Volume 20, number 2
PHYSICS LETTERS
K S AND K L INTERFERENCE
CP INVARIANCE
AND THE
1 February 1966
IN THE y+y- DECAY MODE,
Ks-K L MASS DIFFERENCE
C. A L F F - S T E I N B E R G E R , W. HEUER *, K. KLEINKNECHT **, C. RUBBIA, A. SCRIBANO ***
J. STEINBERGER t, M . J . TANNENBAUM t t and K. T I T T E L *
CERN, Geneva
Received 28 December 1965
We r e p o r t h e r e i n i t i a l r e s u l t s of e x p e r i m e n t s
in which we study the i n t e r f e r e n c e of K~ and I ~L
m e s o n s in the t i m e dependence of the i n t e n s i t y
of the ~+~- decay mode. The i n t e r e s t in the exp e r i m e n t s l i e s in the fact that on the one hand
they p e r m i t a s e n s i t i v e check on the validity of
the i n t e r p r e t a t i o n of the e x p e r i m e n t of C h r i s t e n son et al. [1] in t e r m s of CP violation and on the
other hand, if i n t e r f e r e n c e is found, they p e r m i t
d e t e r m i n a t i o n of the K s - K L m a s s difference as
well as the r e l a t i v e phase of the ~+lr- decay a m plitudes of KS and K L m e s o n s . Indication of the
e x i s t e n c e of the i n t e r f e r e n c e has been p r e s e n t e d
by F i t c h et al. [2].
In the e x p e r i m e n t r e p o r t e d h e r e we study the
~+~- decay as a function of d i s t a n c e f r o m a plate
of copper placed in a n e u t r a l b e a m at a distance
(33 m e t r e s ) such that the s h o r t - l i v e d component
has decayed to a n e g l i g i b l e level. In the copper,
a s h o r t - l i v e d component of the K° is r e g e n e r a t e d ,
so that the i n t e n s i t y of the ~+y- decay following
the r e g e n e r a t o r is expected to have the following
f o r m , if the i n t e r p r e t a t i o n of the C h r i s t e n s o n exp e r i m e n t [1] in t e r m s of K L -~ ~+~- decay and
CP violation is c o r r e c t :
f + ( 7 ) = t o [ I P l 2 e ' r s r + 17t 2 e - r L T +
(1)
+ 2 IPll 7 ] c o s (9 0 - 9 7 + a m r ) e - ½ ( r s + r L ) ~ ] ,
where I+_ (7) is the y+~" decay i n t e n s i t y ; ~- is the
p r o p e r time of the Ko at the i n s t a n t of decay: r is
r e l a t e d to the d i s t a n c e z f r o m the d o w n s t r e a m
edge of the r e g e n e r a t o r "r = m K Z / P K , where m K
and PK a r e the kaon m a s s and m o m e n t u m , r e * Visitor from III. Phys. Inst. tier TH, Aachen.
** Visitor from Max-Planck Inst. f. Kernphysik,
Heidelberg.
*** Visitor from Istituto di Fisica dell'UniversitY,
Pisa.
t On leave from Columbia University, New York.
## Ernest Kempton Adams Fellow.
spectively; p = IP Ie i 9 p is the amplitude of the
t r a n s m i s . s i o n r e g e n e r a t e d KS r e l a t i v e to the KL;
77 = 171e197 is the r a t i o of the decay a m p l i t u d e s
(KL -~ ~+~-)/(KS ~ ~+y-); Am = m L - mS is the
m a s s difference of the K L and KS m e s o n s .
