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Search for CP-violation in K0 → π+π−π0 decays
Volume 35B, number 3
PHYSICS
SEARCH
FOR
LETTERS
CP-VIOLATION
F. JAMES,
IN K °
24 M3y 1971
~
n+n-~ro DECAYS
L. MONTANET, E. PAUL, E. PAULI, P. SAETRE, D.M. SENDALL CERN, Geneva, Switzerland
G. B U R G U N , E. L E S Q U O Y , A. M U L L E R , S. Z Y L B E R A J C H
CEN, Saelay, France O. S K J E G G E S T A D
University of Oslo, Norway Received 16 April 1971
We have studied the time distribution of y+~-TT° decays of the neutral K meson produced in the reaction K+p ~K°p~+ with K+ momenta at 1.4 and 1.7 GeV/c. Withinour fidueial volume we have 98 unique[y identified ?r+?T-y° decnys with proper times between 0.04 and 20 Ks lifetimes. For the ratio ?/+-o of the nmplitude K ~ y+~-~ o to the nmplitude KL~ ~+~-7~o it is found that. Re 77+ = 0 01 :~022 • s
4
,
-
-o
•
0.20
'
Im 7+-0 = 0.33 :~ 0~52. This result is consistent with no CP-viol~tion. Assuming ~]---o = 0, we find the rute I~(KL ~ + y - T r °) = (2.5 ~0.3) 106 see-1.
The K s ~ ~+Tr-Tro decay can proceed e i t h e r a s a C P - v i o l a t i n g (CPV) t r a n s i t i o n to f i n a l - s t a t e s - w a v e pions or a s a C P - c o n s e r v i n g (CPC) t r a n s i t i o n to higher a n g u l a r m o m e n t u m s t a t e s . The l a t t e r t r a n s i t i o n i s strongly s u p p r e s s e d by a n g u l a r m o m e n t u m b a r r i e r s ; theoretical e s t i m a t e s [ i , 2] give a factor of the o r d e r of 10 -2 to 10 -4 for the ratio of the amplitudes (Ks ~ + T r - n O ) c pC to K L ~ 7r+Tr-no. Any observation of an appreciable e x c e s s of 3g decays at s h o r t t i m e s m u s t t h e r e f o r e be i n t e r p r e t e d a s due to a CPV transition. Starting at time t = 0 with a pure K o state and neglecting any CPC contribution to the Ks ~ ~+~-no decay we can define the p a r a m e t e r ~?+-o a s 7+-0 = Amplitude (Ks ~ n+Tr-~O)/Amplitude (KL ~ v+n-~o)
(i)
and obtain for the 3~ decay r a t e at time t the e x p r e s s i o n
N(t, 7+-0) = ½No F ( K L ~ ~+~-~°) [l 7+-0 [2 exp (-~t s t) + exp (-~t L t) + 2(Re 71+-o c o s 6t - I m
7?+-0 sin 6/) exp {-7( s + XL) t}]
w h e r e N o is the n u m b e r of KO's p r o d u c e d at t = 0, F(K L -4 n+~-Tro) is the d e c a y r a t e f o r K L - n + n - v o , k s and ~tL a r e the t o t a l d e c a y r a t e s f o r the K s and K L and 6 = m K L - i n K s . G l a s h o w and W e i n b e r g [3] h a v e p o i n t e d out that when the a m p l i t u d e s (K S-~ 3 n ) C P V and (KL-~ 3g)CPC a r e of c o m p a r a b l e m a g n i t u d e , then C P T i n v a r i a n c e and AI < 3 / 2 r e q u i r e the r e l a t i v e p h a s e of the a m 1 p l i t u d e s to be c l o s e to ~n, i . e . , Re 71+-o should be a p p r o x i m a t e l y z e r o . T h e n e u t r a l K - m e s o n s w e r e p r o d u c e d in the r e a c t i o n K+p ~ KOp n+ in the C E R N 2 m h y d r o g e n b u b b l e c h a m b e r . A b o u t 300 000 p i c t u r e s K + m o m e n t a of 1.4 and 1.7 G e V / c h a v e b e e n a n a l y z e d y i e l d i n g about 40 000 v i s i b l e K o d e c a y s . An a d d i t i o n a l 4 0 0 0 0 0 p i c t u r e s at 1.2 and 1.3 G e V / c a r e c u r r e n t l y b e i n g m e a s ured. T h e p i c t u r e s w e r e s c a n n e d t w i c e f o r V ' s p o s s i b l y a s s o c i a t e d with p r o d u c t i o n v e r t i c e s i n s i d e a f i d u c i a l v o l u m e that a l l o w e d at l e a s t 6 c m of m e a s u r a b l e l e n g t h f o r a l l t r a c k s . A l l V ' s that g a v e a t h r e e c o n s t r a i n t (3C) fit to the t w o - b o d y d e c a y K o ~ n+~- w e r e r e m o v e d f r o m the s a m p l e . T h e r e m a i n d e r w e r e e x a m i n e