Time-dependent interference effects in two-pion decays of neutral kaons

Volume 20, number 2

PHYSICS LETTERS

1February 1966

TIME-DEPENDENT INTERFERENCE EFFECTS IN TWO-PION DECAYS OF NEUTRAL KAONS M. BOTT-BODENHAUSEN, R. MERMOD **, I. SAVIN

X. DE BOUARD, D. G. CASSEL ***, P. SCHARFF, M. VIVARGENT,

*, D. DEKKERS, T.R. WILLITTS

R. FELST, and K. WINTER

CERN, Geneva

Received 28 December 1965

We r e p o r t h e r e p r e l i m i n a r y r e s u l t s f r o m an e x p e r i m e n t designed to s e a r c h for t i m e - d e p e n d e n t i n t e r f e r e n c e between s h o r t - l i v e d and l o n g - l i v e d neutral K mesons. We have placed a r e g e n e r a t o r in a b e a m of l o n g - l i v e d n e u t r a l K m e s o n s , produced in the CERN PS, and have o b s e r v e d the r a t e of the (~+~-) decay mode as a function of d i s t a n c e f r o m the end of the r e g e n e r a t o r . The a i m of the exp e r i m e n t was the m e a s u r e m e n t of the beat f r e quency between the decay a m p l i t u d e s for the (u+~r-) decay mode of I ~L and r e g e n e r a t e d K~ and their phase r e l a t i o n . While the r e s u l t s a r e p r e l i m i n a r y in that only a f r a c t i o n of the total data is included, we believe that they e s t a b l i s h the e x i s t e n c e of a t i m e - d e p e n dent i n t e r f e r e n c e p a t t e r n . The m a s s difference, m S - mL, as d e t e r m i n e d f r o m the o b s e r v e d i n t e r f e r e n c e a g r e e s with the data of r e c e n t e x p e r i m e n t s [1] which did not use the 2~ decay of I ~L. Hence, the r e s u l t s d e m o n s t r a t e d i r e c t l y the e x i s t e n c e of a CP violation amplitude in the K ~ - I ~L s y s t e m . C o n s t r u c t i v e i n t e r f e r e n c e between I ~L and r e g e n e r a t e d K~S decaying into two c h a r g e d pions has a l r e a d y been o b s e r v e d in a r e c e n t e x p e r i m e n t [2] designed to c o m p a r e the b r a n c h i n g r a t i o of K° decaying to (~+~-) in v a c u u m and in m a t t e r . Howe v e r , the b r a n c h i n g r a t i o in m a t t e r was m e a s u r e d in an " i n f i n i t e l y " extended r e g e n e r a t o r and gives a n upper l i m i t on the effective K~Q- K~T m a s s difJLA f e r e n c e of a p p r o x i m a t e l y 0.6 in units of 1 / 7 S. Let us a s s u m e , as suggested by the o b s e r v a tion of 277 decays of l o n g - l i v e d K° [3], that the physical state tilL) , defined by its m a s s and l i f e - t i m e , has an amplitude D L ~ for decay into u+~r-. The state I ~L is changed ~¢hen a I ~L b e a m p a s s e s through m a t t e r . Matter acts on the b e a m * National Science Foundation Postdoctoral Fellow. ** University of Geneva. *** Visitor from the Joint Institute for Nuclear Research, Dubna (U. S. S. R.). 212

as an a b s o r p t i v e and d i s p e r s i v e m e d i u m which in g e n e r a l has different (strong i n t e r a c t i o n ) prope r t i e s for ~.o and K°. The difference in the forward s c a t t e r i n g a m p l i t u d e s of K"~ and K°, f21(0) = ½~f(0) - f ( 0 ) } p r o d u c e s a c o h e r e n t r e g e n e r a t i o n of K~ f r o m I ~L. The state, after p a s s a g e through m a t t e r , is then II~L) + A IK'~8) (1) and its amplitude for decay into (Tr+u-) is D L , " + A D s , ~ = DS,,(A+7/+_ ) ,

