- Email: [email protected]
2+ octuplet
Volume 12 number 3
PHYSICS LETTERS
1 0 ~ t o ~ r 1964
2~" ~ C T U P L E T M. SUZUKI De#artm~ml of Physics, Univ~rslly of Tokyo. Tokyo, ,Iaban
Received 25 August 1964 The purpose of this letter ~s to propose a 2+ octuplet meson family of SU 3 on the basis of the recentlydincovered ~rp r e s o n ~ e e around 1310 M e V l ' 2 , )~ R w a s reported that this resonance, hereafter abb-reviated a s the R meson, decays into ~/2) as well as into KI~ I). This observation severely restrictsthi:~lUantum numbers of R.
b'~mceit decays into the '~wo pseudosca}~u'm e sons (2P8), J ~ must be I-, 2 +, 3", 4 + and so on. According to the Bose s t a t i s t i c s , the ~rreducthle representations composed f r o m 2P8, with which R i~ coupled, are restrictedas follows; 1, 8D a n d 2 7 f o r J ~ = 2
+, 4 +, . . . .
(1)
8A, 10av, d l 0 * f o r J ~ = l
", 3 - , . . . .
(2)
The i r ~ r i n n e e under the G-conjugation and its anatog~, s -in SU3, however; prohibitthe 1 and the 27 d ~ , ,~stonal representations of 2P 8 i t e m being eoupleu .~'tth the corretrpon~ing representations of ille octupietvector meson (V8) and P8- Indeed, for enmmple, the T = 2 m e m b e r of 2P 8 has a positive G-parRy, while the T = 2 m e m b e r of V S P 8 has a negative G-parRy. Therefore, the channel couplings between 2P 8 and V8P 8 occur a s VsP8
2-P8
e~
~sD
8D 8A 10+ 10" ~ 1 0 - 10" 10
-
and theV~SPS conp~ga from the ¢~ mtxing theory o- I, a s s u m i n g gcpp~ = 0, we obtain
g2(vlvere)/r~(vsvepe) = } cot2 o,
10" ~ 1 0 + 10"
(4)
with the definitionsg~.ip+~" =(I/48)/~VIVsP8) and g ~ p + ~ - :~(b~)g(V'~,VaPs), where 0 is the socalled ~ mixing angle. ~ w e take o = 30°, the right-hand side i s 4.8. T h e r e f o r e , the con~rllmt i o s s f r o m the V 1- and r e - e x c h a n g e s n ~ l y cancel each other; we cannot expect a f o r c e a t r a e rive enough to m a k e (10+ 10") resonate. We find by detailed n u m e r i c e l estim~.~ee 6) that a f o r c e is stillnot strong enoag~ to cause resonances L= one of the (SA, 8D) eigenchannels ot ( V s P s , 2P8). R i s important to aceo~mt f o r the s - w a v e channel of 2V 8 and VsV 1 in o r d e r to e s t i m a t e c o r r e c t l y the m a s s level of the 2÷ octtrpint. We can conelude, taking also into accmmt the branching ratinof the 2P 8 decays estimated below, that the R meson should belong to the 8A representation of V s P 8 with J~ = 2 + , 4 +.... Let us Rdopt the lowest spin-p-~rityassignment 2+~ to continue the discussions. The branching rat~ of the 2P 6 decays is calculated to be r(R ~ KI~)/i~(R ~ ~/) = ~ 5 0
(3)
Since .8D and i~0 "I0") of VSP 8 do not contain .~p, We have only t~ r.~:,sider8A and (I0 + I0"). ~P~ is 2~, 4+°., we can oniquely assign R to the 8A representation of VsP8, since 2P 8 m u s t be symmetric: u~der interchange of them, II J~ is 1", 3 L . . , ~IC ÷I0") should be adopted. As f o r the d~term:':.~.:~of the ~pin-p~xity, We will resort to the .~:.-~teal c~nsidsrations. As far as t~e on=- !~.xtlcleexchange processes 274
a r e concerned, the f o r c e in (10+ 10") o r i g l m ~ e s f r o m the V 1- and the V 8 - e x c h a s g e s in the u - c h ~ l nsi c~ VSPS. Tt.-e unitary c r o s s i n g m a t r i x ele merits of these two p r e c e d e s ave -~ m ~ ~, r e spectively, w we e s t i m a t e the r~tio of &he V ! V 8 P 8
(5)
after phase volume corrections, while R ~ K K is forbidden ff R belongs to the icosup!et 7). A s a candidate for the other m e m b e r s of this ocinplet, we have the fo m e s o n wRh J~ = 2+ and T = 0. It i,~ quite r e a s o ~ b l e to t~ke i ° a s the T= Y=O m e m h e r of the 2 + oCtuplet now under considerations. Indeed, the KI~ dee~y mode of fo h a s not been observed yet. It fo belongs to the unitary slnglet, r(fo ~ i¢~)/r(£o~ ~ ) =0.13, while it reduces to 0.03 in the case of fo belonging to the oetuplet. The present experiments appear to: : favour the 0ctuplet assignment of fo~ This assign-