d by a p h y s i c i s t to r e m o v e o b v i o u s b a c k g r o u n d s u c h a s e l e c t r o n p a i r s , c h a r g e d K d e c a y s , and A d e c a y s . F o r the p o s s i b l e t h r e e - b o d y c a n d i d a t e s (about 1000) a 3 C - f i t w a s a t t e m p t e d to the h y p o t h e s i s K+p ~ KOp 7+ f o l l o w e d by a 1 C - f i t at the V v e r t e x f o r the f o l l o w i n g d e c a y m o d e s of the KO: ~+~-~o, ~+~-~, ~+l-v, and n-l+v, w h e r e l is a m u o n o r e l e c t r o n . We r e q u i r e d two good m e a s u r e m e n t s 265
Volume 35B, n u m b e r 3
PHYSICS L E T T E R S
2 4 M a y 1971
f o r e a c h of t h e s e t h r e e - b o d y c a n d i d a t e s , w h i c h w e r e c h e c k e d b y p h y s i c i s t s a t t h e s c a n t a b l e ; 115 e v e n t s g a v e a K o ~ ~ + 7 - 7 o fit. T o a v o i d l o s s of V ' s d e c a y i n g c l o s e to t h e i r o r i g i n a n d w h i c h c o u l d t h u s b e m i s s - s c a n n e d a s a f o u r prong event, all four-prongs were also measured. For those four-prong events that gave a kinematic f i t to t h e h y p o t h e s i s K+p ~ p 7 + ~ + ~ - 7 o we a l s o t r i e d t h e two h y p o t h e s e s c o r r e s p o n d i n g to K+p ~ p ~+K o f o l l o w e d b y K o ~ ~ + ~ - ~ o a n d t h e c a n d i d a t e s w e r e i n s p e c t e d b y p h y s i c i s t s f o r p o s s i b l e s e p a r a t i o n of p r o d u c t i o n a n d d e c a y v e r t i c e s . T h i s i n s p e c t i o n r e s u l t e d in n o K o --* 37 e v e n t a t l o n g e r d i s t a n c e s t h a n 0.2 c m f r o m t h e p r o d u c t i o n v e r t e x . W e h a v e t h e r e f o r e n o s c a n n i n g l o s s f o r V ' s a t s m a l l d i s t a n c e s if we m a k e a c u t a t a m i n i m u m K o l e n g t h of 0.3 c m . T h i s i s c o n f i r m e d f r o m a s t u d y of t h e l i f e t i m e of K o ~ ~ + ~ w h i c h d o e s n o t v a r y a s a f u n c t i o n of t h e m i n i m u m l e n g t h c u t p r o v i d e d t h i s c u t i s b i g g e r t h a n 0.2 c m . F o r o u r f i n a l s a m p l e of t h r e e - b o d y d e c a y s we i m p o s e d t h e f o l l o w i n g c r i t e r i a : a) T h e m e a s u r a b l e p r o j e c t e d l e n g t h s of b o t h c h a r g e d t r a c k s w e r e g r e a t e r t h a n 6 c m u n l e s s t h e r e w a s a measurable pion-proton scatter or 7 - ~ - e decay. b) T h e d i p a n g l e s of t h e K o a s w e l l a s of t h e c h a r g e d t r a c k s w e r e l e s s t h a n 70 ° a n d t h e p r o j e c t e d o p e n i n g a n g l e b e t w e e n t h e c h a r g e d t r a c k s of t h e V w a s l e s s t h a n 170 o. c) T h e p r o j e c t e d d i s t a n c e b e t w e e n p r o d u c t i o n a n d d e c a y p o i n t s w a s g r e a t e r t h a n 0.3 c m , a n d t h e m a x i m u m d i s t a n c e w a s 20 c m u p s t r e a m a n d 80 c m d o w n s t r e a m w i t h r e s p e c t to t h e i n c o m i n g K +. d) T h e K o m o m e n t u m a s d e t e r m i n e d f r o m t h e 3C p r o d u c t i o n f i t w a s g r e a t e r t h a n 100 M e V / c . e) T h e i o n i z a t i o n of t h e t r a c k s of t h e V w a s c o n s i s t e n t w i t h t h a t e x p e c t e d f o r p i o n s . A f t e r i m p o s i n g t h e s e c u t s , w e a r e l e f t w i t h 104 e v e n t s f i t t i n g t h e K ° ~ 7 + 7 - 7 ° h y p o t h e s i s . W e c o n s i d e r t h r e e p o s s i b l e s o u r c e s of c o n t a m i n a t i o n : T h r e e - b o d y d e c a y s , o t h e r t h a n 37, w h i c h s i m u l a t e a 7 + 7 - 7 ° d e c a y . T h e k i n e m a t i c a l c o n s t r a i n t s a r e such that no event is found ambiguous between the 7+7-~ o and the other three-body