(2)

where Ds is the (~+~-) amplitude of K~ and ~/~ = DL, y / D s , y = !77+_ i el ~h t. The cohere~nt regelne r a t i o n amplitude at the end of the r e g e n e r a t o r of t h i c k n e s s x is: d -

if21 (0) ~NA S i6---~~ (1 - exp ( - i 5 / - ½/) ,

(3)

h e r e ~ i s the K° w a v e length, 5 is m s - m L i n u n i t s of 1/TS, N is the n u m b e r of s c a t t e r i n g cent r e s per cm3, AS is the m e a n decay length of and l : x/A s

We o b s e r v e d K° decays into (~+~-) as a function of distance f r o m the r e g e n e r a t o r over a r a n g e of about s e v e n K~ m e a n decay lengths. The i n t e n s i t y d i s t r i b u t i o n o b s e r v e d in space can be c o n v e r t e d into a time d i s t r i b u t i o n with the help of the K° m o m e n t u m which is d e t e r m i n e d for each event. The time d i s t r i b u t i o n expected on the b a s i s of our a s s u m p t i o n s is it Rate (t) = C {R2 e- t + 1 + 2 R e- 2 cos (St + go)}, (4) where R = ! A I / ] ~ +.! , t = t ' / T S with e the p r o p e r time of decay, and go = (arg q+_ - a r g A). A I ~L b e a m was d e r i v e d at 8.3 ° f r o m an int e r n a l t a r g e t of the CERN P r o t o n Synchrotron and was defined by a s y s t e m of c o l l i m a t o r s subtending t We follow here the notations of ref. 4.

Volume 20, number 2

PHYSICS LETTERS

a s o l i d angle of 5 x 10 - 6 s r at the t a r g e t . 7.5 c m of Pb w e r e put into the b e a m to r e d u c e the n u m b e r of photons. C h a r g e d p a r t i c l e s w e r e e l i m i n a t e d by a s w e e p i n g magnet. The b e a m t r a v e l l e d 41 m f r o m the t a r g e t to the r e g e n e r a t o r . The m o m e n t u m v e c t o r s of c h a r g e d s e c o n d a r i e s f r o m K ° d e c a y s behind the r e g e n e r a t o r w e r e m e a s u r e d in a s p e c t r o m e t e r c o n s i s t i n g of an ana l y s i n g m a g n e t and two s e t s of s p a r k c h a m b e r s . A plan view of this a p p a r a t u s is shown in fig. 1. A sixfold c o i n c i d e n c e of the c o u n t e r s N1, N2, N3, P1, P2 and P3 is r e q u i r e d to t r i g g e r the s p a r k c h a m b e r s . This t r i g g e r was d e s i g n e d to make u se of a s i n g u l a r k i n e m a t i c p r o p e r t y of two-body decay s ; the t r a n s v e r s e m o m e n t a of the s e c o n d a r i e s e m i t t e d at c.m. a n g l e s a r o u n d 90 ° a r e n e a r l y constant. In this way we e m p h a s i z e the s o l id angle for 2~ d ec a y s . Leptonic decay m o d e s w e r e l a b e l l e d by the d e t e c t i o n of e l e c t r o n s f r o m K,~.~ in a g a s - f i l l e d t h r e s h o l d ~ e r e n k o v c o u n t e r (C~~and of muons f r o m K~3 in c o u n t e r s N 4 and P4, b ehind 600 g / c m 2 of i r o n . The a c c e p t a n c e of this d e t e c t o r f o r the d i f f e r e n t decay m o d e s as a function of the K° m o m e n t u m and p o s i t i o n of the decay apex was e v a l u a t e d by M o n t e - C a r l o methods. The f i el d d i s t r i b u t i o n of the a n a l y s i n g m a g n e t had been m a p p e d f o r this p u r p o s e . N4 PI

