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Physical properties of quarks
Volume 15, rmmber 4
PHYSICS LE TTE RS
PHYSICAL
PROPERTIES
15 April 1965
OF QUARKS *
P. G. O. FREUND**
lnstitute for Advanced Study, Princeton~ New Jersey Receive~ 8 March1965
Quarks[l] or a c e s [2] have been proposed as L~itding blocks of all hadrons. It has been v a r i ously suggested that, i) quarks are only mathematical objects that need not reveal t h e m s e l v e s as particles [3]; it) quarks are very heavy p a r tlcles (mQ ~ 10 GeV) [4]. In this note we shall assume thht quarks can exist as p a r t i c l e s and ca!l attention to some p r o p e r t i e s of these p a r t i t l e s ~. We s t a r t by estimating the strength of the coupling of quarks to the 35 odd parity mesons V;~61 P = 1") and Pi(J P = 0"). Assuming the meson-quark vertex F to be dictated by the r e quirement of M(12) invariance [6] we find +t 1 r = g(o%,JQ+++')(+].+%j + ~ N . v s q . P i +
+ )'5Pi + a~uq~,+V~i] ~iUQ(P) + h e r e u is the central meson m a s s and q+~ the four-moment?+m transfer+ Assuming the matrix elemeats of the divergence of the axial vector c u r r e n t of weak interactions to be dominated the pseudoscalar meson pole, and using M(12), o+~e can w r l ~ the G o l d b e r g e r - T r e i m a n relations
2ran ~ ~ g~Nf~ and
2 mQ ~ gltQfrt w h e r e g~Q, g~N a r e the effective p s - p s ~Q and ~N couplirig constants and f~ is the pion decay amplitude. Hence s mQ g+tQ ~ ~+~ gTtN
(I)
and for large quark m a s s g+ro >> g~N" F r o m (1) and M(12) invariance we find-for t f i e D i r a c - t y p e coupling of~ say, the p - m e s o n
gpQ = gpN •
(2)
Similar r e l a t i o n s then ensue for all other vector m e s o n s . The universality of Dirac-type vector m e s o n couplings is thus retained in spite of the fact that vector m e , o n couplings are not "minimal" in a gauge-~:he+?~e~mal sense. Assuming .:~'~ quark magnetic moment to be determined ~ e lowest lying vector meson pole (of m a s s . we find gQan = e ' / u
* The study was ~upimrted by the Air Force Office o f .~%|entlfic Research, Grant No.AF-AFOSR-42-64. ** ~ leave of absence from the Enrico Fermi Institute f<~ Nuclear ~ d i e s and the Departmeat of Physics of the Ueiverml~yof Chicago, Chicago, Illinois. * We do mot ~ommlt o~r~elvee to any particular values of ~+e quark m_rossmQ or charge (fractional or integrat~ and o~r res~;lt~ (¢qs. (1) and (2)) are valid for a~y type of quarks. At ~ i s point it may be useful to r ~ a l l that with a single type of fractionally charged qua2~, the exiotence of a 56-plet of baryons is not easily reconciled with the requLr~mente of Fermi statietI~ (5]. One can, however, consider theories with three gpectea of quarks (which now could be integrally charged) in which case the symmetry of the t l ~ r y can be further increased to M(12) ~ M(12) ~ M(12). After the completion of th~B ~ , we received a preprtut by Y.Nambv where similar po~lblllty is considered. ** We d~ar~Cal'dhere the lack of propagation of the intrinsically broken M(12) rule~ ltlrough the condition of elastic unltarity.
352
w h e r e e' is the e l e c t r i c charge of the quark Q. Similar considerations give for the proton (e = proton charge)
;*Pan = e/~ . Thus
e ~
gQan =~e- +UPan "
(3)
Thus, for a quark of charge ½, the anomalous magnet'Jr moment c o m e s out to be ~ × 1.79 x × (e/2mp) ~ 0.6 (e/2mp) w h e r e a s for an integrally charged quark (e' = e), #Oan = # P a n = 1.79 e / 2 m p t t ~ Should quarks I~+ o b s e r v e d as p a r t i c l e s , a verification of the relations (1), (2) and (3) will provide an unambigous t e s t for in"iN" Note that in either ease thte is a very large anomalous magnetic moment if mQ >~3 GeV.
Volume 15, number4
PHYSICS
LETTERS
trinsically broken M(12) invariance [6] of strong interactions.