hypotheses. T w o - b o d y d e c a y s K o ~ ~ + ~ - w h e r e o n e of t h e p i o n s d e c a y s o r s c a t t e r s w i t h o u t l e a v i n g a v i s i b l e k i n k o r p r o t o n r e c o i l . W e h a v e a t t e m p t e d a 4 C - m u l t i v e r t e x f i t to t h e h y p o t h e s i s K+p ~ w+p K o (3C) f o l l o w e d b y K o ~ ~ (7) (1C) w h e r e o n e t r a c k of t h e V o i s i g n o r e d ; t h e s e f i t s w e r e u n s u c c e s s f u l f o r a l l o u r c a n d i dates. D a l i t z p a i r s f r o m t h e d e c a y K o ~ 7o7o. T h e e f f e c t i v e m a s s of e a c h V w a s c o m p u t e d , a s s u m i n g b o t h t r a c k s w e r e e l e c t r o n s . W e e l i m i n a t e d 6 e v e n t s f o r w h i c h t h e e f f e c t i v e m a s s w a s l e s s t h a n 135 M e V a n d f o r w h i c h t h e i o n i z a t i o n of b o t h t r a c k s of t h e V w a s c o n s i s t e n t w i t h t h e i r b e i n g e l e c t r o n s . T h i s l e a v e s a s a m p l e of 98 e v e n t s f o r t h e f i n a l a n a l y s i s * W e h a v e u s e d t h e m a x i m u m l i k e h o o d m e t h o d to e v a l u a t e 7 + - o a s d e f i n e d in eq. (1). T h e l i k e h o o d f u n c t i o n L(~?+_o) i s t h e p r o d u c t of t h e n o r m a l i s e d a p r i o r i p r o b a b i l i t i e s f o r e a c h e v e n t :
L('O+-o ) =
in]
i:l
N(li,~+_o)/j.tmaxN(t,~
"r/+-o)d/
/train
w h e r e n i s t h e n u m b e r of e v e n t s a n d t i i s t h e o b s e r v e d p r o p e r t i m e f o r t h e i t h e v e n t . F o r e a c h e v e n t t r a i n i s t h e t i m e d e t e r m i n e d b y t h e 0.3 c m m i n i m u m p r o j e c t e d l e n g t h , a n d t m a x i s t h e p o t e n t i a l t i m e d e t e r m i n e d b y a f i d u c i a l v o l u m e t h a t a l l o w s a t l e a s t 6 c m of o b s e r v a b l e p r o j e c t e d l e n g t h of b o t h t r a c k s f o r t h a t p a r t i c u l a r e v e n t , o r 20 K~ l i f e t i m e s , w h i c h e v e r i s s m a l l e r . In c a l c u l a t i n g N t h e f o l l o w i n g n u m e r i c a l v a l u e s of t h e c o n s t a n t s h a v e b e e n u s e d [4] 5 = 0.46 k S ,
kS = 1/TS = 1.16 X 1010 s e c -1 ,
kL = 1 / T L = 1.86 × 107 s e c - 1 .
T h e e r r o r in t h e d e t e r m i n a t i o n of t h e p r o p e r t i m e of t h e KO i s d o m i n a t e d b y t h e u n c e r t a i n t y in t h e K o m o m e n t u m w h i c h i s t y p i c a l l y 2%. T h e t i m e d i s t r i b u t i o n of o u r s a m p l e of K o ~ 7 + ~ - ~ o d e c a y s i s s h o w n in fig. 1. T h e s o l i d c u r v e , s h o w n f o r c o m p a r i s o n , i s t h e d i s t r i b u t i o n e x p e c t e d f o r 7/+-o = 0, a n d i s e s s e n t i a l l y o u r g e o m e t r i c d e t e c t i o n e f f i c i e n c y a s d e t e r m i n e d f r o m t h e t w o - b o d y K o -* 7+7 - d e c a y s . T h e d o t t e d c u r v e c o r r e s p o n d s to o u r b e s t e s t i m a t e of 7 + - o o b t a i n e d b y t h e m a x i m u m l i k e h o o d m e t h o d : 0.22 0.42 R e 7 + - o = 0.01 ± 0.20 I m ~?+-o = 0.33 + 0.50 * 50 of these events were included in r e s u l t s p r e s e n t e d at the Kiev Conference 1970. 266
Volume 35B, number 3 20
]
I
I
PHYSICS 1
98 events -
-
I
I
I
I
LETTERS
24 May 1971
I
I I I I I I I
1 l l i i i i
K% y + • - • o
1.2
98 events Ko _ •
"r}+. 0 =0
", I0 ~
- o
~Lmax
~ ~ o,~2'°Lrnax
0.4
o i
c
0
g-+
w
~-~ -0.4 0
]
I
I
2
4
6
I
S Time
I
I
I0
12
(units
of
I
I
14
16
18
20
T s) -1.2
Fig. 1. Time distribution of our decays K° ~ 7r+~-Tr°. The solid curve c o r r e s p o n d s to ?7+-o = 0 and the dotted curve to our fitted value. The detection efficiency d e t e r m i n e d from 6000 K° ~ ~r+Tr- is folded into the curves.