V

P2

1February 1966

w e r e i n t e g r a t e d o v e r the fiducial d ecay v o l u m e and the K° m o m e n t u m s p e c t r u m . The b r a n c h i n g r a t i o is

r( LL

= (1.78,± 0.18) x 10 -3

ged)

in good a g r e e m e n t with p r e v i o u s data [3]. The an g u l ar d i s t r i b u t i o n of K° d e c a y i n g into two pions as o b s e r v e d behind m a t t e r is shown in fig. 2. The i n v a r i a n t m a s s of t h e s e e v e n t s with 0 2 < 10 -5 is peaked at 496.6 MeV with a 3.0 MeV r . m . s , width. The n a r r o w peak in the f o r w a r d d i r e c t i o n is due to 2~ d e c a y s of t r a n s m i t t e d K°; it has a r . m . s , width of 1.1 m r a d , c o m p a t i b l e with probable m e a s u r i n g e r r o r s and m u l t i p l e s c a t t e r i n g . We have i n v e s t i g a t e d the t i m e d i s t r i bution of t h e s e e v e n t s . The background c o n s i s t s of i n c o h e r e n t r e g e n e r a t i o n and a n e g l i g i b l e amount of Ke3 d e c a y s due to i n e f f i c i e n c y of the C e r e n k o v counter. In al l c a s e s a single G a u s s i a n g i v e s an e x c e l l e n t fit to the background o v e r the r e g i o n 1 0 - 5 < O 2 < 5 x 1 0 - 4 t a d 2.

N3 [7"~ ~J

Anti

~__~

all c

F _

.

1

Absorber

NI

N21

1

CH~ /

" ~/~

,P+

e3~e4

Fig. 1. Plan view of the detector for charged K° decays. IO

90 ° s t e r e o - v i e w s of the s p a r k c h a m b e r s w e r e photographed t o g e t h e r with the d ig it a l d i s p l a y of l a b e l s identifying leptonic d e c a y s and w e r e m e a s u r e d with a c o m p u t e r c o n t r o l l e d f l y i n g - s p o t d i g i t i z e r [5]. The a n a l y s i s p r o g r a m m e computed the m o m e n t u m v e c t o r s of the two c h a r g e d s e c o n d a r i e s , the i n v a r i a n t m a s s m* of the p a i r using the i d e n t i f i c a t i o n label, the angle O between the sum of the two m o m e n t u m v e c t o r s and the K ° dir e c t i o n , the position of the d e c a y apex and the m o m e n t u m of the p a r e n t K° (two s o l u t io n s fo r leptonic decays). As a check on the p e r f o r m a n c e of the d e t e c t o r , s o m e data w e r e taken on I ~L d e c a y s in vacuum. The K° m o m e n t u m s p e c t r u m was d e t e r m i n e d f r o m K~3 d e c a y s t and the d i f f e r e n t a c c e p t a n c e s

I I t I I i e i i I J i i i LI 5 I0 15 e2 10.5 rod 2

I

Fig. 2. Angular distribution of K° decaying into two pions behind a regenerator. All 2y c a n d i d a t e s in the m a s s r a n g e 480 < rn* < 515 MeV w e r e s o r t e d into 14 t i m e bins e a c h 0.5 x 10 -10 s e c wide. The m o m e n t a of d e t e c t e d K° w e r e l i m i t e d to the r a n g e 3 . 5 - 8.0 GeV/c; t h e i r a v e r a g e is 4.8 GeV/c. The b ack ground under the peak of t r a n s m i t t e d K° was then e v a l u a t e d s e p a r a t e l y in e a c h t i m e bin by e x t r a polating the fitted Gaussian to z e r o solid angle. The s a m e p r o c e d u r e was applied to s e a r c h s e p a t The method is described in ref. 3, De Bouard et al.

