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Decay of the K0 meson into three pions: Test of CP conservation and ΔI = 12 non leptonic selection rule
Volume 22, n u m b e r 4
DECAY
OF
THE
PHYSICS
LETTERS
1 S e p t e m b e r 1966
K ° MESON INTO THREE PIONS: TEST AND AI = ½ NON LEPTONIC SELECTION
L. BEHR,
V. BRISSON,
OF CP RULE
CONSERVATION
P. PETIAU
Ecole Polytechnique , Paris
E. BELLOTTI,
A. PULLIA
Istituto di F i s i c a d e l l ' U n i v e r s i t Y , Milano I s t i t u t o N a z i o n a l e di F i s i e a N u c l e a t e , S e z i o n e di M i l a n o
M. BALDO
CEOLIN,
E. CALIMANI,
S. CIAMPOLILLO,
H. HUZITA,
A. SCONZA
I s t i t u t o di F i s i c a "Galileo G a l i l e i " d e l l ' U n i v e r s i t h , P a d o v a I s t i t u t o N a z i o n a l e di F i s i c a N u c l e a r e , S e z i o n e di P a d o v a
B. AUBERT,
L.M.
CHOUNET,
J.P. LOWYS
and C. FASCAUD
L a b o r a t o i r e de l ' A c c ~ l ~ r a t e u r L i n S a i r e , E c o l e N o r m a l e S u p O r i e u r e Facult5 des Sciences, Orsay
Received 25 July 1966
C P invariance mid AI = ½ rule a r e tested by analysing 136 K ° decays of the type K "J ~Tr+Tr-zr° and 54 of the type K o --~TroTroTro o b s e r v e d in a heavy liquid bubble c h a m b e r . T h e r e is no evidence against e i t h e r hypothesis.
Preliminary results on the K ° decays in the modes v+v-v ° and vovovo have been already reported [1,2]. The relevant feature of this experiment is that transitions from both states K°S and K°L are observable in such a way that both amplitudes l a s ] a n d ] a L l a r e m e a s u r a b l e a s w e l l a s their relative phase. This allows to test both CP i n v a r i a n c e a n d Af = ½ s e l e c t i o n r u l e f o r t h r e e p i o n d e c a y s of n e u t r a l K m e s o n s . T h e K ° ' s w e r e p r o d u c e d by K + c h a r g e e x c h a n g e s in t h e E c o l e P o l y t e c n n i q u e h e a v y l i q u i d b u b b l e c h a m b e r . T h r e e s a m p l e s of p i c t u r e s w e r e taken at CERN using different mixtures; the exp e r i m e n t a l c o n d i t i o n s a r e s u m m a r i z e d in t a b l e 1. T h e K ° -~ ~+Tr-w ° d e c a y m o d e i s d e t e c t e d by t h e p r e s e n c e of a V ° w i t h 1 o r 2 y ' s p o i n t i n g t o w a r d s i t s a p e x . M o s t of t h e b a c k g r o u n d s h a v e b e e n e l i m i n a t e d by a p p l i c a t i o n of c u t - o f f s on t h e distance between the V ° apex and every possible o r i g i n f o r t h e K °, on t h e l e n g t h a n d d i p a n g l e of t h e c h a r g e d s e c o n d a r i e s a n d of t h e ~/ r a y l i n e of f l i g h t , a n d on t h e ~ r a y e n e r g y . F o r e a c h e v e n t , the three following hypothesis have been tested: K°---~yr+Tr -,
K°~Tr+~r-y,
½N FL(K ° -* 3~J) E(t) {(x2 + y2) exp(_t/Ts) + + exp(-ffTL) + 2exp[-(t/2TS + t/2TL)]X (i)
K ° ~ + T r - ~ r °.
A t o t a l n u m b e r of 136 e v e n t s h a s b e e n r e t a i n e d .