I
I
I
-1.2
I
I
[
i
-0.4
1 0
I 0.4
I
I
I
i 1.2
Re ~ +_0
Fig. 2. Maximum likelihood point and contours for L = e -0"5 Lma x and L = e -2 Lma x . T h e l i k e l i h o o d c o n t o u r p l o t i s s h o w n in f i g . 2 . O u r v a l u e i s c o m p a t i b l e w i t h no d e c a y K S ~ 3~, a n d a g r e e s w i t h t h e r e s u l t s f r o m e a r l i e r m e a s u r e m e n t s [ 5 - 1 0 ] . S i n c e o u r b e s t v a l u e of R e 77+-o i s s o c l o s e to z e r o , w e g e t e s s e n t i a l l y no c h a n g e in t h e v a l u e of I m 77+-o b y i m p o s i n g t h e c o n d i t i o n Re 77+_o = 0 [3]. A s c a n b e s e e n f r o m t h e c o n t o u r p l o t , fig. 2, t h e e r r o r in Im 77+_o w i l l a l s o b e u n a f f e c t e d . In fig. 3 a r e d i s p l a y e d t h e r e s u l t s on 77+-o f r o m a l l e x p e r i m e n t s k n o w n to us. T h e w e i g h t e d a v e r a g e of a l l p o i n t s d i s p l a y e d i s +0.22 R e ~?+-o = 0.08 - 0 . 2 4
+0.18 I m ~ + - o = 0.11 - 0 . 2 1
w h e r e t h e e r r o r on t h e r e a l p a r t c o n t a i n s a s c a l e f a c t o r of 1.9 a s d e f i n e d in r e f . [4]. If t h e v a l u e of r e f . [7] i s n o t i n c l u d e d , no s c a l e f a c t o r i s n e c e s s a r y a n d the a v e r a g e b e c o m e s +0.12 R e ~?+-o = 0.04 - 0 . 1 3
+0.18 I m ~?+-o = 0.07 - 0 . 2 2
A s s u m i n g no e v e n t K S ~ ~+~-~o w e c a n now c a l c u l a t e t h e a b s o l u t e r a t e of K L ~ ~ + n - ~ o , n o r m a l i s i n g to t h e n u m b e r of K ° ~ ~ + ~ - d e c a y s a n d u s i n g t h e g e o m e t r i c d e t e c t i o n e f f i c i e n c y c a l c u l a t e d f r o m t h e m . We find F ( K L - ~ + ~ - ~ ° ) = ( 2 . 5 ± 0 . 3 ) × 10 6 s e c - 1 .
2.0
'
I
i
I
'
I
this experl~at
1.0
E o g~
-I .0
-2.0 210
Ampl. (Kf-/r+lr - T*) ')~+-0 • Ampl.(Kc-/r÷-//-"W-e)
,
I - 1.0
,
, 0
I 1.0
,
[ 2.0
,
I 3.0
Re "r/+_0
Fig. 3. Comparison of our result with e a r l i e r e x p e r i m e n t s . A. Aubert et el., [8]. B. Abashian et al., [9]. C. Webber et al., [6]. D. C h o ~ t al., [10]. E. M e i s n e r e t el., [7]. 267
Volume 35B, number 3
PHYSICS
LETTERS
24 May 1971
T h i s v a l u e i s in good a g r e e m e n t w i t h t h e w o r l d a v e r a g e [4] a n d t h e v a l u e of F ( K L ~ ~+~-~o) = (2.44 + 0.10) 106 s e c -1 a s d e t e r m i n e d b y B u d a g o v e t al. [11]. It m a y b e n o t e d t h a t to i m p o s e t h e k n o w n r a t e F(K L ~ ~+~-~o) a s a c o n s t r a i n t on t h e m a x i m u m l i k e l i h o o d e s t i m a t e of 77+_o w i l l , in o u r e x p e r i m e n t , d e c r e a s e the e r r o r s on ~?+-o o n l y s l i g h t l y , a n d it h a s t h e e f f e c t of i n c r e a s i n g s o m e w h a t t h e c o r r e l a t i o n b e t w e e n R e ~?+-o a n d I m ~?+-o"
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
268
T.D. Lee and C.W. Wu, Ann. Rev. Nucl. Sci. 16 (1966) 471. S. E l i e z e r and P. Singer, Phys. Rev. 165 (1968) 1843. S. L. Glashow and S. Weinberg, Phys. Rev. L e t t e r s 14 {1965) 835. Review of P a r t i c l e P r o p e r t i e s , Rev. Mod. Phys. 42 (1970). L. Behr. V. Brisson, P. Petiau, E. Bellotti, A. Pullia, M. Baldo-Ceolin, E. Calameti, S. Ciampolillo, H. Huzita, A. Sconza, B. Aubert, M. Chounet, L . P . Lowys, P. Pascaud, Phys. L e t t e r s 22 (1966) 540. B. R. Webber, F. Solmitz, F. Crawford, M. Alston-Gain, Phys. Rev. 1D (1970) 1967. G.W. Meisner et al., Phys. Rev. 3D (1971) 59. J. J. Aubert et al., Kiev Conf. Report (1970). A.Abashian et al., Kiev Conf. Report (1970). Y. Cho et al., BNL-Report 15468 (Phys. Rev., to be published). I. A. Budagov, It. B u r m e i s t e r , O. Cundy, W. Krenz, G. Myatt, B. Aubert, P. Heusse, I. Le Dong, E. Nagy, P. Pascaud, L. Behr, P. Beillere, G. Boutang, J. Van der Velde, Nuovo Cimento 57A (1968)182.
