C,eV otur re=mR Lho'#s a s t r u c t u r e , which a g r e e s with the s t r u c t u r e found In r e f . 2 and follows f r o m a peak in the d i f f e r e n c e <~_ - cy+ of the total c r o s s s e c t i o n s of Diddens et al. 3), which was not noticed b e f o r e . Above T w = 2.8 GeV t h e r e a r e d e v i a t i o n s and t h e r e f o r e it was of i n t e r e s t to r e c a / c u l a t e the p r e d i c t i o n w/th the new and v e r y a c c u r a t e total c r o s s s e c t i o n s of C i t r o n et at. 4). The method waJ the s a m e =us tn r e f . I. F r o m 5 GeV to infinity we have u s e d the e n e r g y d e p e n d e n c e (h =c : m w : I, k =plon lab. n~ome'Iblm}
~(.)
0.378 -..~ -
,
.,(+)
~.
1 . 0 9 2 , --~,-~-1.818.
(qFb)ex ~. -./2 q_u(')F,. : q F b r = ~.; [(J *
-~'-~-q ;) (_u a~- F
'=)[Olgrexpl1281j T -
1+~ 2)
1
'
°'il
T
I
tr
'
fl..
1
;!',
"
'!
i
,
Fig. !. Prediction for the chaxge exchange forward cross ~oction and experimental results ~ 5). At 10 GeV .'-ex(0~, 0.24 m b / s r with our interpol,~tinn (1) of :'(-).
X : IM q F b ( ' ) - 3.01 x 10 -2 ~
.
(3)
The m a x i m a and m i n i m a of Z (fig. 3) c o r r e s p o n d to possible T = .~ and ~ resonances, which are denoted by N(K') and ~fll,') r e s v e c t i v e l y , w h e r e F c~ i ~"qFb
(2)
7 . . . . '~---
/
/,.
|~)*I l ,
l,J w h e r e q. F b a r e m o m e n t u m and f o r w a r d axnplttude tn the c m. s y s t e m and ~>, 0 a r e the a b s o r p ti,,n p a r a m e t e r and the r e a l p a r t of the p h a s e shift. It is s e e n that at the e n e r g i e s of the m a x i m a of ~± the c u r v e d e s c r i b e s an a r c of a c i r c l e in a c o u n t e r clockwise d i r e c t i o n . T h i s f a v o u r s the a s s u m p t i o n that the m a x i m a a r e c a u s e d by r e s o n a n c e s . In o r d e r to d e t e r m i n e the r e s o n a n c e e n e r g i e s , we ~ubtract f r o m Im qJ~o( ' ) an e s t i m a t e d b a c k ground contribution (eq. (4.4) of r e / . I), o~2 =
. . . . . . . . . .
=~" !'" ~\~
o.~
F~
~
'T
(1)
which Ls sUghtly d i f f e r e n t f r o m the assuraptlon~ in r e f . 1. Since s o m e of the e x p e r i m e n t a l data are still p r e t L m t n a r y , the agreement in flg. I i s as good a s can be eR~ected. When the f~nal r e s u l t s axe a v a i l a b l e , they will be u s e d l o r an i m p r o v e d d e t e r m i n a t t o n 04 the d i s p e r s i o n integral over o . - o÷ f r o m t h r e s h o l d to Lnf/rLtty I). Fig. 2 shows the c o m p l e x d i a g r a m I) of the charge exchange forward anaplttude between 1.7
and 4 5 C~,V.
4 . . . . . . . o~,{0"}
J,
L,:.~o,,, _Z
/"
t',.
\~.
-2r
1
t
Fig. ~. Complex diagram for the forward amplitude qFb(-). The energy parameter gives Tn in MeV. The arrows show the position of the resonances proposed in ref. 7. Tim straight line corresponds to the asymptotic behavinur following from eq. (1).
149
PHYSIC8
Volume 12, number 2
~7 i s / h e m a s s in MeV. T a b l e 1 g i v e s o q r e s t i m a . :ions of t h e r e ~ . n a n e e e n e r g i e s a n d of t h e e n e r g i e s , w h e r e t h e r e a l p a r t s of t h e r e s o n a n t a m p l i t u d e s ~have t h e i r ma.xin~a a n d m i n i m a . ~ihts i n formation on the halI-wldths follows from our res u l t s f o r R e qFb T a n d d e p e n d s on a r a t h e r a r bitrary assumption about the background Isospm
15 8eptember 19~4
LE'~'T ER3 it "
o
...
._
,...