540
A few ambiguous events have been weighted, taking into account the probability given by the ×2 for each hypothesis and the a priori probability. The K°-~ 3v° decay mode is detected by the presence of 5 or 6 ~ rays coming from the same neutral vertex. Suitable cut-offs on the length of the supposed K° line of flight and on the minimum angle between the directions of the y's were made to avoid the two main backgrounds, i.e. K°--*~r°Tr° produced in association with a ~r°, and K° ~ ~°Tr° with Bremsstrahlung products of the electrons from the ~ rays conversion. After kinematical analysis, 54 events have been retained, among which 6 events have six materialized ~ rays inside the fiducial volume. On the assumption of CPT invariance and in the approximation K° = ½J 2 (K°S + K°L) (owing to the results found by Christenson et al. [3]), the most general expression for the expected number of K° - ' 3~r decays at time t is given by
× i x c o s ( S r n t ) - y s i n ( A m t ) ]}dr,
Volume 22, number 4
PHYSICS
1 September 1966
LETTERS
Table 1 1st exposure
2nd exposure
Beam
800 MeV/c K +
800 MeV/c K +
900 MeV/c K +
Liquid
C3H 8 + CF3Br
C2F5C1 + CF3Br
CF3Br
22 cm
17 cm
11 cm
?r +y-T;°
180 000
230 000
115 000
Y°Tr%r°
//
230 000
115 000
Rad. Length Number of pictures for
w h e r e N i s the t o t a l n u m b e r of K ° ' s p r o d u c e d at t = 0 c a l c u l a t e d f r o m the o b s e r v e d K°S ~ 1T+Xd e c a y s ; F L i s the t r a n s i t i o n r a t e f o r K ° L ~ ( p a r t i c u l a r 3x c h a n n e l ) ; TS and TL a r e the m e a n l i f e t i m e s of K ° S and K ° L ; A m i s the m a s s d i f f e r e n c e mKO~ mKOo; ~
x = Re
0
l a(K S
3~)
.--S:-6-o ~ -~--~); y = Im
a(K L
a (K°s ___ 31r) a(--~-°L -* 31r)
E(t) i s the d e t e c t i o n e f f i c i e n c y f u n c t i o n w h i c h w a s c o m p u t e d f r o m a s a m p l e of a b o u t 2000 K ° S ~ + ~ " d e c a y s by m e a n s of a M o n t e C a r l o c a l c u l a t i o n , g e n e r a t i n g e v e n t s of the t y p e K ° ~ 31r t a k i n g into account the experimental conditions. T h e p r e d i c t i o n s of the h y p o t h e s e s to be t e s t e d are as follows*: a) CP i n v a r i a n c e r e q u i r e s x = y = 0 b) I = 1 3~ f i n a l s t a t e r e q u i r e s x ~ 0 (1), c) AI = ½ r e q u i r e s
p(+-o)_ .+oo, rL(+_o ) = 2~T~)v+t Fr+(++-) r+(+oo) (1 +y2)rL(ooo ) =p(ooo)L p(---7~+-)- p(+oo) ] (1 + y2)
( w h e r e p ' s a r e the p h a s e - s p a c e f a c t o r s ) . U s i n g the t i m e s of f l i g h t of o u r K ° ~ ~ + ~ - ~ o e v e n t s a s w e l l a s t h e i r t o t a l n u m b e r in e x p r e s s i o n (1), we h a v e c o m p u t e d a l i k e l i h o o d f u n c t i o n of the t h r e e p a r a m e t e r s x, y and F L. The likelihood ratio test gives agreement with 65% of c o n f i d e n c e w i t h t h e p r e d i c t i o n a) and with 68% of c o n f i d e n c e g i v e s 0 --< F S ( + - o ) / F L ( + - o ) --< i . T h e r e f o r e , o u r d a t a a r e c o n s i s t e n t with the CP c o n s e r v a t i o n and a f o r t i o r i w i t h I = 1 t h r e e p i o n s f i n a l s t a t e ( p r e d i c t i o n b). T h e l i k e l i h o o d r a t i o i s a l s o in a g r e e m e n t w i t h * Higher angular momentum contributions to the channel KO S ~ 7;÷ y - y 0 are neglected.