213

Volume 20, number 2

PHYSICS

r a r e l y f o r 2~ d e c a y s w h i c h w e r e l a b e l l e d K~3 b e c a u s e one pion s u c c e e d e d in t r a v e r s i n g the i r o n a b s o r b e r , and t h e s e e v e n t s w e r e a d d e d into the corresponding time bins. To c o m p a r e the e x p e r i m e n t a l and the e x p e c t e d t i m e d i s t r i b u t i o n s f o r v a r i o u s v a l u e s of the f o u r p a r a m e t e r s in eq. (4), C, R, 5 and ~ we h a v e c h o s e n to w e i g h t the e x p e c t e d d i s t r i b u t i o n w i t h the d e t e c t i o n p r o b a b i l i t y a s a f u n c t i o n of t i m e ; the o r i g i n is d e f i n e d a s the t i m e w h e n a K ° l e a v e s the r e g e n e r a t o r . The d e t e c t i o n p r o b a b i l i t y a s a f u n c t i o n of p r o p e r t i m e w a s o b t a i n e d by i n t e g r a t ing the a c c e p t a n c e f o r d i f f e r e n t K ° m o m e n t a and d e c a y p o s i t i o n s o v e r the K ° m o m e n t u m s p e c t r u m . Preliminary results have been obtained from a s a m p l e of 1600 and 650 e v e n t s obser-¢ed w i t h two d i f f e r e n t r e g e n e r a t o r s c o n s i s t i n g of 4 c m of c a r b o n and 1.6 c m p l a s t i c s c i n t i l l a t o r , and 2 c m of c a r b o n and 0.8 c m s c i n t i l l a t o r , r e s p e c t i v e l y . The t i m e d i s t r i b u t i o n of e v e n t s o b s e r v e d b e hind 4 c m of c a r b o n is s h o w n in fig. 3a. V a l u e s of the f o u r p a r a m e t e r s in the e x p e c t e d t i m e d i s t r i b u t i o n (eq. (4)) w e r e d e t e r m i n e d by m i n i m i z i n g X2. A s s u m i n g no i n t e r f e r e n c e by r e q u i r i n g 5 = 0 and ~p= ~ , the b e s t fit g i v e s x 2 = 85 f o r 12 d e g r e e s of f r e e d o m , e x c l u d i n g t h i s h y p o t h e s e s c o m p l e t e l y . W i t h the h y p o t h e s e s of i n t e r f e r e n c e ,

LETTERS

1 F e b r u a r y 1966

an e x c e l l e n t fit to the d a t a i s o b t a i n e d w i t h ×2 = 10 f o r 10 d e g r e e s of f r e e d o m and R = 4.3, ~ = - 1 . 6 and ~ = 0.59. The K~ l i f e - t i m e h a s b e e n t a k e n [6] a s r S = (0.909 * 0.015) × 10 - 1 0 s e c . The d a t a o b t a i n e d w i t h the two d i f f e r e n t r e g e n e r a t o r s w e r e t h e n n o r m a l i z e d to the s a m e KK°Lflux by c o m p a r i n g the n u m b e r s of i d e n t i f i e d ~3 d e c a y s . A s i m u l t a n e o u s fit w i t h the c o n s t r a i n t R = R4c m = 2R2c m g i v e s X2 = 18.7 f o r 18 d e g r e e s of f r e e d o m . The p a r a m e t e r s a s d e t e r m i n e d by t h i s fit and t h e i r e r r o r s a s d e t e r m i n e d by one s t a n d a r d d e v i a t i o n on ×2 of the fit ( s e e fig. 3b) a r e R = 3.4 +1"0 -0.8

