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A possible higher symmetry scheme for strongly interacting particles
Volume 9, number 2
PHYSICS
coni f o r s t i m u l a t i n g d i s c u s s i o n s . We thank e s p e c i a l l y D r . G. Z w e i g f o r d i s c u s s i n g h i s t h e o r y with u s in d e t a i l b e f o r e publication. We a r e g r a t e ful f o r the s u p p o r t and g u i d a n c e of P r o f e s s o r s A. L a g a r r i g u e , Ch. P e y r o u and R. A r m e n t e r o s . We thank the m a n y p e o p l e whose o p e r a t i o n of the c h a m b e r , b e a m and PS m a d e the e x p o s u r e p o s s i b l e , and o u r s c a n n e r s for t h e i r c a r e f u l work.
LETTERS
1 April 1964
1) M . G e l l - ] ~ a ~ Physics Letters 8 (1964) 214. 2) G. Zwetg, CERN r e p o r t 8182/TH 401, 1964 and to be published in Phys. Rev. ; and private communication. 3) D.R.O.Morrison, Physics Letters 9 (1964) 199. 4) CERN Neutrino Group, private communication. 5) M. Bloch et a l . , Rev. Sci. Instr. 32 (1961) 1302. 6) J. J. Vefllet, CERN report TC/COM 63-22 (1963). 7) See e . g . , H.Bradner, ARNS 10 (1960) 109; D.V .Bugg, Prog.Nucl.Phys.7 (1959) 1. 8) B.Rosst, High energy particles. 9) W. F. Baker et a l . , Phys.Rev. Letters 7 (1961) 1Ol and CERN PS Users Handbook.
A POSSIBLE HIGHER SYMMETRY SCHEME FOR STRONGLY INTERACTING PARTICLES
H. J. L I P K I N • D e p a r t m e n t o f P h y s i c s , The W e i z m a n n I n s t i t u t e o f S c i e n c e , R e h o v o t h , I s r a e l
Received 25 February 1964
It w a s noted s o m e t i m e ago 1) that the SU 3 c l a s s i f i c a t i o n of the b a r y o n , v e c t o r and p s e u d o s c a l a r m e s o n and a n t i b a r y o n o c t e t s p o s s e s s e d a p e c u l i a r s y m m e t r y . It r e m a i n s i n v a r i a n t u n d e r the s i m u l t a n e o u s i n t e r c h a n g e of i s o s p i n with o r d i n a r y s p i n and h y p e r c h a r g e with b a r y o n n u m b e r , a s i l l u s t r a t e d in t a b l e 1. The n o r m a l c l a s s i f i c a tion p l a c e s p a r t i c l e s having the s a m e o r d i n a r y s p i n S and b a r y o n n u m b e r B into m u l t i p l e t s and c h a r a c t e r i z e s the s t a t e s within the m u l t i p l e t by the v a l u e s of the i s o s p i n T and the h y p e r c h a r g e Y. An a l t e r n a t i v e c l a s s i f i c a t i o n , the ' ~ a r b a r y o n " c l a s s i f i c a t i o n i n t e r c h a n g e s the r o l e s of t h e s e quantum n u m b e r s , p l a c i n g p a r t i c l e s having the s a m e i s o s p i n and h y p e r c h a r g e into m u l t t p l e t s whose s t a t e s a r e c h a r a c t e r i z e d by the v a l u e s of the o r d i n a r y s p i n and b a r y o n n u m b e r . The two c l a s s i f i c a t i o n s a r e i l l u s t r a t e d by the s q u a r e a r r a y of t a b l e 1. T h e p a r t i c l e s in the s a m e v e r t i c a l c o l u m n a r e m e m b e r s of the s a m e o c t e t in the o r d i n a r y c l a s s i f i c a t i o n , while t h o s e in the s a m e h o r i z o n t a l r o w a r e m e m b e r s of the s a m e o c t e t in the b a r b a r y o n c l a s s i f i c a t i o n . One m i g h t c o n s i d e r combining the f o u r o c t e t s into a " h y p e r s u p e r m u l t i p l e t " c o r r e s p o n d i n g to the g r o u p SU 3 × SU3, the d i r e c t p r o d u c t of two SU 3 g r o u p s . T h i s m i g h t be c o n s i d e r e d a s a g e n e r a l i s a t i o n of the W i g n e r s u p e r m u l t i p l e t s , which c o m b i n e d o r d i n a r y s p i n and i s o s p i n into SU 2 × SU2, by the a d d i t i o n s of B and Y r e s p e c t i v e l y to e a c h
Table 1
s=½
s=o
S=l
s=½
B =+1
B=O
B=0
B=-I
T=½; Y = + I T=0; Y= O T = I ; Y=0
N
K
K*
A
I]
~g(~)
E
u
p
T = ½; Y = - I
=_.