3rd exposure
i
85% of c o n f i d e n c e with the p r e d i c t i o n c), AI = ~, without any a s s u m p t i o n on CP. A l t h o u g h , o w i n g to the l i m i t e d s t a t i s t i c s , t h i s t y p e of a n a l y s i s i s not s e n s i t i v e e n o u g h on i n d e p e n d e n t t e s t s of CP c o n s e r v a t i o n and A I = ½ r u l e , n e v e r t h e l e s s it s h o w s c o n s i s t e n c y with e i t h e r of t h e m . T h e n we a r e l e d to t e s t e a c h h y p o t h e s i s a s s u m i n g the v a l i d i t y of the o t h e r . T h e A f = ½ r u l e , on the a s s u m p t i o n of CP i n v a r i a n c e , l e a d s to the f o l l o w i n g r e l a t i o n s b e t w e e n K + and K ° L r a t e s $ FL(+-o) = 2P(+-°)F
(+oo) = (2.74 + 0.10) × 106s -1
p(+oo) + Fr+(++-) r+(+oo)
rL(OOO) = p(ooo) L P(++-)
p(+oo)
]-
= (5.02 + 0.15) x 106 s -1. I n t e g r a t i n g e x p r e s s i o n (1), a s s u m i n g CP i n v a r i a n c e , we obtain the f o l l o w i n g r e s u l t s : F L ( + - o ) = (2.62 +- 0.28 0.27 ) × 106 s _ l FL(OOO) = (5.22 + 1.03 ) × 106 s _ l 0.84 in good a g r e e m e n t w i t h the a b o v e p r e d i c t i o n s . T h e c o m p a r i s o n b e t w e e n the a b s o l u t e d e c a y r a t e s rL(ooo) and r L ( + - o ) on the a s s u m p t i o n of CP i n v a r i a n c e , g i v e s a f u r t h e r c h e c k of the i s o t o p i c s p i n s t a t e of t h e f i n a l t h r e e p i o n s s y s t e m , w h i c h i s r e s t r i c t e d to odd v a l u e s (l = 1 and I = 3). If t h e r e a r e only I = 1 s y m m e t r i c s t a t e s (i.e. no M = ~ t r a n s i t i o n s ) , the r a t i o r L(OOO)/FL(+-o) m u s t be FL(OOO)/FL(+-o) = 1.84 .
$ The values are obtained from the experimental data on K + decays [4] and adding the constraint that the K+ rates must be related by I = 1 37r final state. 541
Volume 22, n u m b e r 4
PHYSICS
We get for this ratio
LETTERS We obtain:
F L ( O O O ) / F L ( + - o ) = 1.99 + 0.40 These two numbers are not significantly diff e r e n t a n d we m a y l i k e l y c o n c l u d e t h a t t h e r e i s little or no A! = ~ transition. On t h i s a s s u m p t i o n , we c a n s e t a l i m i t f o r t h e r e a l p a r t of a p o s s i b l e s m a l l c o n t r i b u t i o n of t h e a m p l i t u d e S 3 (A/ = ~}) r e l a t i v e t o S 1 (A[ = ½) u s i n g the relations FL(+_o) F + (+oo) - 1.97
S1 + 8 3
(the s i g n of y i s r e l a t i v e to A m ) . In t e r m s of r e l a t i v e p h a s e 2 ¢ b e t w e e n K ° a n d K ° a m p l i t u d e f o r 31r d e c a y s : = -(19 + - 933 ) d e g r e e s T h e l i m i t s w i t h 90% of c o n f i d e n c e a r e :
2
2 .
