LETTERE AL NUOVO CIMENTO
VOL. 36, N. 6
12 Febbraio 1983
The Spin Kinetic Energy and Intrinsic Mass o f Elementary Particles. III.
- Hyperons and Nucleon Resonances as High-Spin Nucleons.
L. S. LEVITT
The Institute ]or Theoretical Studies - Box 12292 - E1 1)aso, Texas 79912 (ricevuto il 23 Giugno 1982)
We have recently shown (~) t h a t the rest mass of elementary particles of spin 1/2 can be conceived of as being composed of two additive terms: the intrinsic mass, mi, and the mass equivalent of the spin kinetic energy, m 8 (the spin mass). Thus 3~2
(1)
m~ = mi + ~ . = mi + Smic3~~ ,
where r o is the particle radius, which is equal to its Compton wave-length (3): (2)
r o = h/m i e .
For particles of spin 1/2 having a rest mass, eqs. (1) and (2) lead (1) to
(3)
qn0 = m i 1 + ~
.
For particles of any spin value, S, eq. (3) can be generalized, giving
(4)
mo= m~[1 + S(S8zr3+ 1)].
We may now be in a position to account for the observed masses of the hyperons (3,4) and nucleon ((resonances )) (3,~), which might represent higher.spin states of the nucleons to which they all decay, after average lifetimes of 10-~0 to 10-3~ s. A higher-spin state (1) (~)
•. S. LEVITT: Left. Nuovo Oimento, 34, 333 (1982); 36, 167 (1983). L. S. LEVITT: Bull. A m . P h y s . Soc., II-2, 211 (1956); Experientia, 14, 223 (1958); Lett. Nuovo Cimeuto, 12, 537 (1975). (3) H. FRAUENFELI)ER and E. ~r HENLEY: Subatomic Physics (Englewood Cliffs, N.J., 1974). (4) E. SECURe: NucZei and Particles (Reading', Mass., 1977).
171
172
~. 8. LEVITT
of 3/2 for a n e u t r o n has p r e v i o u s l y been p o s t u l a t e d (5) for t h e A(1236) p a r t i c l e or F e r m i :resoYlanee.
W e d e m o n s t r a t e n o w t h a t eq. (4) can, w i t h a n e w (and r a t h e r esoteric) a s s u m p t i o n , be m a d e to a c c o u n t for t h e masses of a l m o s t all k n o w n (and u n k n o w n ) h y p e r o n s and resonances. W e begin first b y using eq. (4) w i t h no a d d i t i o n a l postulates, e x c e p t h i g h e r h a l f - i n t e g e r v a l u e s of S for h y p e r o n s . As p r e v i o u s l y calculated (1) for t h e n e u t r o n , m i = 930.5 MeV, w h i c h ~with S ~ 1/2 gives, of course, m o = 939.6 MeV. W i t h S = 5/2, one obtains m 0 = 1034.1, t h e M-particle. W i t h S = 7/2 we find m 0 = 1116.0, t h e A~ a n d w i t h S = 9/2, m o = 1223, w h i c h is close to A(1236). I t is t r u e t h a t t h e s e r e p r e s e n t r a t h e r - h i g h - s p i n states, b u t t h e y should, p e r h a p s , n o t be r u l e d o u t on t h a t basis alone. F o r t h e c h a r g e d h y p e r o n s , m i should be t a k e n as t h a t for p r o t o n s or a n t i p r o t o n s for w h i c h (1) m~ = 929.5. T h i s gives rise to m o = 1221 )/[eV (E-(1197)) for S = 9/2; mo = 1350 M e v
(s-(1321))
for s = 11/2, ~ n d m0 = 1 6 8 0 M e V
(n-(1673))
~or S = 15/2.
