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An upper limit on the Kso → μ− μ+ decay rate
Volume 29B, n u m b e r 8
AN
PHYSICS
UPPER
LIMIT
ON
THE
LETTERS
K ° -" ~ -
21 July 1969
bL+ D E C A Y
RATE
B. D. HYAMS, W. K O C H * a n d D. C. P O T T E R * * CERN and L. V o n L I N D E R N , E. L O R E N Z , G. L O T J E N S , U. S T I E R L I N a n d P . W E I L H A M M E R Max-Planck-lnstitut Jar Physik und .4 strophysik, Munich, Germany Received 4 June 1969
F r o m an e x p e r i m e n t , studying ~ p a i r and ?r pair production under s i m i l a r e x p e r i m e n t a l conditions in ~'-p collisions at 11 G e V / c b e a m momentum, we drive an upper limit for the decay mode K~ -~ - T. We find the b r a n c h i n g r a t i o F(K ° ~ ~ - ~ + ) / F ( K ~ ~ all) ~< 7.3 × 10 -6 at 90% confidence. S
We present here a determination limit on the branching ratio B
of a n u p p e r
(z)
B = F ( K ~ --* b L - / l + ) / r ( I ~ ~ a l l ) obtained from a measurement (2) a n d (3)
A d e t a i l e d d e s c r i p t i o n of t h e e x p e r i m e n t m e a s u r i n g r e a c t i o n (2) i s g i v e n i n a n e a r l i e r p u b l i c a t i o n [1]. T h e m e a s u r e m e n t of r e a c t i o n (3) w a s m a d e w i t h a n a p p a r a t u s s i m i l a r to t h a t u s e d i n t h e ~ p a i r experiment. Details on the experimental arrangement, the film measurement and the event reconstruction can be obtained from paragraphs 2 a n d 3 of a p r e v i o u s p u b l i c a t i o n [2]. O n l y t h e
of t h e r e a c t i o n s
(2) (3)
y - p -~ ~ - ~ + + (1 o r m o r e p a r t i c l e s ) y - p -~ y - ~ + + (1 o r m o r e p a r t i c l e s )
* Now at the M a x - P l a n c k - I n s t i t u t fur Physik und A s t r o physik, Munich, Germany. ** Now at the Physics Department, University of Pennsylvania, Philadelphia, USA.
a t 11 G e V / c ~ - m e s o n m o m e n t u m .
200
16C c~ ~12C
40
o~.Jo'.3
I
0k
0:s
0!6
07
0:8
INVARIANT MASS(lI-~*) -
08
G,v
I
+
Fig. 1. I n v a r i a n t m a s s s p e c t r u m of all y p a i r s f r o m the r e a c t i o n y-p--* ~ y + (1 or m o r e p a r t i c l e s ) . Unweighted data. 521
Volume 29B. number 8
PHYSICS LETTERS
21[
i
200
21 July 1969
EVENTSIlmm
EVENTSIlmm
rT;-q
150
(o}
t~ 1
100
50
0[
i 10
16
20
30
40
50 mm
12
o
10
20
30
40
50 mm
DISTANCE BEAM-VERTEX
DISTANCE BEAM-VERTEX J J i EVE NTSI002 GeV
EVENTS/0.02 GeV ~'~
(C)
8
t
J
[
12 1( ,
(d)
8
4 0
0.2
0.3
0.6 0.5 0.6 0.7 GeV INVARIANT MASS (p+jJ')
o
0.2
0.3
- - I I-I
0.4 0.5 0.6 0.7 GeV INVARIANTMASS(1'I+'n")
Fig. 2. Distribution of beam vertex distance for /~ pair events (a) and ?rpair events (b), respectively, with F_,gg(Eyr~)>i 10.0 GeV. The invariant mass of all events, which lie to the right side of the dotted line drawn in (a) and (b) is shown in (c) and (d) for p pairs and 7r pairs, respectively. t a r g e t position and the t r i g g e r condition in this e x p e r i m e n t w e r e different f r o m that d e s c r i b e d in ref. [2]. Here the t a r g e t was in the s a m e p o s i tion as in the ~t p a i r e x p e r i m e n t , and in the t r i g ger not only a neutron, but also m o r e than one p a r t i c l e a c c o m p a n y i n g the 7r p a i r w e r e admitted. About 45 000 photographs w e r e r e c o r d e d a t t e m p t ing to s e l e c t r e a c t i o n (3). Among these 6 396 were found to be ~ p a i r events of this type. Fig. 1 shows the lr p a i r i n v a r i a n t m a s s d i s t r i bution f r o m r e a c t i o n (3). A c l e a r signal of about 130 I ~ events, with M = 497 MeV, is s e e n above a smooth background. We m a y obtain an upper l i m i t B < 2 × 10 - ° at 90% confidence u s i n g these
K?
1
/i Y
Fig. 3. Feynman diagram for the weak X electromagnetic transition K~ -*y-y*.