We get:
Re ($3/S1) = - 0 . 0 1 + 0 . 0 3 A f u r t h e r t e s t of t h e A l = ½ r u l e i s t h e c o m p a r i s o n of t h e m a t r i x e l e m e n t s f o r K ° L ~ v+lr-~ ° a n d K + ~ ~r+~°~ ° d e c a y s . A s s u m i n g a l i n e a r d e p e n d e n c e of t h e s q u a r e d matrix element
I MI 2 c~ 1-o~ TOr°)/mKO w h e r e T0r °) i s t h e k i n e t i c e n e r g y of t h e u n l i k e p i o n , we get: +0.9 - 1 . 1
This value is in agreement f r o m K + d e c a y [4]
T h e r a t i o of t h e r a t e s FS(+-o)/FL(+-o) i s 19. 0"16" w i t h 90% of c o n f i d e n c e t h e l i m i t i s •- - - 0 . 1 2 ' F S / F L ~< 0.45 In c o n c l u s i o n , t h e e x p e r i m e n t a l r e s u l t s a r e c o n s i s t e n t w i t h CP i n v a r i a n c e a n d g i v e a l i m i t f o r t h e p r e s e n c e of K ° S --* 37. T h e a g r e e m e n t w i t h t h e ~1 = ½ r u l e , a s s u m i n g CP c o n s e r v a t i o n , a p p e a r s t o b e q u i t e good. We w i s h t o t h a n k P r . A . L a g a r r i g u e , C . D i l worth, E. Fiorini for enlightening discussions, we a r e g r a t e f u l a l s o t o F. M a t t i o l i a n d C. M i a r i for their cooperation. W e a r e i n d e b t e d t o t h e C E R N P . S . Staff, t o the Ecole Polytechnique chamber team, to the C N A F c o m p u t i n g C e n t r e a n d to a l l s c a n n e r s , who made this experiment possible.
"
with that obtained
or+_ o = 7.55 ± 0 . 3 5 . A s s u m i n g n o w t h e v a l i d i t y of ~xI = ½ s e l e c t i o n r u l e , we c a n t e s t CP i n v a r i a n c e , w h i c h r e q u i r e s v a n i s h i n g of t h e only p a r a m e t e r y n o w a p p e a r i n g i n t h e e x p r e s s i o n (1).
542
y = -(0.34 + 0.19. 0.59 )
- 3 4 ° < ¢ < + 22 °
FL(OOO ) S1 + S3 F + (+oo) - 3.61 [S Z _ ~ 3
(~+-o = 7.7
1 September 1966
References 1. L . B e h r et al., Proc. Intern. Conf. Dubna 1964. 2. L . B e h r et al., P r o c . Intern. Conf. on Weak inter_ actions, Argonne 1965, p. 59. 3. J . H . C h r i s t e n s o n et a1., Phys. Rev. L e t t e r s 13 (1964) 138. 4. G . H . T r i l l i n g , P r o c . Intern. Conf. on Weak i n t e r actions, Argonne 1965, p. 115.
DECAY
OF
THE
PHYSICS
LETTERS
1 S e p t e m b e r 1966
K ° MESON INTO THREE PIONS: TEST AND AI = ½ NON LEPTONIC SELECTION
L. BEHR,
V. BRISSON,
OF CP RULE
CONSERVATION
P. PETIAU
Ecole Polytechnique , Paris
E. BELLOTTI,
A. PULLIA
Istituto di F i s i c a d e l l ' U n i v e r s i t Y , Milano I s t i t u t o N a z i o n a l e di F i s i e a N u c l e a t e , S e z i o n e di M i l a n o
M. BALDO
CEOLIN,
E. CALIMANI,
S. CIAMPOLILLO,
H. HUZITA,
A. SCONZA
I s t i t u t o di F i s i c a "Galileo G a l i l e i " d e l l ' U n i v e r s i t h , P a d o v a I s t i t u t o N a z i o n a l e di F i s i c a N u c l e a r e , S e z i o n e di P a d o v a
B. AUBERT,
L.M.
CHOUNET,
J.P. LOWYS
and C. FASCAUD
L a b o r a t o i r e de l ' A c c ~ l ~ r a t e u r L i n S a i r e , E c o l e N o r m a l e S u p O r i e u r e Facult5 des Sciences, Orsay
Received 25 July 1966
C P invariance mid AI = ½ rule a r e tested by analysing 136 K ° decays of the type K "J ~Tr+Tr-zr° and 54 of the type K o --~TroTroTro o b s e r v e d in a heavy liquid bubble c h a m b e r . T h e r e is no evidence against e i t h e r hypothesis.