Volume 12, number 3
PHYSICS LETTERS
! Ocb0b~r 1964
m e e t i s contradictory to the conjecture that t ° w e can expect an appreciable amount of enhancem a y belong to the Pomcranchak~Regge t r a j e c ment in the K~ effective m a s s plot around 1270 t o r y , since the Pomeranehuk t r a j e c t o r y n e c e s MeV, a s weU a s i n the K*~ and pK plots. narfly i s the unitary sfnglet 8), If we take fo a s tbe T = Y = 0 m e m b e r of the octuplet, we do not find an enhancement in any VSP8 s y s t e m , since the T = Y = 0 m e m b e r of the 8A representation of VSP 8 18 composed of only K ~ and ~ K . : References A-ppiying the Gell-Mann Okubo formula. W e i 1) S.U.Chung et aL, Phys. Rev. Letters 12 (196~) ~;~1. find that the l a s t m e m b e r ( ~ ) w i t h T =½ and 2) M.Aderholz et al., Physics Letters I0 (1964) 226. iYt = 1 shenld he situated ar0und 1270MeV. No : 3) S.L.Glashow, Phys. Rev. Letters t1(1963) 4& evidence has been reported for i t yet, The branch ~ 4) S~Okubo, Physics Le~ers S (1963) 165. ing ratio of this not yet discovered meson i s s i r e 5) J . J . Sakurall P h ~ Rev 132 (1963) 434. ply calculated to be F ( ~ Krt)/1-(K ~K~r) = 0.016. 61 M. Suzuki, to be published. The term "Icosuplet" was used in B.W. Lee, ~. ODaSince F(~ K~)/F(R ~ # ~ ) = 2.2, (6) bo ~ J.Schecter; Phys. Rev. 135 0964) B219. 8) M Suzuki; Ph ,siss Letters 6 (1963) 204.
TRANSVERSE INTERACTIONS
MUON POLARIZATION IN NEUTRINO INDUCED AS A TEST FOR TIME REVERSAL VIOLATION
S. M. BERMAN Stanford Linea>"Accete~'a~o~" Centre, Stanford, Cali/b~nia, U.S.A., and CERN, Geneva, Switzerland and M. VELTMAN CERN, Geneva, Swilzczland ReCeived 25 August 1964 The experiments of Christensen et aL 1) i n t e r and the elastic p r o c e s s preted a s a violatiO~ oi C P lnvariance have opened v + n ~ ~" ÷ p (~) the question a s to whether t h e r e m a y he: indeed other weak interaction p r o c e s s e s which violate which a r e especially well suited for the ~u~ty ~ CP invarianee. If the c P T theorem 2) i s assUmed weak interactions at appreciable momentum then a violation o f C P invarlance i m p l i e s the c o r t r a n s f e r s . In particular we exanline the p o s s i responding :vi0lation of t i m e r e v e r s a l Invariance. i : b l i i t y of studying the produced muon t r a n s v e r ~ E x p e r i m e n t s 3),studying the/3 decay of p01arize:i ( i . e . , perpendicular to the plane containing eeuneutrons a l r e a d y p e r f o r m e d indicate t h a t only a trine and muon momenta) polarization a s a means s m a l l violation of t i m e ~ r e v e r e n I invarianee :is of detecting a possible violation of t i m e - r e v e r m t t p e r m i t t e d in the aU0wed t3 0ransiti0ns~ However, invariznee. should t h e r e be: t i m e - r e v e r s a l violations i n ~ e r m s We f i r s t show that if t i m e r e v e r s a l is a ra~k~ which vanish for smali: m o m e n t u m transfers then symmetry operation, that the transverse m u ~ there exists no AS = 0 experiments which explicit-- : POlarlz~tion vanishes for an arbitrary neutrh~ ly t e s t f o r possible violations, : induced n~elear p r o c e s s like (I}, provided ~ e In t h i s note we Investigate p r o c e s s e s oflthe a v e r a g e s over all strongly inte'~aeting partie~e~ type (for definiteness we r~strict ourselves to inin the final state and uses an unpolartzed i~rget. cident neutrinos); ~ i Thus, a non-zero value ~or the t r a l ~ s v e r ~ mtam polarization indicates violatio~ of time r e v e r ~ ] i V ~-nucleiis-, :bt" + all final States (I) i invaria.ncs.