A plan view of the d e t e c t o r for the two pions
is shown in fig. 1. It c o n s i s t s of an e l e c t r o n i c
t r i g g e r i n g a r r a n g e m e n t , and a m a g n e t and s p a r k
c h a m b e r s for the m e a s u r e m e n t of the two m o m e n ta. The t r i g g e r i n g c o u n t e r s c o n s i s t of a 5 m m
thick a n t i c o i n c i d e n c e counter d i r e c t l y behind the
r e g e n e r a t o r , a 2 m m thick coincidence counter
before the s p a r k c h a m b e r and m a g n e t a r r a n g e ment, and 10 n a r r o w c h a n n e l s of 3 c o u n t e r s each,
which s e l e c t t r a c k s whose h o r i z o n t a l m o m e n t u m
p r o j e c t i o n i s p a r a l l e l to the b e a m to within ± 1°
after the magnet. The magnet c u r r e n t is adjusted
so that p a r t i c l e s , whose h o r i z o n t a l t r a n s v e r s e
m o m e n t u m component is n e a r 206 M e V / c (the
m a x i m u m for K -~ v+y- decay), a r e bent n e a r l y
p a r a l l e l to the beam. This condition is independent of K m o m e n t u m , and the a c c e p t a n c e in space
is u n i f o r m except for l i m i t a t i o n s of the m a g n e t
a p e r t u r e . The leptonic K decays, which constitute
the d o m i n a n t background, in g e n e r a l do not m e e t
this condition. The leptonic a c c e p t a n c e s a r e typically 30 to 100 t i m e s s m a l l e r than the pion acceptances. The hodoscope is followed in s u c c e s sion by an e l e c t r o n shower detector, 50 cm of i r o n
and two c o u n t e r s in coincidence to detect the s u r v i v o r s , now p r e d o m i n a n t l y muons. The muon
counter p u l s e s , as well as pulse heights in the
shower detector, a r e r e c o r d e d on f i l m together
with the s p a r k c h a m b e r t r a c k s ; however, this inf o r m a t i o n is not u t i l i z e d in the p r e s e n t r e p o r t .
The e x p e r i m e n t c o n s i s t of t h r e e p a r t s which
differ in the type of r e g e n e r a t o r :
P a r t I: no r e g e n e r a t o r ;
P a r t II: r e g e n e r a t o r 12 cm copper of d e n s i t y
8.9 g / c c ;
P a r t IH: r e g e n e r a t o r of the s a m e d i m e n s i o n s
as in p a r t II, but c o n s i s t i n g of 0.5 m m
207
V o l u m e 20, n u m b e r 2
PHYSICS
LETTERS
1February
1966
SCINTILLATION
COUNTERS
ANTI
COUNTER
COINCIDENCE
COUNTER
,
II Ihlll,ld
'
U,,,,,,,
\\
BOUNDARIL~
OF FIDUCIAL
REGION
-
ilttl'lll
SPARK
CHAMBERS
REGENERATOR
10 CHANNEL SCINTILLATION
COUNTER HODOSCOPE
ELECTRON
DETECTOR
MUON
DETECTOR
F i g . 1. P l a n v i e w of t h e d e t e c t o r .
copper s h e e t s s p a c e d 0.8 c m a p a r t ,
so that the a v e r a g e d e n s i t y is 0.55
g/ca.
P a r t IH c o n s i s t s of two r u n s of r o u g h l y eq u al
duration. In IIIa the r e g e n e r a t o r p o s i t i o n is the
s a m e as in p a r t II and as shown in fig. 1; in IIIb
the r e g e n e r a t o r and a n t i c o u n t e r a r e d i s p l a c e d
38 c m d o w n s t r e a m . The r e a s o n f o r c h o o s i n g the
s a m e p h y s i c a l d i m e n s i o n s for p a r t II and p a r t HI
is that in this way the r e l a t i v e p h a s e of r e g e n e r a t e d K S to t r a n s m i t t e d K L is the s a m e in the two
cases.
In a p r e l i m i n a r y e x p o s u r e in a n e u t r a l b e a m at
24 ° with r e s p e c t to 20 GeV/c p r o t o n s s t r i k i n g an
i n t e r n a l t a r g e t , about 40 000 e v e n t s w e r e r e c o r d e d . The r e s u l t s p r e s e n t e d h e r e a r e b a s e d
on a p p r o x i m a t e l y o n e - h a l f of t h e s e e v e n t s . E a c h
p i c t u r e which contained two t r a c k s in e a c h c h a m b e r was m e a s u r e d . The V was s p a t i a l l y r e c o n s t r u c t e d , and e v e n t s outside a f i d u c i a l v o l u m e
1 c m inside the s u r f a c e d e t e r m i n e d by the antic o u n t e r and c o i n c i d e n c e c o u n t e r (see fig. 1) w e r e
dropped. We now c a l c u l a t e the i n v a r i a n t m a s s ,
b a s e d on pion m a s s e s f o r the two o b s e r v e d t r a c k s :
m2 = (E++E_)2 _ (p++p_)2
E+, - = m2 + p2"Jr,- "
The d i s t r i b u t i o n s f o r the t h r e e c o n v e r t e r condit i o n s a r e shown in fig. 2a. In the c a s e of the
d e n s e c o n v e r t e r , p r a c t i c a l l y all e v e n t s a r e conc e n t r a t e d at the K m a s s , showing that the y+~d ecay d o m i n a t e s . In the o th e r two c a s e s t h e r e is
a s u b s t a n t i a l b a c k g r o u n d of leptonic d e c a y s , but
208
the t w o - p i o n peak is v i s i b l e . The i m p r o v e m e n t
in technique r e p r e s e n t e d by this g e o m e t r y is
c l e a r if t h e s e d i s t r i b u t i o n s a r e c o m p a r e d with
the c o r r e s p o n d i n g d i s t r i b u t i o n of C h r i s t e n s o n et
al. [1].