Preliminary results on the K ° decays in the modes v+v-v ° and vovovo have been already reported [1,2]. The relevant feature of this experiment is that transitions from both states K°S and K°L are observable in such a way that both amplitudes l a s ] a n d ] a L l a r e m e a s u r a b l e a s w e l l a s their relative phase. This allows to test both CP i n v a r i a n c e a n d Af = ½ s e l e c t i o n r u l e f o r t h r e e p i o n d e c a y s of n e u t r a l K m e s o n s . T h e K ° ' s w e r e p r o d u c e d by K + c h a r g e e x c h a n g e s in t h e E c o l e P o l y t e c n n i q u e h e a v y l i q u i d b u b b l e c h a m b e r . T h r e e s a m p l e s of p i c t u r e s w e r e taken at CERN using different mixtures; the exp e r i m e n t a l c o n d i t i o n s a r e s u m m a r i z e d in t a b l e 1. T h e K ° -~ ~+Tr-w ° d e c a y m o d e i s d e t e c t e d by t h e p r e s e n c e of a V ° w i t h 1 o r 2 y ' s p o i n t i n g t o w a r d s i t s a p e x . M o s t of t h e b a c k g r o u n d s h a v e b e e n e l i m i n a t e d by a p p l i c a t i o n of c u t - o f f s on t h e distance between the V ° apex and every possible o r i g i n f o r t h e K °, on t h e l e n g t h a n d d i p a n g l e of t h e c h a r g e d s e c o n d a r i e s a n d of t h e ~/ r a y l i n e of f l i g h t , a n d on t h e ~ r a y e n e r g y . F o r e a c h e v e n t , the three following hypothesis have been tested: K°---~yr+Tr -,
K°~Tr+~r-y,
½N FL(K ° -* 3~J) E(t) {(x2 + y2) exp(_t/Ts) + + exp(-ffTL) + 2exp[-(t/2TS + t/2TL)]X (i)
K ° ~ + T r - ~ r °.
A t o t a l n u m b e r of 136 e v e n t s h a s b e e n r e t a i n e d .
540
A few ambiguous events have been weighted, taking into account the probability given by the ×2 for each hypothesis and the a priori probability. The K°-~ 3v° decay mode is detected by the presence of 5 or 6 ~ rays coming from the same neutral vertex. Suitable cut-offs on the length of the supposed K° line of flight and on the minimum angle between the directions of the y's were made to avoid the two main backgrounds, i.e. K°--*~r°Tr° produced in association with a ~r°, and K° ~ ~°Tr° with Bremsstrahlung products of the electrons from the ~ rays conversion. After kinematical analysis, 54 events have been retained, among which 6 events have six materialized ~ rays inside the fiducial volume. On the assumption of CPT invariance and in the approximation K° = ½J 2 (K°S + K°L) (owing to the results found by Christenson et al. [3]), the most general expression for the expected number of K° - ' 3~r decays at time t is given by
× i x c o s ( S r n t ) - y s i n ( A m t ) ]}dr,
Volume 22, number 4
PHYSICS
1 September 1966
LETTERS
Table 1 1st exposure
2nd exposure
Beam
800 MeV/c K +
800 MeV/c K +
900 MeV/c K +
Liquid
C3H 8 + CF3Br
C2F5C1 + CF3Br
CF3Br
22 cm
17 cm
11 cm
?r +y-T;°
180 000
230 000
115 000
Y°Tr%r°
//
230 000
115 000
Rad. Length Number of pictures for
w h e r e N i s the t o t a l n u m b e r of K ° ' s p r o d u c e d at t = 0 c a l c u l a t e d f r o m the o b s e r v e d K°S ~ 1T+Xd e c a y s ; F L i s the t r a n s i t i o n r a t e f o r K ° L ~ ( p a r t i c u l a r 3x c h a n n e l ) ; TS and TL a r e the m e a n l i f e t i m e s of K ° S and K ° L ; A m i s the m a s s d i f f e r e n c e mKO~ mKOo; ~
x = Re
0
l a(K S
3~)