PHYSICS
SEARCH
FOR
LETTERS
CP-VIOLATION
F. JAMES,
IN K °
24 M3y 1971
~
n+n-~ro DECAYS
L. MONTANET, E. PAUL, E. PAULI, P. SAETRE, D.M. SENDALL CERN, Geneva, Switzerland
G. B U R G U N , E. L E S Q U O Y , A. M U L L E R , S. Z Y L B E R A J C H
CEN, Saelay, France O. S K J E G G E S T A D
University of Oslo, Norway Received 16 April 1971
We have studied the time distribution of y+~-TT° decays of the neutral K meson produced in the reaction K+p ~K°p~+ with K+ momenta at 1.4 and 1.7 GeV/c. Withinour fidueial volume we have 98 unique[y identified ?r+?T-y° decnys with proper times between 0.04 and 20 Ks lifetimes. For the ratio ?/+-o of the nmplitude K ~ y+~-~ o to the nmplitude KL~ ~+~-7~o it is found that. Re 77+ = 0 01 :~022 • s
4
,
-
-o
•
0.20
'
Im 7+-0 = 0.33 :~ 0~52. This result is consistent with no CP-viol~tion. Assuming ~]---o = 0, we find the rute I~(KL ~ + y - T r °) = (2.5 ~0.3) 106 see-1.
The K s ~ ~+Tr-Tro decay can proceed e i t h e r a s a C P - v i o l a t i n g (CPV) t r a n s i t i o n to f i n a l - s t a t e s - w a v e pions or a s a C P - c o n s e r v i n g (CPC) t r a n s i t i o n to higher a n g u l a r m o m e n t u m s t a t e s . The l a t t e r t r a n s i t i o n i s strongly s u p p r e s s e d by a n g u l a r m o m e n t u m b a r r i e r s ; theoretical e s t i m a t e s [ i , 2] give a factor of the o r d e r of 10 -2 to 10 -4 for the ratio of the amplitudes (Ks ~ + T r - n O ) c pC to K L ~ 7r+Tr-no. Any observation of an appreciable e x c e s s of 3g decays at s h o r t t i m e s m u s t t h e r e f o r e be i n t e r p r e t e d a s due to a CPV transition. Starting at time t = 0 with a pure K o state and neglecting any CPC contribution to the Ks ~ ~+~-no decay we can define the p a r a m e t e r ~?+-o a s 7+-0 = Amplitude (Ks ~ n+Tr-~O)/Amplitude (KL ~ v+n-~o)
(i)
and obtain for the 3~ decay r a t e at time t the e x p r e s s i o n
N(t, 7+-0) = ½No F ( K L ~ ~+~-~°) [l 7+-0 [2 exp (-~t s t) + exp (-~t L t) + 2(Re 71+-o c o s 6t - I m
7?+-0 sin 6/) exp {-7( s + XL) t}]
w h e r e N o is the n u m b e r of KO's p r o d u c e d at t = 0, F(K L -4 n+~-Tro) is the d e c a y r a t e f o r K L - n + n - v o , k s and ~tL a r e the t o t a l d e c a y r a t e s f o r the K s and K L and 6 = m K L - i n K s . G l a s h o w and W e i n b e r g [3] h a v e p o i n t e d out that when the a m p l i t u d e s (K S-~ 3 n ) C P V and (KL-~ 3g)CPC a r e of c o m p a r a b l e m a g n i t u d e , then C P T i n v a r i a n c e and AI < 3 / 2 r e q u i r e the r e l a t i v e p h a s e of the a m 1 p l i t u d e s to be c l o s e to ~n, i . e . , Re 71+-o should be a p p r o x i m a t e l y z e r o . T h e n e u t r a l K - m e s o n s w e r e p r o d u c e d in the r e a c t i o n K+p ~ KOp n+ in the C E R N 2 m h y d r o g e n b u b b l e c h a m b e r . A b o u t 300 000 p i c t u r e s K + m o m e n t a of 1.4 and 1.7 G e V / c h a v e b e e n a n a l y z e d y i e l d i n g about 40 000 v i s i b l e K o d e c a y s . An a d d i t i o n a l 4 0 0 0 0 0 p i c t u r e s at 1.2 and 1.3 G e V / c a r e c u r r e n t l y b e i n g m e a s ured. T h e p i c t u r e s w e r e s c a n n e d t w i c e f o r V ' s p o s s i b l y a s s o c i a t e d with p r o d u c t i o n v e r t i c e s i n s i d e a f i d u c i a l v o l u m e that a l l o w e d at l e a s t 6 c m of m e a s u r a b l e l e n g t h f o r a l l t r a c k s . A l l V ' s that g a v e a t h r e e c o n s t r a i n t (3C) fit to the t w o - b o d y d e c a y K o ~ n+~- w e r e r e m o v e d f r o m the s a m p l e . T h e r e m a i n d e r w e r e e x a m i n e d by a p h y s i c i s t to r e m o v e o b v i o u s b a c k g r o u n d s u c h a s e l e c t r o n p a i r s , c h a r g e d K d e c a y s , and A d e c a y s . F o r the p o s s i b l e t h r e e - b o d y c a n d i d a t e s (about 1000) a 3 C - f i t w a s a t t e m p t e d to the h y p o t h e s i s K+p ~ KOp 7+ f o l l o w e d by a 1 C - f i t at the V v e r t e x f o r the f o l l o w i n g d e c a y m o d e s of the KO: ~+~-~o, ~+~-~, ~+l-v, and n-l+v, w h e r e l is a m u o n o r e l e c t r o n . We r e q u i r e d two good m e a s u r e m e n t s 265