~
~*
~.
SU2 g r o u p to m a k e SU 3. The c o m b i n i n g of o r d i n a r y s p i n and i s o s p i n into the s a m e a l g e b r a h a s b e e n a l s o s u g g e s t e d by the s t r o n g coupling i s o b a r m o d e l . H o w e v e r , the i d e a of putting b o s o n s and f e r m i o n s into the s a m e m u l t i p l e t s e e m e d r a t h e r f a n t a s t i c and h a r d l y w o r t h y of s e r i o u s publication. Since p o s s i b i l i t i e s a r e now being c o n s i d e r e d 2) which s e e m j u s t a s f a n t a s t i c a s the b a r b a r y o n c l a s s i f i c a t i o n , p e r h a p s the l a t t e r is not s o c r a z y a f t e r a l l and d e s e r v e s m o r e s e r i o u s c o n s i d e r a tion. One n o t e s , in p a r t i c u l a r , that the " q u a r k " o r e l e m e n t a r y t r i p l e t f o r SU3 f i t s v e r y n a t u r a l l y into the b a r b a r y o n c l a s s i f i c a t i o n . By including a s p i n z e r o b e s o n t r i p l e t , one o b t a i n s the " h y p e r s u p e r m u l t i p l e t " of t a b l e 2, the d i r e c t p r o d u c t of two t r i p l e t s in the o r d i n a r y SU 3 and b a r b a r y o n SU 3 s p a c e s . The b o s o n t r i p l e t a l s o h a s t h i r d int e g r a l v a l u e s for the b a r y o n n u m b e r and h y p e r charge. 203
Volume 9, number 2
PHYSICS LETTERS
1 April 1964
Table 2
Table 3
S=½ T = ½; Y = ] T = 0; Y = -~
S=0
Quark Quark
Boson Boson
s:~
S:l
s=½
s=0
B=+I
B=0
B=-I
B =-2
T = ~; Y = 1
N*
?
?
?
T=I; Y=0
Y* ~* f~*
? ? ?
? ? ?
? ? ?
T = ½; Y = -1 T=0; Y=-2
The m o s t obvious p r e d i c t i o n of this c l a s s i f i cation, ~f it is taken s e r i o u s l y , i s that h y p e r s u p e r m u l t i p l e t s should be c o n s t r u c t e d a r o u n d all new r e s o n a n c e s . The r e q u i r e m e n t that the b a r y o n decuplet (N*, Y*, E*, $2-) belongs to such a h y p e r s u p e r m u l t i p l e t p r e d i c t s the e x i s t e n c e of additional b o s o n and f e r m i o n decuplet r e s o n a n c e s . The b a r yon d e c u p l e t , having S = ~ and B = 1 can be fitted only into decuplet or a 2 7 - d i m e n s i o n a l m u l t i p l e t in the b a r b a r y o n c l a s s i f i c a t i o n . The decuplet c l a s s i f i c a t i o n then p r e d i c t s the e x i s t e n c e of a boson decuplet with S = 1, an a n t i b a r y o n decuplet t with S = ~, and a decuplet with B = - 2 L S = 0. Since t h e r e e x i s t s the c o r r e s p o n d i n g 10 r e p r e s e n t a t i o n with the a n t i p a r t i c l e s of all t h e s e m u l t i plets, these p r e d i c t i o n s can be s u m m a r i z e d as r e q u i r i n g two v e c t o r boson decuplets. 10 and iO, a s p i n ½ b a r y o n decuplet and a decuplet of b a r y o n baryon resonances with spin zero (this cannot include the deuteron, since the latter has spin one). If the baryon decuplet is placed in a 27-dimensional barbaryon multiplet, the states of B = ± 2 have spin one, and can therefore include the deuteron. However, a large n u m b e r of other states are predicted, including baryon decuplets with S = ~ and I belonging to both 10 and i-O decuplets in the or-
Table 4
T = 0; y = 0
s:½
s:o
s:l
s=½
B = +1
B = 0
B= 0
B = -1
Yo*
?