.--S:-6-o ~ -~--~); y = Im
a(K L
a (K°s ___ 31r) a(--~-°L -* 31r)
E(t) i s the d e t e c t i o n e f f i c i e n c y f u n c t i o n w h i c h w a s c o m p u t e d f r o m a s a m p l e of a b o u t 2000 K ° S ~ + ~ " d e c a y s by m e a n s of a M o n t e C a r l o c a l c u l a t i o n , g e n e r a t i n g e v e n t s of the t y p e K ° ~ 31r t a k i n g into account the experimental conditions. T h e p r e d i c t i o n s of the h y p o t h e s e s to be t e s t e d are as follows*: a) CP i n v a r i a n c e r e q u i r e s x = y = 0 b) I = 1 3~ f i n a l s t a t e r e q u i r e s x ~ 0 (1), c) AI = ½ r e q u i r e s
p(+-o)_ .+oo, rL(+_o ) = 2~T~)v+t Fr+(++-) r+(+oo) (1 +y2)rL(ooo ) =p(ooo)L p(---7~+-)- p(+oo) ] (1 + y2)
( w h e r e p ' s a r e the p h a s e - s p a c e f a c t o r s ) . U s i n g the t i m e s of f l i g h t of o u r K ° ~ ~ + ~ - ~ o e v e n t s a s w e l l a s t h e i r t o t a l n u m b e r in e x p r e s s i o n (1), we h a v e c o m p u t e d a l i k e l i h o o d f u n c t i o n of the t h r e e p a r a m e t e r s x, y and F L. The likelihood ratio test gives agreement with 65% of c o n f i d e n c e w i t h t h e p r e d i c t i o n a) and with 68% of c o n f i d e n c e g i v e s 0 --< F S ( + - o ) / F L ( + - o ) --< i . T h e r e f o r e , o u r d a t a a r e c o n s i s t e n t with the CP c o n s e r v a t i o n and a f o r t i o r i w i t h I = 1 t h r e e p i o n s f i n a l s t a t e ( p r e d i c t i o n b). T h e l i k e l i h o o d r a t i o i s a l s o in a g r e e m e n t w i t h * Higher angular momentum contributions to the channel KO S ~ 7;÷ y - y 0 are neglected.
3rd exposure
i
85% of c o n f i d e n c e with the p r e d i c t i o n c), AI = ~, without any a s s u m p t i o n on CP. A l t h o u g h , o w i n g to the l i m i t e d s t a t i s t i c s , t h i s t y p e of a n a l y s i s i s not s e n s i t i v e e n o u g h on i n d e p e n d e n t t e s t s of CP c o n s e r v a t i o n and A I = ½ r u l e , n e v e r t h e l e s s it s h o w s c o n s i s t e n c y with e i t h e r of t h e m . T h e n we a r e l e d to t e s t e a c h h y p o t h e s i s a s s u m i n g the v a l i d i t y of the o t h e r . T h e A f = ½ r u l e , on the a s s u m p t i o n of CP i n v a r i a n c e , l e a d s to the f o l l o w i n g r e l a t i o n s b e t w e e n K + and K ° L r a t e s $ FL(+-o) = 2P(+-°)F
(+oo) = (2.74 + 0.10) × 106s -1
p(+oo) + Fr+(++-) r+(+oo)
rL(OOO) = p(ooo) L P(++-)
p(+oo)
]-
= (5.02 + 0.15) x 106 s -1. I n t e g r a t i n g e x p r e s s i o n (1), a s s u m i n g CP i n v a r i a n c e , we obtain the f o l l o w i n g r e s u l t s : F L ( + - o ) = (2.62 +- 0.28 0.27 ) × 106 s _ l FL(OOO) = (5.22 + 1.03 ) × 106 s _ l 0.84 in good a g r e e m e n t w i t h the a b o v e p r e d i c t i o n s . T h e c o m p a r i s o n b e t w e e n the a b s o l u t e d e c a y r a t e s rL(ooo) and r L ( + - o ) on the a s s u m p t i o n of CP i n v a r i a n c e , g i v e s a f u r t h e r c h e c k of the i s o t o p i c s p i n s t a t e of t h e f i n a l t h r e e p i o n s s y s t e m , w h i c h i s r e s t r i c t e d to odd v a l u e s (l = 1 and I = 3). If t h e r e a r e only I = 1 s y m m e t r i c s t a t e s (i.e. no M = ~ t r a n s i t i o n s ) , the r a t i o r L(OOO)/FL(+-o) m u s t be FL(OOO)/FL(+-o) = 1.84 .