4. F. Gffrsey, M. Nauenberg and T.D. l,ee, Phyvl. Rev.
135 (1964) B467. 5, P . G . O . F r e u n d and B.W.Lee, Phys. I~ev. t,etter~ 13 (1964) 592; O.W.Greenberg, ibid 13 (1964) 59~. 6. K. Bardakei, J.M. Cornwall, P. G, O. Freur~d ~a¢l B. W. Lee, Phys. Rev. Le~ers 14 (1965) 48. See also subsequent work on the intrinsic symmetry-breaking mechanism by R. Delboargo, A. Salam, J. Stxadhee, Proc.Rov.Soe. (to be published), and B. Sakita and K. C. Wall, Phys. Ray. Lvt'~er ~ (~o be published). See also M.B~g and A. Pais, Phys. Ray. Letters 14 (1965} 267.
T h e a u t h o r w o u l d like to t h a n k P r o f e s s o r R. O p p e n h e i m e r f o r h i s h o s p i t a l i t y at t h e I n s t i t u t e f o r A d v a n c e d Study. Refe~'enees 1. M.Gell-Mann, Physics Letters 8 (1964) 214. 2. G.Zweig, CERN report (1964). 3. M.Gell-Man~, Physics 1 (1964} 63.
PARITY
DETERMINATION
P. L. C 8 O N K A ,
15 April 1!#~5
IN
PARTICLE
M. J. M O R A V C S I K
PHYSICS
*
and M. D. S C A D R O N
Lawrence Radiation Laboratory, University of California, Liver~nore, California Received I March 1965
T h e p u r p o s e of t h i s note i s to e s t a b l i s h s o m e v e r y g e n e r a l t h e o r e m s a b o u t t h e type of e x p e r i m e n t s w h i c h c a n be u s e d f o r t h e d e t e r m i n a t i o n of t h e p a r i t y of one of t h e p a r t i c l e s in a r e a c t i o n (henceforth callea briefly parity experiments), It s h o u l d be s t a t e d at the o u t s e t t h a t p a r i t y e × p e r i m e n t s a r e of t h r e e k i n d s : 1. T h o s e b a s e d only on r o t a t i o n a n d r e f l e c t i o n invarianae. 2. T h o s e i n v o l v i n g a l s o s o m e a s s u m p t i o n s about the angular momentum states which cont r i b u t e s i g n i f i c a n t l y to t h e p r o c e s s , but w h i c h do n o t involve a s s u m p t i o n s a b o u t t h e d y n a m i c s of t h e r e a c t i o n (e.g. t h e v a r i o u s t h r e s h o l d theorems). 3. T h o s e built on a n e x p l i c i t d y n a m i c a l m o d e l of t h e i n t e r a c t i o n (e.g, d i s p e r s i o n r e l a t i o n s ) . T h e r e s u l t s of t h i s note a r e r e l e v a n t only to the e x p e r i m e n t s of t h e f i r s t kind, w h i c h a r e , h o w e v e r , the most attractive since they are the most general and hence, theoretically, the most conclusive. Let us consider the particle reaction A 1 + A2 -- B1 + B2
it is i m p o s s i b l e to d e t e r m i n e the p a r i t y of B 2 (or
A2). Proof, L e t u s denote t h e m a t r i x e l e m e n t o~ eq. (1) by Me1 d e p e n d i n g on w h e t h e r the i32 (or A2) p a r i t y is p o s i t i v e o r n e g a t i v e . Let u~3 fur'thermore denote the matrix element of the re~ctlon O+ +A 2 - , B 1 + B2
(2)
by M~2 depending again on whether the B2 (or A2) parity is positive or nagative. Here O ~ denoteu a pariticle with zero spin and positive internal parity. Furthermore, we denote the matrix element of the reaction O+ +A I - , O + +O :~
(3)
by M ~ depending on whether the second particle on the right-hand side has positive or neg;itlve parity. Then we can write ** MI and
(I)
and the spins of the particles are arbitrary. Let us assume that the parity of all particles in eq. (I) is known e x c e p t t h a t of B 2 (but t h i s p a r t i c l e could j u s t a s well be A2) Theorem 1. In an e x p e r i m e n t in w h i c h A 1 is a b o s o n and no s p i n i n f o r m a t i o n is o b t a i n e d a b o u t A1,
* Work done under the auspices of the U.g.Atomie Energy Comissien. ** The details of the formalism which decomposes general M matrix into the outer product~ of simpler particle reaction matrices ,Nil be discussed in a forthcoming paper (11.