¢Vl(~)
YO*
d i n a r y c l a s s i f i c a t i o n and m e s o n decuplets of spin 0.1 and 2. Since the decuplet does not conrain a T = 0, Y= 0 state, the u n i t a r y s i n g l e t vector m e s o n which m i x e s with the octet to f o r m the co-q~ m e s o n s cannot be included. A (singiet × octet) is the m i n i m u m s i z e h y p e r s u p e r m u l t i p l e t to accomodate this m e s o n . T h i s would include a u n i t a r y s i n g l e t b a r y o n of spin ½ (the Yo* at 1405 MeV?) and a u n i t a r y s i n g l e t spin z e r o m e s o n . T a b l e s 3 and 4 show s o m e of these p o s s i b i l i t i e s .
Refe~'ences 1) H . J . Lipkin, "The Barbaryon Classification for E l e m e n t a r y P a r t i c l e s SU3" , J o c u l a r P h y s i c s for P e d e s t r i a n s , unpublished (1962). 2) M. C e l l - M a n n , P h y s i c s L e t t e r s 8 (1964) 214.
* * * * *
A STUDY
OF
THE
K-P~+Tr
- STATE
S. P. A L M E I D A
PRODUCED * and G. R. L Y N C H
BY
K--P
AT
1.5
GeV/c
**
CERN, Geneva Received 27 February 1964
We have studied the r e a c t i o n K - P ~ K - I ~ + ~ in an a t t e m p t to s e a r c h for the r e p o r t e d 2, 3, 7) kappa m~'3on, K*(730) MeV r e s o n a n c e . The a v a i l able c e n t r e of m a s s e n e r g y of 2 GeV is j u s t at t h r e s h o l d for p r o d u c t i o n of the K*(880) and one 1 would expect little or no c o m p e t i t i o n f r o m the p r o duction of this r e s o n a n c e . We do not o b s e r v e any K*(880) e v e n t s in our data. The kappa m e s o n is 204
not o b s e r v e d to be produced to any s t r o n g extent. Some upper l i m i t s for kappa m e s o n production c r o s s s e c t i o n s a r e given. The Yo*(1520) K - P * On leave of absence from Cambridge University, Cavendish Laboratory, Cambridge, England. ** On leave of absence from the University of California, Lawrence Radiation Laboratory, Berkeley.
PHYSICS
coni f o r s t i m u l a t i n g d i s c u s s i o n s . We thank e s p e c i a l l y D r . G. Z w e i g f o r d i s c u s s i n g h i s t h e o r y with u s in d e t a i l b e f o r e publication. We a r e g r a t e ful f o r the s u p p o r t and g u i d a n c e of P r o f e s s o r s A. L a g a r r i g u e , Ch. P e y r o u and R. A r m e n t e r o s . We thank the m a n y p e o p l e whose o p e r a t i o n of the c h a m b e r , b e a m and PS m a d e the e x p o s u r e p o s s i b l e , and o u r s c a n n e r s for t h e i r c a r e f u l work.
LETTERS
1 April 1964
1) M . G e l l - ] ~ a ~ Physics Letters 8 (1964) 214. 2) G. Zwetg, CERN r e p o r t 8182/TH 401, 1964 and to be published in Phys. Rev. ; and private communication. 3) D.R.O.Morrison, Physics Letters 9 (1964) 199. 4) CERN Neutrino Group, private communication. 5) M. Bloch et a l . , Rev. Sci. Instr. 32 (1961) 1302. 6) J. J. Vefllet, CERN report TC/COM 63-22 (1963). 7) See e . g . , H.Bradner, ARNS 10 (1960) 109; D.V .Bugg, Prog.Nucl.Phys.7 (1959) 1. 8) B.Rosst, High energy particles. 9) W. F. Baker et a l . , Phys.Rev. Letters 7 (1961) 1Ol and CERN PS Users Handbook.