PHYSICS LETTERS
1 0 ~ t o ~ r 1964
2~" ~ C T U P L E T M. SUZUKI De#artm~ml of Physics, Univ~rslly of Tokyo. Tokyo, ,Iaban
Received 25 August 1964 The purpose of this letter ~s to propose a 2+ octuplet meson family of SU 3 on the basis of the recentlydincovered ~rp r e s o n ~ e e around 1310 M e V l ' 2 , )~ R w a s reported that this resonance, hereafter abb-reviated a s the R meson, decays into ~/2) as well as into KI~ I). This observation severely restrictsthi:~lUantum numbers of R.
b'~mceit decays into the '~wo pseudosca}~u'm e sons (2P8), J ~ must be I-, 2 +, 3", 4 + and so on. According to the Bose s t a t i s t i c s , the ~rreducthle representations composed f r o m 2P8, with which R i~ coupled, are restrictedas follows; 1, 8D a n d 2 7 f o r J ~ = 2
+, 4 +, . . . .
(1)
8A, 10av, d l 0 * f o r J ~ = l
", 3 - , . . . .
(2)
The i r ~ r i n n e e under the G-conjugation and its anatog~, s -in SU3, however; prohibitthe 1 and the 27 d ~ , ,~stonal representations of 2P 8 i t e m being eoupleu .~'tth the corretrpon~ing representations of ille octupietvector meson (V8) and P8- Indeed, for enmmple, the T = 2 m e m b e r of 2P 8 has a positive G-parRy, while the T = 2 m e m b e r of V S P 8 has a negative G-parRy. Therefore, the channel couplings between 2P 8 and V8P 8 occur a s VsP8
2-P8
e~
~sD
8D 8A 10+ 10" ~ 1 0 - 10" 10
-
and theV~SPS conp~ga from the ¢~ mtxing theory o- I, a s s u m i n g gcpp~ = 0, we obtain
g2(vlvere)/r~(vsvepe) = } cot2 o,
10" ~ 1 0 + 10"
(4)
with the definitionsg~.ip+~" =(I/48)/~VIVsP8) and g ~ p + ~ - :~(b~)g(V'~,VaPs), where 0 is the socalled ~ mixing angle. ~ w e take o = 30°, the right-hand side i s 4.8. T h e r e f o r e , the con~rllmt i o s s f r o m the V 1- and r e - e x c h a n g e s n ~ l y cancel each other; we cannot expect a f o r c e a t r a e rive enough to m a k e (10+ 10") resonate. We find by detailed n u m e r i c e l estim~.~ee 6) that a f o r c e is stillnot strong enoag~ to cause resonances L= one of the (SA, 8D) eigenchannels ot ( V s P s , 2P8). R i s important to aceo~mt f o r the s - w a v e channel of 2V 8 and VsV 1 in o r d e r to e s t i m a t e c o r r e c t l y the m a s s level of the 2÷ octtrpint. We can conelude, taking also into accmmt the branching ratinof the 2P 8 decays estimated below, that the R meson should belong to the 8A representation of V s P 8 with J~ = 2 + , 4 +.... Let us Rdopt the lowest spin-p-~rityassignment 2+~ to continue the discussions. The branching rat~ of the 2P 6 decays is calculated to be r(R ~ KI~)/i~(R ~ ~/) = ~ 5 0
(3)
Since .8D and i~0 "I0") of VSP 8 do not contain .~p, We have only t~ r.~:,sider8A and (I0 + I0"). ~P~ is 2~, 4+°., we can oniquely assign R to the 8A representation of VsP8, since 2P 8 m u s t be symmetric: u~der interchange of them, II J~ is 1", 3 L . . , ~IC ÷I0") should be adopted. As f o r the d~term:':.~.:~of the ~pin-p~xity, We will resort to the .~:.-~teal c~nsidsrations. As far as t~e on=- !~.xtlcleexchange processes 274
a r e concerned, the f o r c e in (10+ 10") o r i g l m ~ e s f r o m the V 1- and the V 8 - e x c h a s g e s in the u - c h ~ l nsi c~ VSPS. Tt.-e unitary c r o s s i n g m a t r i x ele merits of these two p r e c e d e s ave -~ m ~ ~, r e spectively, w we e s t i m a t e the r~tio of &he V ! V 8 P 8
(5)
after phase volume corrections, while R ~ K K is forbidden ff R belongs to the icosup!et 7). A s a candidate for the other m e m b e r s of this ocinplet, we have the fo m e s o n wRh J~ = 2+ and T = 0. It i,~ quite r e a s o ~ b l e to t~ke i ° a s the T= Y=O m e m h e r of the 2 + oCtuplet now under considerations. Indeed, the KI~ dee~y mode of fo h a s not been observed yet. It fo belongs to the unitary slnglet, r(fo ~ i¢~)/r(£o~ ~ ) =0.13, while it reduces to 0.03 in the case of fo belonging to the oetuplet. The present experiments appear to: : favour the 0ctuplet assignment of fo~ This assign-