353
PHYSICS LE TTE RS
PHYSICAL
PROPERTIES
15 April 1965
OF QUARKS *
P. G. O. FREUND**
lnstitute for Advanced Study, Princeton~ New Jersey Receive~ 8 March1965
Quarks[l] or a c e s [2] have been proposed as L~itding blocks of all hadrons. It has been v a r i ously suggested that, i) quarks are only mathematical objects that need not reveal t h e m s e l v e s as particles [3]; it) quarks are very heavy p a r tlcles (mQ ~ 10 GeV) [4]. In this note we shall assume thht quarks can exist as p a r t i c l e s and ca!l attention to some p r o p e r t i e s of these p a r t i t l e s ~. We s t a r t by estimating the strength of the coupling of quarks to the 35 odd parity mesons V;~61 P = 1") and Pi(J P = 0"). Assuming the meson-quark vertex F to be dictated by the r e quirement of M(12) invariance [6] we find +t 1 r = g(o%,JQ+++')(+].+%j + ~ N . v s q . P i +
+ )'5Pi + a~uq~,+V~i] ~iUQ(P) + h e r e u is the central meson m a s s and q+~ the four-moment?+m transfer+ Assuming the matrix elemeats of the divergence of the axial vector c u r r e n t of weak interactions to be dominated the pseudoscalar meson pole, and using M(12), o+~e can w r l ~ the G o l d b e r g e r - T r e i m a n relations
2ran ~ ~ g~Nf~ and
2 mQ ~ gltQfrt w h e r e g~Q, g~N a r e the effective p s - p s ~Q and ~N couplirig constants and f~ is the pion decay amplitude. Hence s mQ g+tQ ~ ~+~ gTtN
(I)
and for large quark m a s s g+ro >> g~N" F r o m (1) and M(12) invariance we find-for t f i e D i r a c - t y p e coupling of~ say, the p - m e s o n
gpQ = gpN •
(2)
Similar r e l a t i o n s then ensue for all other vector m e s o n s . The universality of Dirac-type vector m e s o n couplings is thus retained in spite of the fact that vector m e , o n couplings are not "minimal" in a gauge-~:he+?~e~mal sense. Assuming .:~'~ quark magnetic moment to be determined ~ e lowest lying vector meson pole (of m a s s . we find gQan = e ' / u
* The study was ~upimrted by the Air Force Office o f .~%|entlfic Research, Grant No.AF-AFOSR-42-64. ** ~ leave of absence from the Enrico Fermi Institute f<~ Nuclear ~ d i e s and the Departmeat of Physics of the Ueiverml~yof Chicago, Chicago, Illinois. * We do mot ~ommlt o~r~elvee to any particular values of ~+e quark m_rossmQ or charge (fractional or integrat~ and o~r res~;lt~ (¢qs. (1) and (2)) are valid for a~y type of quarks. At ~ i s point it may be useful to r ~ a l l that with a single type of fractionally charged qua2~, the exiotence of a 56-plet of baryons is not easily reconciled with the requLr~mente of Fermi statietI~ (5]. One can, however, consider theories with three gpectea of quarks (which now could be integrally charged) in which case the symmetry of the t l ~ r y can be further increased to M(12) ~ M(12) ~ M(12). After the completion of th~B ~ , we received a preprtut by Y.Nambv where similar po~lblllty is considered. ** We d~ar~Cal'dhere the lack of propagation of the intrinsically broken M(12) rule~ ltlrough the condition of elastic unltarity.
352
w h e r e e' is the e l e c t r i c charge of the quark Q. Similar considerations give for the proton (e = proton charge)
;*Pan = e/~ . Thus
e ~
gQan =~e- +UPan "
(3)
Thus, for a quark of charge ½, the anomalous magnet'Jr moment c o m e s out to be ~ × 1.79 x × (e/2mp) ~ 0.6 (e/2mp) w h e r e a s for an integrally charged quark (e' = e), #Oan = # P a n = 1.79 e / 2 m p t t ~ Should quarks I~+ o b s e r v e d as p a r t i c l e s , a verification of the relations (1), (2) and (3) will provide an unambigous t e s t for in"iN" Note that in either ease thte is a very large anomalous magnetic moment if mQ >~3 GeV.
Volume 15, number4
PHYSICS
LETTERS
trinsically broken M(12) invariance [6] of strong interactions.