We now drop all e v e n t s outside the m a s s int e r v a l 491 < m < 509 MeV, and show the d i s t r i butions in the an g u l ar v a r i a b l e ot = 105[(px/p) 2 +
+ (py/2p)2] in fig. 2b. H e r e Px and py are the
h o r i z o n t a l and v e r t i c a l components of the total
m o m e n t u m p = p+ +p_, t r a n s v e r s e to the K °
b e a m . The f a c t o r of ½ is included b e c a u s e the
v e r t i c a l an g u l ar m e a s u r e m e n t e r r o r is twice that
of the h o r i z o n t a l . In all t h r e e c a s e s t h e r e is a
n a r r o w angular peak, due p r e s u m a b l y to c o h e r e n t
K --* v+y- decay, and a b r o a d b a c k g r o u n d of leptonic d e c a y s , n e u t r o n s t a r s and, in the c a s e s
with r e g e n e r a t o r , d i f f r a c t i o n s c a t t e r e d I~ s decaying to y+ + ~ - .
F o r the following d i s c u s s i o n we have e x t r a c t e d
the c o h e r e n t K ~ ~+y- r a t e s by taking the numb e r of e v e n t s with a < 3 and s u b t r a c t i n g o n e - h a l f
of the e v e n t s in the i n t e r v a l 4 < ~ < 10. The data
have been divided into p r o p e r t i m e - b i n s and a r e
shown in fig. 3. The t i m e - d e p e n d e n t e f f i c i e n c y
functions ( a r b i t r a r i l y n o r m a l i z e d ) a r e a l s o shown.
They a r e b a s e d on the m o m e n t u m s p e c t r u m of the
kaons o b s e r v e d with the thick r e g e n e r a t o r , and
Monte C a r l o c a l c u l a t i o n s of the g e o m e t r i c a l ac cep t an ce.
If the o r i g i n a l i n t e r p r e t a t i o n of the e x p e r i m e n t
of C h r i s t e n s o n et al., in t e r m s of a K L ~ lr+y d e c a y which v i o l a t e s C P i n v a r i a a c e , is c o r r e c t ,
then it should be p o s s i b l e to fit the t h r e e t i m e d i s t r i b u t i o n s with t h r e e functions of the f o r m (1)
V o l u m e 20, n u m b e r 2
PHYSICS
HEAVY REGENERATOR
LETTERS
1February1966
LIGHT REGENERATOR 50I
61111
NO REGENERATOR
IOO
400
50
21Xt
Z
W
hi
U.
.48
.50
.48
.52
.50
m
o
,~
.52
.50
.52
I00
IE
z
50
100
0
5
15
10
0
5
10
15
5
0
15
1o
o(
F i g . 2a. M a s s d i s t r i b u t i o n s f o r t h e t h r e e c o n v e r t e r c o n d i t i o n s . U n i t s a r e i n GeV.
F i g . 2b. A n g u l a r d i s t r i b u t i o n s f o r the t h r e e c o n v e r t e r c o n d i t i o n s . F o r t he d e f i n i t i o n of ot s e e t e x t .
DENSE REGENERATOR
LIGHT REGENERATOR
NO REGENERATOR
Interference. Best Fit
No Interference. Best Fit
Calculated Efficiency
"%
' r2_
•
~..
~
'-+, 1"-4.
8~
I
I
2
3
4
5
" ~ , ,,
6
7
! ,
0
I
!
I
2
l
3
IN UNITSOF
I
4
5
6
7
I
I
i
2
[
3
I
6
I
5
i
6
I
I
7 II
10"10 sec
F i g . 3. O b s e r v e d K--* 7T+Y- d e c a y r a t e a s a f u n c t i o n of p r o p e r t i m e . T h e b e s t f i t s o l u t i o n s f o r t h e
c a s e s of i n t e r f e r e n c e a n d no i n t e r f e r e n c e a r e s h o w n , a s w e l l a s t h e c a l c u l a t e d e f f i c i e n e i e s .