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f o r e a c h of t h e s e t h r e e - b o d y c a n d i d a t e s , w h i c h w e r e c h e c k e d b y p h y s i c i s t s a t t h e s c a n t a b l e ; 115 e v e n t s g a v e a K o ~ ~ + 7 - 7 o fit. T o a v o i d l o s s of V ' s d e c a y i n g c l o s e to t h e i r o r i g i n a n d w h i c h c o u l d t h u s b e m i s s - s c a n n e d a s a f o u r prong event, all four-prongs were also measured. For those four-prong events that gave a kinematic f i t to t h e h y p o t h e s i s K+p ~ p 7 + ~ + ~ - 7 o we a l s o t r i e d t h e two h y p o t h e s e s c o r r e s p o n d i n g to K+p ~ p ~+K o f o l l o w e d b y K o ~ ~ + ~ - ~ o a n d t h e c a n d i d a t e s w e r e i n s p e c t e d b y p h y s i c i s t s f o r p o s s i b l e s e p a r a t i o n of p r o d u c t i o n a n d d e c a y v e r t i c e s . T h i s i n s p e c t i o n r e s u l t e d in n o K o --* 37 e v e n t a t l o n g e r d i s t a n c e s t h a n 0.2 c m f r o m t h e p r o d u c t i o n v e r t e x . W e h a v e t h e r e f o r e n o s c a n n i n g l o s s f o r V ' s a t s m a l l d i s t a n c e s if we m a k e a c u t a t a m i n i m u m K o l e n g t h of 0.3 c m . T h i s i s c o n f i r m e d f r o m a s t u d y of t h e l i f e t i m e of K o ~ ~ + ~ w h i c h d o e s n o t v a r y a s a f u n c t i o n of t h e m i n i m u m l e n g t h c u t p r o v i d e d t h i s c u t i s b i g g e r t h a n 0.2 c m . F o r o u r f i n a l s a m p l e of t h r e e - b o d y d e c a y s we i m p o s e d t h e f o l l o w i n g c r i t e r i a : a) T h e m e a s u r a b l e p r o j e c t e d l e n g t h s of b o t h c h a r g e d t r a c k s w e r e g r e a t e r t h a n 6 c m u n l e s s t h e r e w a s a measurable pion-proton scatter or 7 - ~ - e decay. b) T h e d i p a n g l e s of t h e K o a s w e l l a s of t h e c h a r g e d t r a c k s w e r e l e s s t h a n 70 ° a n d t h e p r o j e c t e d o p e n i n g a n g l e b e t w e e n t h e c h a r g e d t r a c k s of t h e V w a s l e s s t h a n 170 o. c) T h e p r o j e c t e d d i s t a n c e b e t w e e n p r o d u c t i o n a n d d e c a y p o i n t s w a s g r e a t e r t h a n 0.3 c m , a n d t h e m a x i m u m d i s t a n c e w a s 20 c m u p s t r e a m a n d 80 c m d o w n s t r e a m w i t h r e s p e c t to t h e i n c o m i n g K +. d) T h e K o m o m e n t u m a s d e t e r m i n e d f r o m t h e 3C p r o d u c t i o n f i t w a s g r e a t e r t h a n 100 M e V / c . e) T h e i o n i z a t i o n of t h e t r a c k s of t h e V w a s c o n s i s t e n t w i t h t h a t e x p e c t e d f o r p i o n s . A f t e r i m p o s i n g t h e s e c u t s , w e a r e l e f t w i t h 104 e v e n t s f i t t i n g t h e K ° ~ 7 + 7 - 7 ° h y p o t h e s i s . W e c o n s i d e r t h r e e p o s s i b l e s o u r c e s of c o n t a m i n a t i o n : T h r e e - b o d y d e c a y s , o t h e r t h a n 37, w h i c h s i m u l a t e a 7 + 7 - 7 ° d e c a y . T h e k i n e m a t i c a l c o n s t r a i n t s a r e such that no event is found ambiguous between the 7+7-~ o and the other three-body hypotheses. T w o - b o d y d e c a y s K o ~ ~ + ~ - w h e r e o n e of t h e p i o n s d e c a y s o r s c a t t e r s w i t h o u t l e a v i n g a v i s i b l e k i n k o r p r o t o n r e c o i l . W e h a v e a t t e m p t e d a 4 C - m u l t i v e r t e x f i t to t h e h y p o t h e s i s K+p ~ w+p K o (3C) f o l l o w e d b y K o ~ ~ (7) (1C) w h e r e o n e t r a c k of t h e V o i s i g n o r e d ; t h e s e f i t s w e r e u n s u c c e s s f u l f o r a l l o u r c a n d i dates. D a l i t z p a i r s f r o m t h e d e c a y K o ~ 7o7o. T h e e f f e c t i v e m a s s of e a c h V w a s c o m p u t e d , a s s u m i n g b o t h t r a c k s w e r e e l e c t r o n s . W e e l i m i n a t e d 6 e v e n t s f o r w h i c h t h e e f f e c t i v e m a s s w a s l e s s t h a n 135 M e V a n d f o r w h i c h t h e i o n i z a t i o n of b o t h t r a c k s of t h e V w a s c o n s i s t e n t w i t h t h e i r b e i n g e l e c t r o n s . T h i s l e a v e s a s a m p l e of 98 e v e n t s f o r t h e f i n a l a n a l y s i s * W e h a v e u s e d t h e m a x i m u m l i k e h o o d m e t h o d to e v a l u a t e 7 + - o a s d e f i n e d in eq. (1). T h e l i k e h o o d f u n c t i o n L(~?+_o) i s t h e p r o d u c t of t h e n o r m a l i s e d a p r i o r i p r o b a b i l i t i e s f o r e a c h e v e n t :
L('O+-o ) =
in]
i:l
N(li,~+_o)/j.tmaxN(t,~
"r/+-o)d/
/train
w h e r e n i s t h e n u m b e r of e v e n t s a n d t i i s t h e o b s e r v e d p r o p e r t i m e f o r t h e i t h e v e n t . F o r e a c h e v e n t t r a i n i s t h e t i m e d e t e r m i n e d b y t h e 0.3 c m m i n i m u m p r o j e c t e d l e n g t h , a n d t m a x i s t h e p o t e n t i a l t i m e d e t e r m i n e d b y a f i d u c i a l v o l u m e t h a t a l l o w s a t l e a s t 6 c m of o b s e r v a b l e p r o j e c t e d l e n g t h of b o t h t r a c k s f o r t h a t p a r t i c u l a r e v e n t , o r 20 K~ l i f e t i m e s , w h i c h e v e r i s s m a l l e r . In c a l c u l a t i n g N t h e f o l l o w i n g n u m e r i c a l v a l u e s of t h e c o n s t a n t s h a v e b e e n u s e d [4] 5 = 0.46 k S ,
kS = 1/TS = 1.16 X 1010 s e c -1 ,
kL = 1 / T L = 1.86 × 107 s e c - 1 .
T h e e r r o r in t h e d e t e r m i n a t i o n of t h e p r o p e r t i m e of t h e KO i s d o m i n a t e d b y t h e u n c e r t a i n t y in t h e K o m o m e n t u m w h i c h i s t y p i c a l l y 2%. T h e t i m e d i s t r i b u t i o n of o u r s a m p l e of K o ~ 7 + ~ - ~ o d e c a y s i s s h o w n in fig. 1. T h e s o l i d c u r v e , s h o w n f o r c o m p a r i s o n , i s t h e d i s t r i b u t i o n e x p e c t e d f o r 7/+-o = 0, a n d i s e s s e n t i a l l y o u r g e o m e t r i c d e t e c t i o n e f f i c i e n c y a s d e t e r m i n e d f r o m t h e t w o - b o d y K o -* 7+7 - d e c a y s . T h e d o t t e d c u r v e c o r r e s p o n d s to o u r b e s t e s t i m a t e of 7 + - o o b t a i n e d b y t h e m a x i m u m l i k e h o o d m e t h o d : 0.22 0.42 R e 7 + - o = 0.01 ± 0.20 I m ~?+-o = 0.33 + 0.50 * 50 of these events were included in r e s u l t s p r e s e n t e d at the Kiev Conference 1970. 266
Volume 35B, number 3 20
]
I
I
PHYSICS 1
98 events -
-
I
I
I
I
LETTERS
24 May 1971
I
I I I I I I I
1 l l i i i i
K% y + • - • o
1.2
98 events Ko _ •
"r}+. 0 =0
", I0 ~
- o
~Lmax
~ ~ o,~2'°Lrnax
0.4
o i
c
0
g-+
w
~-~ -0.4 0
]
I
I
2
4
6
I
S Time
I
I
I0
12
(units
of
I
I
14
16
18
20
T s) -1.2
Fig. 1. Time distribution of our decays K° ~ 7r+~-Tr°. The solid curve c o r r e s p o n d s to ?7+-o = 0 and the dotted curve to our fitted value. The detection efficiency d e t e r m i n e d from 6000 K° ~ ~r+Tr- is folded into the curves.