4. F. Gffrsey, M. Nauenberg and T.D. l,ee, Phyvl. Rev.
135 (1964) B467. 5, P . G . O . F r e u n d and B.W.Lee, Phys. I~ev. t,etter~ 13 (1964) 592; O.W.Greenberg, ibid 13 (1964) 59~. 6. K. Bardakei, J.M. Cornwall, P. G, O. Freur~d ~a¢l B. W. Lee, Phys. Rev. Le~ers 14 (1965) 48. See also subsequent work on the intrinsic symmetry-breaking mechanism by R. Delboargo, A. Salam, J. Stxadhee, Proc.Rov.Soe. (to be published), and B. Sakita and K. C. Wall, Phys. Ray. Lvt'~er ~ (~o be published). See also M.B~g and A. Pais, Phys. Ray. Letters 14 (1965} 267.
T h e a u t h o r w o u l d like to t h a n k P r o f e s s o r R. O p p e n h e i m e r f o r h i s h o s p i t a l i t y at t h e I n s t i t u t e f o r A d v a n c e d Study. Refe~'enees 1. M.Gell-Mann, Physics Letters 8 (1964) 214. 2. G.Zweig, CERN report (1964). 3. M.Gell-Man~, Physics 1 (1964} 63.
PARITY
DETERMINATION
P. L. C 8 O N K A ,
15 April 1!#~5
IN
PARTICLE
M. J. M O R A V C S I K
PHYSICS
*
and M. D. S C A D R O N
Lawrence Radiation Laboratory, University of California, Liver~nore, California Received I March 1965
T h e p u r p o s e of t h i s note i s to e s t a b l i s h s o m e v e r y g e n e r a l t h e o r e m s a b o u t t h e type of e x p e r i m e n t s w h i c h c a n be u s e d f o r t h e d e t e r m i n a t i o n of t h e p a r i t y of one of t h e p a r t i c l e s in a r e a c t i o n (henceforth callea briefly parity experiments), It s h o u l d be s t a t e d at the o u t s e t t h a t p a r i t y e × p e r i m e n t s a r e of t h r e e k i n d s : 1. T h o s e b a s e d only on r o t a t i o n a n d r e f l e c t i o n invarianae. 2. T h o s e i n v o l v i n g a l s o s o m e a s s u m p t i o n s about the angular momentum states which cont r i b u t e s i g n i f i c a n t l y to t h e p r o c e s s , but w h i c h do n o t involve a s s u m p t i o n s a b o u t t h e d y n a m i c s of t h e r e a c t i o n (e.g. t h e v a r i o u s t h r e s h o l d theorems). 3. T h o s e built on a n e x p l i c i t d y n a m i c a l m o d e l of t h e i n t e r a c t i o n (e.g, d i s p e r s i o n r e l a t i o n s ) . T h e r e s u l t s of t h i s note a r e r e l e v a n t only to the e x p e r i m e n t s of t h e f i r s t kind, w h i c h a r e , h o w e v e r , the most attractive since they are the most general and hence, theoretically, the most conclusive. Let us consider the particle reaction A 1 + A2 -- B1 + B2
it is i m p o s s i b l e to d e t e r m i n e the p a r i t y of B 2 (or
A2). Proof, L e t u s denote t h e m a t r i x e l e m e n t o~ eq. (1) by Me1 d e p e n d i n g on w h e t h e r the i32 (or A2) p a r i t y is p o s i t i v e o r n e g a t i v e . Let u~3 fur'thermore denote the matrix element of the re~ctlon O+ +A 2 - , B 1 + B2
(2)
by M~2 depending again on whether the B2 (or A2) parity is positive or nagative. Here O ~ denoteu a pariticle with zero spin and positive internal parity. Furthermore, we denote the matrix element of the reaction O+ +A I - , O + +O :~
(3)
by M ~ depending on whether the second particle on the right-hand side has positive or neg;itlve parity. Then we can write ** MI and
(I)
and the spins of the particles are arbitrary. Let us assume that the parity of all particles in eq. (I) is known e x c e p t t h a t of B 2 (but t h i s p a r t i c l e could j u s t a s well be A2) Theorem 1. In an e x p e r i m e n t in w h i c h A 1 is a b o s o n and no s p i n i n f o r m a t i o n is o b t a i n e d a b o u t A1,
* Work done under the auspices of the U.g.Atomie Energy Comissien. ** The details of the formalism which decomposes general M matrix into the outer product~ of simpler particle reaction matrices ,Nil be discussed in a forthcoming paper (11.
353