209
Volume 20, number 2
PHYSICS LETTERS
1 February 1966
Fi(r) = MiEi('r)llpi[2e-FsT + ]Y12 e-FUr + (2)
""
+ 2 }pill~le -~(FL+rs)~" cos (9 + ~mr)j~ ,
where M i a r e the e x p o s u r e s c o r r e c t e d for n u c l e a r
a t t e n u a t i o n in the c o n v e r t e r ; ei('r ) a r e the effic i e n c i e s ; Pl = 0; P3 = P 2 / 1 6 . 1 5 is the r e g e n e r a tion amplitude in the light r e g e n e r a t o r ; P2 =
IP21 exp iq~p is the r e g e n e r a t i o n amplitude in the
dense r e g e n e r a t o r , and ¢ = C p - ~,~.
{P2 {, 17 I, Am and q~ a r e c o n s i d e r e d f r e e to
be chosen in such a way as to give the best poss i b l e a g r e e m e n t between eq. (2) and the e x p e r i m e n t a l data.
In p a r t I we o b s e r v e the t i m e dependence of
the CP violating I ~L decay. Because of the long
K L l i f e t i m e this is j u s t the efficiency function.
In p a r t II the d i s t r i b u t i o n is dominated at s h o r t
t i m e s by the exponential decay of the r e g e n e r a t e d
KS. The Kq and KT 2y i n t e n s i t i e s a r e equal at
~ 5.3 x 1~)-10 sec. In p a r t HI the 2~ i n t e n s i t i e s
of K L and KS a r e n e a r l y equal at t i m e ~- = 0.
We now wish to make the following o b s e r v a t i o n s :
1) The data cannot be u n d e r s t o o d on the b a s i s of
the independent decay of the KS and K L without
the i n t e r f e r e n c e t e r m , that is on the b a s i s of d i s t r i b u t i o n s of the f o r m
Fi(T) =
Miei(7)I,pi'2
e-Fs1-+
'77{2
e-FLY-] .
The best fit p o s s i b l e here, u s i n g a decay cons t a n t F S = 1.136 × 10 -10 sec, gives ×2 of 105
a g a i n s t an expectation of 30. The d i s t r i b u t i o n s
expected on this b a s i s have been drawn in fig. 3.
2) The data can be u n d e r s t o o d on the b a s i s of the
i n t e r f e r e n c e of KS and K L y+~- decays, that is,
e x p r e s s i o n (2). The b e s t ×2 is 31 a g a i n s t an expectation of 28, if F S = 1.136 × 1010 sec -1. The
c o r r e s p o n d i n g d i s t r i b u t i o n s have been drawn in
fig. 3. The i n t e r p r e t a t i o n of the K L 2y decay in
t e r m s of CP violation i s t h e r e f o r e upheld by
this e x p e r i m e n t .
The i n t e r f e r e n c e t e r m has been i s o l a t e d f r o m
the data by s u b t r a c t i n g the expectations for the
b e s t fit solution except for the i n t e r f e r e n c e t e r m ,
and dividing by 2 M i 6i('r)p i ~7exp {- ½(F L + FS)~}.
The r e s u l t a n t t i m e d i s t r i b u t i o n should be then
j u s t cos (q~ + A m r ) . This is shown in fig. 4, which
exhibits an i n t e r f e r e n c e p h e n o m e n o n extending
over nine K S m e a n - l i v e s .
The p o s s i b i l i t y of the fit is not s t r o n g l y dependent on F S. If F S is slightly s m a l l e r , the fit
is i m p r o v e d and if F S i s l a r g e r , the fit b e c o m e s
worse. F o r F S = 1.1 x 1010 s e c - 1 ; ×2 = 30.3. If
F S = 1.20, as r e c e n t , m o r e p r e c i s e d e t e r m i n a 210
0
-.5 t
- 1.0
0
-
I
2
L
3
-
I
4
I
5
I
6
I i II
7
8
Z" IN UNITS OF 10-10sec
Fig. 4. Experimental data treated in such a way (see
text) as to isolate the interference term cos (~o+Am'r).
tions indicate *, then )<2 _-_ 36.5.