$ The values are obtained from the experimental data on K + decays [4] and adding the constraint that the K+ rates must be related by I = 1 37r final state. 541
Volume 22, n u m b e r 4
PHYSICS
We get for this ratio
LETTERS We obtain:
F L ( O O O ) / F L ( + - o ) = 1.99 + 0.40 These two numbers are not significantly diff e r e n t a n d we m a y l i k e l y c o n c l u d e t h a t t h e r e i s little or no A! = ~ transition. On t h i s a s s u m p t i o n , we c a n s e t a l i m i t f o r t h e r e a l p a r t of a p o s s i b l e s m a l l c o n t r i b u t i o n of t h e a m p l i t u d e S 3 (A/ = ~}) r e l a t i v e t o S 1 (A[ = ½) u s i n g the relations FL(+_o) F + (+oo) - 1.97
S1 + 8 3
(the s i g n of y i s r e l a t i v e to A m ) . In t e r m s of r e l a t i v e p h a s e 2 ¢ b e t w e e n K ° a n d K ° a m p l i t u d e f o r 31r d e c a y s : = -(19 + - 933 ) d e g r e e s T h e l i m i t s w i t h 90% of c o n f i d e n c e a r e :
2
2 .
We get:
Re ($3/S1) = - 0 . 0 1 + 0 . 0 3 A f u r t h e r t e s t of t h e A l = ½ r u l e i s t h e c o m p a r i s o n of t h e m a t r i x e l e m e n t s f o r K ° L ~ v+lr-~ ° a n d K + ~ ~r+~°~ ° d e c a y s . A s s u m i n g a l i n e a r d e p e n d e n c e of t h e s q u a r e d matrix element
I MI 2 c~ 1-o~ TOr°)/mKO w h e r e T0r °) i s t h e k i n e t i c e n e r g y of t h e u n l i k e p i o n , we get: +0.9 - 1 . 1
This value is in agreement f r o m K + d e c a y [4]
T h e r a t i o of t h e r a t e s FS(+-o)/FL(+-o) i s 19. 0"16" w i t h 90% of c o n f i d e n c e t h e l i m i t i s •- - - 0 . 1 2 ' F S / F L ~< 0.45 In c o n c l u s i o n , t h e e x p e r i m e n t a l r e s u l t s a r e c o n s i s t e n t w i t h CP i n v a r i a n c e a n d g i v e a l i m i t f o r t h e p r e s e n c e of K ° S --* 37. T h e a g r e e m e n t w i t h t h e ~1 = ½ r u l e , a s s u m i n g CP c o n s e r v a t i o n , a p p e a r s t o b e q u i t e good. We w i s h t o t h a n k P r . A . L a g a r r i g u e , C . D i l worth, E. Fiorini for enlightening discussions, we a r e g r a t e f u l a l s o t o F. M a t t i o l i a n d C. M i a r i for their cooperation. W e a r e i n d e b t e d t o t h e C E R N P . S . Staff, t o the Ecole Polytechnique chamber team, to the C N A F c o m p u t i n g C e n t r e a n d to a l l s c a n n e r s , who made this experiment possible.
"
with that obtained
or+_ o = 7.55 ± 0 . 3 5 . A s s u m i n g n o w t h e v a l i d i t y of ~xI = ½ s e l e c t i o n r u l e , we c a n t e s t CP i n v a r i a n c e , w h i c h r e q u i r e s v a n i s h i n g of t h e only p a r a m e t e r y n o w a p p e a r i n g i n t h e e x p r e s s i o n (1).
542
y = -(0.34 + 0.19. 0.59 )
- 3 4 ° < ¢ < + 22 °
FL(OOO ) S1 + S3 F + (+oo) - 3.61 [S Z _ ~ 3
(~+-o = 7.7
1 September 1966
References 1. L . B e h r et al., Proc. Intern. Conf. Dubna 1964. 2. L . B e h r et al., P r o c . Intern. Conf. on Weak inter_ actions, Argonne 1965, p. 59. 3. J . H . C h r i s t e n s o n et a1., Phys. Rev. L e t t e r s 13 (1964) 138. 4. G . H . T r i l l i n g , P r o c . Intern. Conf. on Weak i n t e r actions, Argonne 1965, p. 115.