A POSSIBLE HIGHER SYMMETRY SCHEME FOR STRONGLY INTERACTING PARTICLES
H. J. L I P K I N • D e p a r t m e n t o f P h y s i c s , The W e i z m a n n I n s t i t u t e o f S c i e n c e , R e h o v o t h , I s r a e l
Received 25 February 1964
It w a s noted s o m e t i m e ago 1) that the SU 3 c l a s s i f i c a t i o n of the b a r y o n , v e c t o r and p s e u d o s c a l a r m e s o n and a n t i b a r y o n o c t e t s p o s s e s s e d a p e c u l i a r s y m m e t r y . It r e m a i n s i n v a r i a n t u n d e r the s i m u l t a n e o u s i n t e r c h a n g e of i s o s p i n with o r d i n a r y s p i n and h y p e r c h a r g e with b a r y o n n u m b e r , a s i l l u s t r a t e d in t a b l e 1. The n o r m a l c l a s s i f i c a tion p l a c e s p a r t i c l e s having the s a m e o r d i n a r y s p i n S and b a r y o n n u m b e r B into m u l t i p l e t s and c h a r a c t e r i z e s the s t a t e s within the m u l t i p l e t by the v a l u e s of the i s o s p i n T and the h y p e r c h a r g e Y. An a l t e r n a t i v e c l a s s i f i c a t i o n , the ' ~ a r b a r y o n " c l a s s i f i c a t i o n i n t e r c h a n g e s the r o l e s of t h e s e quantum n u m b e r s , p l a c i n g p a r t i c l e s having the s a m e i s o s p i n and h y p e r c h a r g e into m u l t t p l e t s whose s t a t e s a r e c h a r a c t e r i z e d by the v a l u e s of the o r d i n a r y s p i n and b a r y o n n u m b e r . The two c l a s s i f i c a t i o n s a r e i l l u s t r a t e d by the s q u a r e a r r a y of t a b l e 1. T h e p a r t i c l e s in the s a m e v e r t i c a l c o l u m n a r e m e m b e r s of the s a m e o c t e t in the o r d i n a r y c l a s s i f i c a t i o n , while t h o s e in the s a m e h o r i z o n t a l r o w a r e m e m b e r s of the s a m e o c t e t in the b a r b a r y o n c l a s s i f i c a t i o n . One m i g h t c o n s i d e r combining the f o u r o c t e t s into a " h y p e r s u p e r m u l t i p l e t " c o r r e s p o n d i n g to the g r o u p SU 3 × SU3, the d i r e c t p r o d u c t of two SU 3 g r o u p s . T h i s m i g h t be c o n s i d e r e d a s a g e n e r a l i s a t i o n of the W i g n e r s u p e r m u l t i p l e t s , which c o m b i n e d o r d i n a r y s p i n and i s o s p i n into SU 2 × SU2, by the a d d i t i o n s of B and Y r e s p e c t i v e l y to e a c h
Table 1
s=½
s=o
S=l
s=½
B =+1
B=O
B=0
B=-I
T=½; Y = + I T=0; Y= O T = I ; Y=0
N
K
K*
A
I]
~g(~)
E
u
p
T = ½; Y = - I
=_.
~
~*
~.
SU2 g r o u p to m a k e SU 3. The c o m b i n i n g of o r d i n a r y s p i n and i s o s p i n into the s a m e a l g e b r a h a s b e e n a l s o s u g g e s t e d by the s t r o n g coupling i s o b a r m o d e l . H o w e v e r , the i d e a of putting b o s o n s and f e r m i o n s into the s a m e m u l t i p l e t s e e m e d r a t h e r f a n t a s t i c and h a r d l y w o r t h y of s e r i o u s publication. Since p o s s i b i l i t i e s a r e now being c o n s i d e r e d 2) which s e e m j u s t a s f a n t a s t i c a s the b a r b a r y o n c l a s s i f i c a t i o n , p e r h a p s the l a t t e r is not s o c r a z y a f t e r a l l and d e s e r v e s m o r e s e r i o u s c o n s i d e r a tion. One n o t e s , in p a r t i c u l a r , that the " q u a r k " o r e l e m e n t a r y t r i p l e t f o r SU3 f i t s v e r y n a t u r a l l y into the b a r b a r y o n c l a s s i f i c a t i o n . By including a s p i n z e r o b e s o n t r i p l e t , one o b t a i n s the " h y p e r s u p e r m u l t i p l e t " of t a b l e 2, the d i r e c t p r o d u c t of two t r i p l e t s in the o r d i n a r y SU 3 and b a r b a r y o n SU 3 s p a c e s . The b o s o n t r i p l e t a l s o h a s t h i r d int e g r a l v a l u e s for the b a r y o n n u m b e r and h y p e r charge. 203
Volume 9, number 2
PHYSICS LETTERS
1 April 1964
Table 2
Table 3
S=½ T = ½; Y = ] T = 0; Y = -~
S=0
Quark Quark
Boson Boson
s:~
S:l
s=½
s=0
B=+I
B=0
B=-I
B =-2
T = ~; Y = 1
N*
?