3) N o n - l i n e a r models of K decay. It has been
proposed [3] that the K L ~ y+~- decay m a y be a
consequence of s m a l l n o n - l i n e a r t e r m s in the
SchrSdinger equation for the K meson. A p r e d i c tion of this model m a y be that the sign of the int e r f e r e n c e t e r m in an e x p e r i m e n t such as this
one is opposite for K m e s o n s 'originating f r o m Ko
and Ko m e s o n s , r e s p e c t i v e l y . This r e d u c e s the
amplitude of the i n t e r f e r e n c e t e r m in eq. (1) with
r e s p e c t to the q u a d r a t i c t e r m s by the factor
(.NKO- N ~ . ) / ( N K ~' + l:~Ou~sN). In o r d e r to be able to
a l s e u s s tins point,
a s s u m e that the r a t i o
K ° / ~ ° is the s a m e as that for K+/K- , m e a s u r e d
by Baker et al. [4] to be ~ 3 for c o m p a r a b l e mom e n t a and production angle. Then the expectation
for the i n t e r f e r e n c e t e r m is r e d u c e d to one-half.
Our r e s u l t s cannot be u n d e r s t o o d with this hypot h e s i s ; the ×2 b e c o m e s 53 i n s t e a d of the 28 which
a r e expected. This e x p e r i m e n t can t h e r e f o r e be
r e g a r d e d as evidence a g a i n s t this hypothesis.
4) The phase q~ = ~Op- ~on. One of the f u n d a m e n t a l
p a r a m e t e r s in K° ~ ~+ ~- y-decay is the r e l a t i v e
phase ~y of the a m p l i t u d e s of the two pions p r o duced by the l o n g - l i v e d and s h o r t - l i v e d K:s. In
this e x p e r i m e n t we m e a s u r e the difference between q~7/ and the phase d i f f e r e n c e ~ p of the r e g e n e r a t e d KS with r e s p e c t to the K L on leaving
the r e g e n e r a t o r . F r o m the e x p e r i m e n t , q =
q~p- ~o7/= :F 1.05 ± 0.25, where the upper and
lower s i g n s r e f e r to p o s i t i v e and negative Am,
* L. Kirsch, P. Schmidt and N. Barash find F KS =
1.20 + 0.022. We wish to thank the authors
for this communication.
Volume 20, number 2
PHYSICS LETTERS
r e s p e c t i v e l y . Cpp can be w r i t t e n in t e r m s of the
K° and ~-o f o r w a r d s c a t t e r i n g a m p l i t u d e s f(0) and
7(o):
Cp = A r g [ i f ( O ) - if(O)] +
Arg ( 1 - e x p [ ½ ( - 1 + 2 i a m / r s ) r s r ] ~
+
i_ ia-X
/r s
j =
be fitted for Am = 0; the X2 then is 74 for 29 constraints.
The b e s t value of the m a s s , a s s u m i n g F S =
1.136 × 1010 s e c - 1 , is I A m / F s I = 0 . 4 4 ± 0.06.
Given the p o s s i b i l i t y of a s u b s t a n t i a l e r r o r in this
value of r S *, we give also the v a r i a t i o n with IS,
although this t u r n s out to be quite s m a l l :
lam/rsl
where T = L m K / P K and L is the length of r e g e n erator.
e a r n can be c a l c u l a t e d and is O. 19 r a d for our
m e a n m o m e n t u m . We t h e r e f o r e obtain ~ / =
~n (1.25 ± 0.25) rad. The phase ~f has not
m e a s u r e d . In any c a s e n o t h i n g i s known exp e r i m e n t a l l y about the scat.tering a m p l i t u d e s in
copper. The imaginary p a r t s of f(0) and f(0) in
hydrogen are known, but v e r y little is known about
the real p a r t s , one might hope that optical model
c a l c u l a t i o n s for copper would y i e l d e s s e n t i a l l y
i m a g i n a r y f(0) - f(0), s u b s t a n t i a l l y independent of
r e a l c o n t r i b u t i o n s in the hydrogen a m p l i t u d e s .