~=

-71 °+21° _25o

0.16 . 5=0.50+0.23.(5,_

The r e s u l t s a r e not s e n s i t i v e to c h a n g e s in the K~S l i f e - t i m e w i t h i n t w i c e the q u o t e d e r r o r [6]. The m a j o r source o f e r r o r s in the values of the p a r a m e t e r s is due to their s t r o n g correlation. T h i s m a y be s e e n in fig. 3b s h o w i n g the 1 s t a n d a r d d e v i a t i o n c o n t o u r f o r X2 in the R - ~ p l a n e f o r 5 = 0.50. The v a l u e of the K S - K L m a s s d i f f e r e n c e a s d e t e r m i n e d f r o m the b e a t f r e q u e n c y of the i n t e r f e r e n c e is in good a g r e e m e n t w i t h the v a l u e of 5 = 0.50 ± 0.10, o b t a i n e d in an e x p e r i m e n t [1]

.X£ = 8 5

4.8~46= 4.4 4.2 4.¢ 5.8

)(-2 _- 2 4 . 7 /"

f

3.6

3.4 3.2

3.G 2.8 2.4 2.2~ 2.0

__

l

I

I

2

I

:3

I

4

I

5

I_

6

I

7

J-_____ i

~-Ios

Fig. 3a. T i m e distribution of 2~ decays observed behind a 4 cm c a r b o n r e g e n e r a t o r . T h e c u r v e with X2 = 85 r e p r e s e n t s the best fit assuming no i n t e r f e r e n c e , the curve with ×2 = 10 is the b e s t fit a s s u m i n g i n t e r f e r e n c e . 214

-1.0o

-.8o

-.at>

Fig. 3b. One s t a n d a r d d e v i a t i o n c o n t o u r f o r X2 in the R-~p p l a n e f o r 5 = 0.5 and v a l u e s f o r b e s t fit.

Volume 20, number 2

PHYSICS

w h i c h did not u s e the 2~ d e c a y of I ~L. T h i s a g r e e m e n t t h e n d e m o n s t r a t e s d i r e c t l y the e x i s t e n c e of a C P v i o l a t i n g a m p l i t u d e in the K ~ - I ~L s y s t e m . The p h a s e ~P c a n n o t be d e t e r m i n e d without an a s s u m p t i o n on the p h a s e of f 2 1 ( 0 ) . In the r a n g e of K ° m o m e n t a a c c e p t e d in t h i s e x p e r i m e n t , i t s i m a g i n a r y p a r t is v a r y i n g s m o o t h l y w i t h o u t i n d i c a t i o n s of r e s o n a n c e s . We t h e r e f o r e w i l l a s s u m e that f21(0) is purely imaginary. C o m p a r i n g ~ = a r g ~/+_ d i r e c t l y to 8 S [3, 7], d e f i n e d a s a r g ( 1 / ( i 8 +½)) we o b t a i n then ~ - 5 S = [¢ + a r g { i f 2 1 ( 0 ) } ] + 45 ° = _26 ° . T h i s is c o m p a t i b l e w i t h the r e s u l t of F i t c h et al. [2] though in t h e i r e x p e r i m e n t the K ° m o m e n t a w e r e in a r e g i o n of r e s o n a n c e in the K - n u c l e o n system. We g r a t e f u l l y a c k n o w l e d g e the h e l p of B. J o r d a n and L. V a l e n t i n in the e a r l y s t a g e s of the e x p e r i m e n t , and the c o m p e t e n t t e c h n i c a l a s s i s t a n c e of B. F r i e n d and L. V e l a t i . We thank P r o f e s s o r s G r e g o r y , P a u l , P r e i s w e r k and W e i s s k o p f f o r t h e i r c o n t i n u o u s i n t e r e s t and s u p p o r t . We s h o u l d l i k e to thank the MPS d i v i s i o n f o r the e f f i c i e n t o p e r a t i o n of the C E R N P r o t o n - S y n chrotron.