Table 1 3-"
W
Real p a r t h a s E a r l i e r u t l n m t e s T~ (GeV) Max Mtn ~1 ref. (W in MeV)
~(1920) N(2210) A(2440) N(2660) L(2870)
N(3080~
1.34 1.98 2.55 3.15 3.78 4.44
1830 2100 2295 2560
2000 2300 2540 2760
"01 2190 2360 2645 + l 0 2825 ± 15
3) 3~ 4) 4)
It is remarkable that abgve N{2210) th_~re s e e m s to be an CClUal spacing of the resonance energies in'the W-scale. The ratio of the heights of two adjacent rt onances with the s a m e isospin is about 4.5 (fig. 3), so this series of resonances probably extends not further than 6 GeV. W h e n the results of future experiments are presented, one should include (~_ - ~+, because this quantity is very sensltlw: to a possible structure. For instance the data of Baker et al. 6) already show evidence for the structures at 7'= = 3.8 and 4.5 GeV. Also the structure above A~2870) in ]is. 3 was not mentioned in rd. 4. It will be interesting to see, i f it i s c o n f i r m e d w i t h the f i n a l data. Evidence for two new r( son,nee, in pl,m photoproduction has been reported by Osborne ':t al. 7). In our opinion the sim vlest interprctatlon is to assume the same situatio[~ ~s for the low energy resonances: There is a large and ~redominantly real background amplitude and the peaks are caused by its inte£ference with the real parts of the resonant multipoles, which have t h e i r m a x i m a o r m i n i m a at a b o u t t h e ~ n e e n e r gy ~ s t h e r v a l p a r t s of t h e r e s o n a n t s c ~ t e r i n g p a x t m l w a v e s . T h e n a c c o r d i n g to fig. 2 t h e s t r u c t u r e a t E~ ~ 2.9 = 0 . I GeV i s n o t a n e w r e s o n a n c e b u t a n e f f e c t of ~ ( 2 4 4 0 ) , t h e r e a l p~trt of w h i c h i s l a r g e a t t h i s e n e r g y . T h e s t r u c t u r e a t E y = F..5
Fig. 3. The qutmttty Z (eq. ,t3}) s~ a fi,ttcttr~n of e ~ r l l y . The ,~etltls above 4 C~V a r e wA reliable, bectmtm took the c-eros section, f r ~ the g r a p h s L~ t e l . 4 only. GeV b e l o n g s to N(2660). T a b l e I i s u s e f u l f o r f u r t h e r d i s c u s s l o n s. W e a r e g r a t e f u l to P r o f . O s b o r n e , D r . Sond , r egger and Dr. Wahlig for sending us preprtnts and p r i v a t e c o m m u n i c a t i o n s a n d to P r o f . S c h o p p e r f o r m a k i n g a p r e p r t n t of r e L 4 a v a i l a b l e to tin. A f t nanc/al support by the "Deutsche Forschungsgem e t n s c h ~ t ' Is g r a t e f u l l y a c k n o w l e d g e d ,
l) O. Ii~hler, G.Ebel and J.Gtes0cke, fubmltt*d t,~ Z. Phystk. z) M.A.Wahllg, ] . M a n . s i l l , L.~.dlck~cm, O Faclder. C.W:trd, T Kan ;~nd E..Cglll~ in. |'hy=. R,w. L~tt~.rs ]3 (l'Jf~l) ]03. 3) A.N Dlddom=, E.W.Jenklna, T. F . K y c l a and K. F. [¢tloy, PhyB. Rev. LetterB I0 (1963) 262. 4) A . C i t r o n , W.C,eJbralth, T . F . K y c f ~ , B.A. Leontie, R . H . P h l H i p 6 and A . R o u s s e t , P h y s . Rev. L e t t e r s 13 (1964) 205. 5) P. BorKeaud. C. B~L~,ton, Y.Ducroa. P. F a l k - V l l rant, O.Gulsan0 J. Movchm,, P . h ~ o n d o r ~ r . A . ~ . l r lin~, M . Y v e r t , A . T r a n Ill and S.D. Warshaw, lthlyM ic~ Letters l0 (I~64} 134. G) W. F. Iktkor, E . W . J e n k l n s . T . F . Kycta, R.H.Pht]Hpe, A . L . R o s d , K. F. Rlley and H . R u d e r m a n n , P r o c . ~ e n na Int. Conf. o~ e l e m e n t a r y pxrticleso Vol. I, p. 634. 7) R.Alva.rez, Z . B a r - Y a m , W . K e r n , D. Luckoy, L.S. Osoorne, 3 . T a z z a r l and R. Fes~el, P h y s . Rev. l,cttors 12 (1964) 7{(}.
150