I
I
I
-1.2
I
I
[
i
-0.4
1 0
I 0.4
I
I
I
i 1.2
Re ~ +_0
Fig. 2. Maximum likelihood point and contours for L = e -0"5 Lma x and L = e -2 Lma x . T h e l i k e l i h o o d c o n t o u r p l o t i s s h o w n in f i g . 2 . O u r v a l u e i s c o m p a t i b l e w i t h no d e c a y K S ~ 3~, a n d a g r e e s w i t h t h e r e s u l t s f r o m e a r l i e r m e a s u r e m e n t s [ 5 - 1 0 ] . S i n c e o u r b e s t v a l u e of R e 77+-o i s s o c l o s e to z e r o , w e g e t e s s e n t i a l l y no c h a n g e in t h e v a l u e of I m 77+-o b y i m p o s i n g t h e c o n d i t i o n Re 77+_o = 0 [3]. A s c a n b e s e e n f r o m t h e c o n t o u r p l o t , fig. 2, t h e e r r o r in Im 77+_o w i l l a l s o b e u n a f f e c t e d . In fig. 3 a r e d i s p l a y e d t h e r e s u l t s on 77+-o f r o m a l l e x p e r i m e n t s k n o w n to us. T h e w e i g h t e d a v e r a g e of a l l p o i n t s d i s p l a y e d i s +0.22 R e ~?+-o = 0.08 - 0 . 2 4
+0.18 I m ~ + - o = 0.11 - 0 . 2 1
w h e r e t h e e r r o r on t h e r e a l p a r t c o n t a i n s a s c a l e f a c t o r of 1.9 a s d e f i n e d in r e f . [4]. If t h e v a l u e of r e f . [7] i s n o t i n c l u d e d , no s c a l e f a c t o r i s n e c e s s a r y a n d the a v e r a g e b e c o m e s +0.12 R e ~?+-o = 0.04 - 0 . 1 3
+0.18 I m ~?+-o = 0.07 - 0 . 2 2
A s s u m i n g no e v e n t K S ~ ~+~-~o w e c a n now c a l c u l a t e t h e a b s o l u t e r a t e of K L ~ ~ + n - ~ o , n o r m a l i s i n g to t h e n u m b e r of K ° ~ ~ + ~ - d e c a y s a n d u s i n g t h e g e o m e t r i c d e t e c t i o n e f f i c i e n c y c a l c u l a t e d f r o m t h e m . We find F ( K L - ~ + ~ - ~ ° ) = ( 2 . 5 ± 0 . 3 ) × 10 6 s e c - 1 .
2.0
'
I
i
I
'
I
this experl~at
1.0
E o g~
-I .0
-2.0 210
Ampl. (Kf-/r+lr - T*) ')~+-0 • Ampl.(Kc-/r÷-//-"W-e)
,
I - 1.0
,
, 0
I 1.0
,
[ 2.0
,
I 3.0
Re "r/+_0
Fig. 3. Comparison of our result with e a r l i e r e x p e r i m e n t s . A. Aubert et el., [8]. B. Abashian et al., [9]. C. Webber et al., [6]. D. C h o ~ t al., [10]. E. M e i s n e r e t el., [7]. 267
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24 May 1971
T h i s v a l u e i s in good a g r e e m e n t w i t h t h e w o r l d a v e r a g e [4] a n d t h e v a l u e of F ( K L ~ ~+~-~o) = (2.44 + 0.10) 106 s e c -1 a s d e t e r m i n e d b y B u d a g o v e t al. [11]. It m a y b e n o t e d t h a t to i m p o s e t h e k n o w n r a t e F(K L ~ ~+~-~o) a s a c o n s t r a i n t on t h e m a x i m u m l i k e l i h o o d e s t i m a t e of 77+_o w i l l , in o u r e x p e r i m e n t , d e c r e a s e the e r r o r s on ~?+-o o n l y s l i g h t l y , a n d it h a s t h e e f f e c t of i n c r e a s i n g s o m e w h a t t h e c o r r e l a t i o n b e t w e e n R e ~?+-o a n d I m ~?+-o"
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
268
T.D. Lee and C.W. Wu, Ann. Rev. Nucl. Sci. 16 (1966) 471. S. E l i e z e r and P. Singer, Phys. Rev. 165 (1968) 1843. S. L. Glashow and S. Weinberg, Phys. Rev. L e t t e r s 14 {1965) 835. Review of P a r t i c l e P r o p e r t i e s , Rev. Mod. Phys. 42 (1970). L. Behr. V. Brisson, P. Petiau, E. Bellotti, A. Pullia, M. Baldo-Ceolin, E. Calameti, S. Ciampolillo, H. Huzita, A. Sconza, B. Aubert, M. Chounet, L . P . Lowys, P. Pascaud, Phys. L e t t e r s 22 (1966) 540. B. R. Webber, F. Solmitz, F. Crawford, M. Alston-Gain, Phys. Rev. 1D (1970) 1967. G.W. Meisner et al., Phys. Rev. 3D (1971) 59. J. J. Aubert et al., Kiev Conf. Report (1970). A.Abashian et al., Kiev Conf. Report (1970). Y. Cho et al., BNL-Report 15468 (Phys. Rev., to be published). I. A. Budagov, It. B u r m e i s t e r , O. Cundy, W. Krenz, G. Myatt, B. Aubert, P. Heusse, I. Le Dong, E. Nagy, P. Pascaud, L. Behr, P. Beillere, G. Boutang, J. Van der Velde, Nuovo Cimento 57A (1968)182.