ON

THE

EXISTENCE

OF

LETTERS

1 F e b r u a r y 1966

References 1. J . H . C h r i s t e n s o n , J . W . Cronin, V . L . F i t c h and R. Turlay, Phys. Rev. 140 (1965) B 74. 2. V . L . F i t c h , R . F . R o t h , J . S . R u s s and W.Vernon, Phys. Rev. Letters 15 (1965) 73. 3. J . H . C h r i s t e n s o n , J.W. Cronin, V . L . F i t c h and R. Turlay, Phys. Rev. Letters 13 (1964) 138; X. De Bouard, D. Dekkers, B. Jordan, R. Mermod, T. R. Willitts and K. Winter, P. Seharff, L. Valentin and M. Vivargent, M. Bott-Bodenhausen, Physics Letters 15 (1965) 58 and Proc. Oxford Intern. Conf. on Elementary P a r t i c l e s , 1965; W. Galbraith, G. Manning, A . E . Taylor, B.D. Jones, J. Malos, A . Astbury, N.H. Lipman and T. G. Walker, Phys. Rev. Letters 14 (1965) 383. 4. T . T . Wu and C. N. Yang, Phys. Rev. Letters 13 (1964) 501. 5. J. -C. Laeotte, P. Scharff, C. Victor and T. R. Willetts, to be published. 6. A.H. Rosenfeld, A. Barbaro-Caltieri, W.H. Barkas, P. L. Bastien, J. Kirz and M. Roos, U . C . R . L . 8030 (March 1965). 7. T . D . L e e and L.Wolfenstein, Phys. Rev. 138 (1965) B 1490; L. Wolfenstein, CERN preprint 65/1086/5-Th. 583, Nuovo Cimento, to be published.

SPIONS

FROM

K + DECAY

*

S-Y. FUNG, R. GOLDBERG, S. L. MEYER and R. J. PLANO Rutgers The State University, New B r u n s w i c k , New J e r s e y -

Received 3 January 1966 A search has been made for spin 1 particles arising from the decay of K mesons No evidence has been seen for either positive or neutral particles of this sort in the ~- and T' decays of K+. New upper limits for the possible occurrence of these particles are presented. One of t h e r e c e n t p r o p o s a l s to e x p l a i n the 2~ d e c a y of K~2 [1] w i t h o u t e x p l i c i t C P v i o l a t i o n w a s a s u g g e s t i o n [2] t h a t a s p i n 1 p a r t i c l e , the spion, exists whose mass is nearly degenerate with that of the o r d i n a r y pion, w h i c h is c o u p l e d to the K m e s o n s by the w e a k i n t e r a c t i o n , and w h i c h a p p e a r s in the a n o m a l o u s d e c a y of K~. S e v e r a l e x p e r i m e n t s in the l i t e r a t u r e [3, 4] r e p o r ~ a ~ - ~ a n g u l a r a s y m m e t r y in the d e c a y of ~+ f r o m T d e c a y , i n c o n s i s t e n t w i t h a l l the p i o n s h a v i n g z e r o spin. One of * Work supported in part by the National Science Foundation.

t h e s e e x p e r i m e n t s [4], a d d u c e d a s e v i d e n c e f o r the s p i o n h y p o t h e s i s , r e q u i r e s an a d m i x t u r e of at l e a s t 5% s p i o n s in T d e c a y . Ref. 2 p o i n t s out s e v e r a l t e s t s of t h i s p i c t u r e . A m o n g the c o n s e q u e n c e s of an a d m i x t u r e of s p i o n s in a s a m p l e of c h a r g e d p i o n s w o u l d be an a n o m a l o u s l y l a r g e b r a n c h i n g r a t i o of the e l e c t r o n i c d e c a y m o d e ( s p i o n s w o u l d h a v e an e + v d e c a y r a t e c o m p a r a b l e to that f o r t~ + v s i n c e the n e u t r i n o h e l i c i t y w o u l d no l o n g e r i n h i b i t the d e c a y ) . F o r a s p i o n a d m i x t u r e in a s a m p l e of n e u t r a l p i o n s , one s h o u l d o b s e r v e an a n o m a l o u s l y l a r g e b r a n c h i n g r a t i o f o r 215