Volume 12, number 3
PHYSICS LETTERS
! Ocb0b~r 1964
m e e t i s contradictory to the conjecture that t ° w e can expect an appreciable amount of enhancem a y belong to the Pomcranchak~Regge t r a j e c ment in the K~ effective m a s s plot around 1270 t o r y , since the Pomeranehuk t r a j e c t o r y n e c e s MeV, a s weU a s i n the K*~ and pK plots. narfly i s the unitary sfnglet 8), If we take fo a s tbe T = Y = 0 m e m b e r of the octuplet, we do not find an enhancement in any VSP8 s y s t e m , since the T = Y = 0 m e m b e r of the 8A representation of VSP 8 18 composed of only K ~ and ~ K . : References A-ppiying the Gell-Mann Okubo formula. W e i 1) S.U.Chung et aL, Phys. Rev. Letters 12 (196~) ~;~1. find that the l a s t m e m b e r ( ~ ) w i t h T =½ and 2) M.Aderholz et al., Physics Letters I0 (1964) 226. iYt = 1 shenld he situated ar0und 1270MeV. No : 3) S.L.Glashow, Phys. Rev. Letters t1(1963) 4& evidence has been reported for i t yet, The branch ~ 4) S~Okubo, Physics Le~ers S (1963) 165. ing ratio of this not yet discovered meson i s s i r e 5) J . J . Sakurall P h ~ Rev 132 (1963) 434. ply calculated to be F ( ~ Krt)/1-(K ~K~r) = 0.016. 61 M. Suzuki, to be published. The term "Icosuplet" was used in B.W. Lee, ~. ODaSince F(~ K~)/F(R ~ # ~ ) = 2.2, (6) bo ~ J.Schecter; Phys. Rev. 135 0964) B219. 8) M Suzuki; Ph ,siss Letters 6 (1963) 204.
TRANSVERSE INTERACTIONS
MUON POLARIZATION IN NEUTRINO INDUCED AS A TEST FOR TIME REVERSAL VIOLATION
S. M. BERMAN Stanford Linea>"Accete~'a~o~" Centre, Stanford, Cali/b~nia, U.S.A., and CERN, Geneva, Switzerland and M. VELTMAN CERN, Geneva, Swilzczland ReCeived 25 August 1964 The experiments of Christensen et aL 1) i n t e r and the elastic p r o c e s s preted a s a violatiO~ oi C P lnvariance have opened v + n ~ ~" ÷ p (~) the question a s to whether t h e r e m a y he: indeed other weak interaction p r o c e s s e s which violate which a r e especially well suited for the ~u~ty ~ CP invarianee. If the c P T theorem 2) i s assUmed weak interactions at appreciable momentum then a violation o f C P invarlance i m p l i e s the c o r t r a n s f e r s . In particular we exanline the p o s s i responding :vi0lation of t i m e r e v e r s a l Invariance. i : b l i i t y of studying the produced muon t r a n s v e r ~ E x p e r i m e n t s 3),studying the/3 decay of p01arize:i ( i . e . , perpendicular to the plane containing eeuneutrons a l r e a d y p e r f o r m e d indicate t h a t only a trine and muon momenta) polarization a s a means s m a l l violation of t i m e ~ r e v e r e n I invarianee :is of detecting a possible violation of t i m e - r e v e r m t t p e r m i t t e d in the aU0wed t3 0ransiti0ns~ However, invariznee. should t h e r e be: t i m e - r e v e r s a l violations i n ~ e r m s We f i r s t show that if t i m e r e v e r s a l is a ra~k~ which vanish for smali: m o m e n t u m transfers then symmetry operation, that the transverse m u ~ there exists no AS = 0 experiments which explicit-- : POlarlz~tion vanishes for an arbitrary neutrh~ ly t e s t f o r possible violations, : induced n~elear p r o c e s s like (I}, provided ~ e In t h i s note we Investigate p r o c e s s e s oflthe a v e r a g e s over all strongly inte'~aeting partie~e~ type (for definiteness we r~strict ourselves to inin the final state and uses an unpolartzed i~rget. cident neutrinos); ~ i Thus, a non-zero value ~or the t r a l ~ s v e r ~ mtam polarization indicates violatio~ of time r e v e r ~ ] i V ~-nucleiis-, :bt" + all final States (I) i invaria.ncs.