I t is seen, h o w e v e r , t h a t t h i s a p p r o a c h c a n n o t account for t h e 5 MeV difference in m a s s o b s e r v e d for t h e E - / E ~ and E - / E ~ pairs. I n an a t t e m p t to calculate t h e masses of t h e nucleon resonances, we m u s t i n t r o d u c e a n e w c o n c e p t - - t h a t of hypcrspin. This can be e x p l a i n e d as follows: w h e n t h e i n t r i n s i c mass, mi, of a p a r t i c l e is spinning, it gains t h e a d d i t i o n a l mass, m,, a d d i n g up to its rest mass, mo. Is now we impose u p o n this p a r t i c l e of t o t a l m a s s m o a h i g h e r spin, n o t j u s t to m~, b u t to m o as a whole, we h a v e w h a t can be r e g a r d e d as hyperspin. L e t us see if t h i s c o n c e p t is capable of a c c o u n t i n g for t h e nucleon resonances. T h e n e u t r o n , w i t h S = 1/2 and m s = 939.6, will be w r i t t e n as J~'1/2. S u p e r i m p o s i n g a spin of 3/2, we h a v e (J~'1/2)3/~w h i c h gives m 0 = 1922 MeV f r o m eq. (4) ; and t h i s is obv i o u s l y q0(1022). A b e t t e r r e p r e s e n t a t i o n of A(1236) is t h e n (J~l/~)s/~-* mo ---- 1234. Similarly, (j~l/2)ls/2--~m, = 1520 w h i c h is t h e well-known resonance j~(1520) ; and (J~1/2)15/~-* - , m o = 1699, t h e j~(1700) resonance. T h e A~ r e s o n a n c e can be c a l c u l a t e d as o (A~/~)v~ ~ ~ (j~7~)7~:-->mo = 1338. U s i n g ~ as t h e h y p e r s p i n q u a n t u m n u m b e r , eq. (4) should be a m e n d e d for t h e
Ta~L~ I. - Experimental and calculated masses (eq. (4)) ]or the hyperons. Hyperon
Spin (S)
Designation
Mass (MeV) (2,3) (experimental)
~r (MeV) (calculated)
(n o)
(1/2)
(~1/2)
(939.6)
(939.6)
?(*)
3/2
0~~
--
)/[
5/2
..N"5/2
1034
Ao
7/2
"J~7/~
1116.0
1116.0
E-
9/2
.N'9/~
1197
1221
.~.-
11/2
.N'n/~
1321
1350
?
13/2
J~la/~
--
1506
s
15/2
J~'15/2
1673
1680
(*)
8(970) fits t h i s m a s s , b u t , is a m e s o n .
(~)
Ko A . BRUECKNER; P h y s . Rev., 86, ! 0 6 (1952).
975 1034
THE
SPIN
KINETIC
ENERGY
AND
INTRINSIC
NASS
ETC.
173
- III
mIcleon resonances N'*, in the following way:
I n this manner, one can also calculate v e r y closely the masses of m a n y ocher transient hyperons and resonances. W e leave this pleasant Cask Co the reader. Table I presents a s u m m a r y of the hyperons discussed here, along with their S values and their experimental and calculated masses. Table I I gives the d a t a for the nucleon resonances, along with the spin and hyperspin numbers. TABLE I I . - - E x p e r i m e n t a l a n d calculated m a s s e s (eq. (5)) for some c o m m o n n u c l e o n Tesonanees
Resonance
Spin (S)
?(*)
1/2
A
Hyperspin (a)
Designation
~ a s s (?r (8,4) (experimental)
~ a s s (MoV) (calculated)
3/2
(,N'1/~)3/~
--
1022
1/2
9/2
(J~ffl/2)9/2
1234
1234
A*
1/2
7/2
(A1/~)~/~ = (~7/2)~1~
1330
1338
J~ff*
1/2
9/2
(Al1~)9/2 = (~/~)9/2
1470
1467
~*
1/2
13/2
(~1/2)1~/2
1520
1520
0~'*
1/2
15/2
(0V1/~)15/2
1700
1699
(*) ~(1022) iits this mass exactly, but,
is a
meson.
The principal problem with this whole approach is, of course: how can the known decay modes be reconciled with the conservation of spin angular momentum?