?
?
T=I; Y=0
Y* ~* f~*
? ? ?
? ? ?
? ? ?
T = ½; Y = -1 T=0; Y=-2
The m o s t obvious p r e d i c t i o n of this c l a s s i f i cation, ~f it is taken s e r i o u s l y , i s that h y p e r s u p e r m u l t i p l e t s should be c o n s t r u c t e d a r o u n d all new r e s o n a n c e s . The r e q u i r e m e n t that the b a r y o n decuplet (N*, Y*, E*, $2-) belongs to such a h y p e r s u p e r m u l t i p l e t p r e d i c t s the e x i s t e n c e of additional b o s o n and f e r m i o n decuplet r e s o n a n c e s . The b a r yon d e c u p l e t , having S = ~ and B = 1 can be fitted only into decuplet or a 2 7 - d i m e n s i o n a l m u l t i p l e t in the b a r b a r y o n c l a s s i f i c a t i o n . The decuplet c l a s s i f i c a t i o n then p r e d i c t s the e x i s t e n c e of a boson decuplet with S = 1, an a n t i b a r y o n decuplet t with S = ~, and a decuplet with B = - 2 L S = 0. Since t h e r e e x i s t s the c o r r e s p o n d i n g 10 r e p r e s e n t a t i o n with the a n t i p a r t i c l e s of all t h e s e m u l t i plets, these p r e d i c t i o n s can be s u m m a r i z e d as r e q u i r i n g two v e c t o r boson decuplets. 10 and iO, a s p i n ½ b a r y o n decuplet and a decuplet of b a r y o n baryon resonances with spin zero (this cannot include the deuteron, since the latter has spin one). If the baryon decuplet is placed in a 27-dimensional barbaryon multiplet, the states of B = ± 2 have spin one, and can therefore include the deuteron. However, a large n u m b e r of other states are predicted, including baryon decuplets with S = ~ and I belonging to both 10 and i-O decuplets in the or-
Table 4
T = 0; y = 0
s:½
s:o
s:l
s=½
B = +1
B = 0
B= 0
B = -1
Yo*
?
¢Vl(~)
YO*
d i n a r y c l a s s i f i c a t i o n and m e s o n decuplets of spin 0.1 and 2. Since the decuplet does not conrain a T = 0, Y= 0 state, the u n i t a r y s i n g l e t vector m e s o n which m i x e s with the octet to f o r m the co-q~ m e s o n s cannot be included. A (singiet × octet) is the m i n i m u m s i z e h y p e r s u p e r m u l t i p l e t to accomodate this m e s o n . T h i s would include a u n i t a r y s i n g l e t b a r y o n of spin ½ (the Yo* at 1405 MeV?) and a u n i t a r y s i n g l e t spin z e r o m e s o n . T a b l e s 3 and 4 show s o m e of these p o s s i b i l i t i e s .
Refe~'ences 1) H . J . Lipkin, "The Barbaryon Classification for E l e m e n t a r y P a r t i c l e s SU3" , J o c u l a r P h y s i c s for P e d e s t r i a n s , unpublished (1962). 2) M. C e l l - M a n n , P h y s i c s L e t t e r s 8 (1964) 214.
* * * * *
A STUDY
OF
THE
K-P~+Tr
- STATE
S. P. A L M E I D A
PRODUCED * and G. R. L Y N C H
BY
K--P
AT
1.5
GeV/c
**
CERN, Geneva Received 27 February 1964
We have studied the r e a c t i o n K - P ~ K - I ~ + ~ in an a t t e m p t to s e a r c h for the r e p o r t e d 2, 3, 7) kappa m~'3on, K*(730) MeV r e s o n a n c e . The a v a i l able c e n t r e of m a s s e n e r g y of 2 GeV is j u s t at t h r e s h o l d for p r o d u c t i o n of the K*(880) and one 1 would expect little or no c o m p e t i t i o n f r o m the p r o duction of this r e s o n a n c e . We do not o b s e r v e any K*(880) e v e n t s in our data. The kappa m e s o n is 204
not o b s e r v e d to be produced to any s t r o n g extent. Some upper l i m i t s for kappa m e s o n production c r o s s s e c t i o n s a r e given. The Yo*(1520) K - P * On leave of absence from Cambridge University, Cavendish Laboratory, Cambridge, England. ** On leave of absence from the University of California, Lawrence Radiation Laboratory, Berkeley.