However, a c t u a l c o m p u t a t i o n s with Re f H ( 0 ) /
Im f H ( 0 ) -~ 0.3, a s i n d i c a t e d by e x p e r i m e n t [5],
give p h a s e s ~ f in copper of the o r d e r of 0.7 r a d i arts. The e r r o r in this n u m b e r m u s t be a s s u m e d
c o m p a r a b l e to the n u m b e r itself. We t h e r e f o r e
do not b e l i e v e it p o s s i b l e to d i s c u s s q~7/with any
p r e c i s i o n without f u r t h e r m e a s u r e m e n t . If one
n e v e r t h e l e s s w i s h e s to take Re f = 0, and t h e r e fore q~f = 0, then cpT/= ± (1.25 ~: 0.25), where the
sign r e f e r s to the sign of Am.
5) The e x p e r i m e n t a l v a l u e s for the KS - K L m a s s
difference have been d e c r e a s i n g as the e x p e r i m e n t a l s e n s i t i v i t y has i n c r e a s e d [6]. The m o s t
r e c e n t of these, and p r o b a b l y m o s t s e n s i t i v e to
s m a l l m a s s e s , gives the value lain~ FS I =
0.50 ~ 0.10 [6]. However, the data a r e also c o m patible with Am = 0; the s t a t i s t i c a l p r o b a b i l i t y
for this r e s u l t is 30~o. In p r e v i o u s e x p e r i m e n t s
the t i m e i n t e r v a l in which i n t e r f e r e n c e could be
r e a s o n a b l y s t u d i e d was of the o r d e r of one to two
KS l i f e t i m e s . This e x p e r i m e n t i s s e n s i t i v e for
8 K S l i f e t i m e s (see fig. 4) and a c o r r e s p o n d i n g ly g r e a t e r s e n s i t i v i t y for s m a l l a m is achieved.
F r o m fig. 4 it can a l s o be s e e n that the i n t e r f e r ence t e r m is c o n s t r u c t i v e at e a r l y t i m e s and bec o m e s d e s t r u c t i v e at l a t e r t i m e s . The data cannot
1February 1966
= (0.44 ± 0.06) +
+ 0.9(F S - 1.136 × 1010 s e c - 1 ) / r S.
We would like to thank the staff of the PS and
in p a r t i c u l a r M e s s r s . Chuinard, Geibel and Munday, for s e t t i n g up the e x p e r i m e n t and for the exp o s u r e , Mr. F. Blythe for design and c o n s t r u c t i o n
of the equipment, Mr. L. T h o r n h i l l for the cons t r u c t i o n of the s c i n t i l l a t o r s , Dr. J. S. Bell for
d i s c u s s i o n s , Prof. R. F r i e d b e r g for c o n t r i b u t i o n s
to the e x p e r i m e n t in its e a r l y s t a g e s and Prof.
V. F. Weisskopf for his e n c o u r a g e m e n t . One of us
(J. S.) wishes to thank CERN for its hospitality,
and Columbia U n i v e r s i t y for its g e n e r o s i t y in
g r a n t i n g extended leave.
References
1. J.H. Christenson, J.W. Cronin, V. L. Fitch and R.
Turlay, Phys. Rev. Letters 13 (1964) 138;
See also A. Abashian, R.J.Abrams, D. W. Carpenter,
G. P. Fisher, B.M.K. Nefkens and J. H. Smith, Phys.
Rev. Letters 13 (1964) 243;
W. Galbraith, G. Manning, A.E. Taylor, B.D. Jones,
J. Malos, A. Astbury, N.H. Lipman and G. T. Walker,
Phys. Rev. Letters 14 (1965) 383;
X. De Bouard, D.Dekkers, B.Jordan, R. Mermod,
T. R. Willitts, K. Winter, P. Scharff, L.Valentin,
M.Vivargent and M. Botts-Bodenhausen, Physics
Letters 15 (1965) 58.
2. V.L.Fiteh, R.F.Roth, J.S.Russ and W.Vernon,
Phys. Rev. Letters 15 (1965) 73.
3. B. Laurent and M.Roos, Physics Letters 13 (1964)
269; 15 (1965) 104.
4. W.F.Baker et al., Phys. Rev. Letters 7 (1961)101.
5. V. Cook, D. Keefe, L.T. Kerth, P.G. Murphy, W.A.
Wenzel and T. F. Zipf, Phys. Rev. Letters 123 (1963)
2743.
6. J.H. Christenson, Thesis. Princeton University Dept.
of Phys., Elementary Particle Lab., Technical Rep.
No. 34, July 1964
* L. Kirsch, P. Schmidt and N. Barash find FKs =
1.20 -~0.022. We wish to thank the authors
for this communication.
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