522
data for K~ p r o d u c t i o n and the /~ p a i r i n v a r i a n t m a s s s p e c t r u m f r o m r e a c t i o n (2). However, the s e n s i t i v i t y of this e x p e r i m e n t i s i m p r o v e d if we make u s e of the fact that the K~ decay v e r t e x is not coincident with the b e a m t r a j e c t o r y . Our ~r p a i r data show, that the have a m e a n t r a n s v e r s e m o m e n t u m of 300 l~eV/c and thus the a v e r a g e t r a n s v e r s e d i s t a n c e f r o m the decay v e r t e x to the b e a m t r a j e c t o r y is 15 m m for a K~ with 10 GeV/c m o m e n t u m . To d e t e r m i n e the b e a m v e r t e x d i s t a n c e d we applied the s a m e m e a s u r e m e n t p r o c e d u r e t ° g p a i r s and rr p a i r s . Fig. 2a and 2b show the d i s t r i b u t i o n of d all g p a i r s and lr p a i r s r e p s e c t i v e l y , with an e n e r g y of the p a i r >/10.0 GeV. The i n v a r i a n t m a s s s p e c t r u m of those e v e n t s , which have d >/10 m m , is depicted i n fig. 2c for g p a i r s and fi T. 3d for Ir p a i r s . No e n h a n c e m e n t is s e e n in the K~ m a s s r e g i o n of the g p a i r d i s t r i b u t i o n , wher e a s in the ~ p a i r d i s t r i b u t i o n a s h a r p ~ peak on top of p r a c t i c a l l y no b a c k g r o u n d i s visibTe. N o r m a l i z i n g these two m a s s d i s t r i b u t i o n s to each other, we can give a n o t h e r upper l i m i t for the b r a n c h i n g r a t i o B. A . ~ i n t e r v a l I ~ of ~-20 MeV a r o u n d the K~ m a s s is chosen, which c o n t a i n s m o r e than 70% of all p o s s i b l e K~ -~ y - g + decays [the g p a i r
Volume 29B, n u m b e r 8
PHYSICS
LETTERS
m a s s r e s o l u t i o n i s A M = ± 1 7 M e V [2]]. T h e n u m b e r of e v e n t s o b s e r v e d i n t h i s i n t e r v a l i s n = 1. T h e n u m b e r of b a c k g r o u n d e v e n t s ~, e x p e c t e d i n lwR, i s d e t e r m i n e d f r o m t w o 4 0 M e V w i d e t e s t . ~ . O . . m t e r v a i s o n b o t h s i d e s of I K ~ , a s s u m i n g a u r n form distribution for the background in these int e r v a l s . F r o m fig. 2c o n e f i n d s ~ = 2. T h e n u m b e r of o b s e r v e d b a c k g r o u n d e v e n t s b and signal events s, are individually samples f r o m P o i s s o n d i s t r i b u t i o n s w i t h m e a n s b a n d ~, t h e r e f o r e a l s o t h e i r s u m n = b+s i s a s a m p l e f r o m a Poisson distribution with mean g = b+~. On t h e b a s i s of t h e o n e s a m p l e p o i n t n = 1, which we have available from the over-all dis t r i b u t i o n , w e c a n c a l c u l a t e t h e u p p e r l i m i t ~o o n t h e m e a n g to b e "< So = 1.9
at 90~ confidence.
T h i s n u m b e r i s o b t a i n e d b y s o l v i n g eq. (4) f o r n o
h=0 h'
exp
-
g o = 0.1,
(4)
w h i c h g i v e s g o -- 3.9 o r ~o -- g o - b o -- 1.9. N o r m a l i z i n g to t h e n u m b e r of i n c o m i n g b e a m particles and correcting for the differences in electronics efficiency, analysis efficiency and a c c e p t a n c e b e t w e e n t h e ~z p a i r a n d 7r p a i r e x p e r iments, one finds an upper limit for the branching ratio B~ B
= 7.3 x 10 - 5 a t 90°~ c o n f i d e n c e . (5) o T h i s v a l u e i s a n i m p r o v e m e n t of o n e o r d e r of m a g n i t u d e w i t h r e s p e c t to t h e p r e s e n t u p p e r l i m i t B ~< 7.3 × 10 - 5 [3].
21 July 1969
The branching ratio B expected a weak and electromagnetic transition with a Feynman diag r a m s h o w n i n fig. 3 i s e x p e c t e d t o b e B g 5 × 10 - 9 [ 4 - 7 ] . T h e a p p e a r a n c e of a b r a n c h i n g r a t i o c o n s i d e r a b l y h i g h e r t h a n 5 × 10 - 9 w o u l d t h u s b e e v i d e n c e f o r t h e e x i s t e n c e of n e u t r a l l e p t o n i c c u r r e n t s c o u p l i n g to s t r a n g e n e s s c h a n g i n g hadronic currents. Our limit B o provides an upper limit on coupling constants occuring in models on neutral leptonic currents [8-10].
References
1. B.D. Hyams, W. Koch, D. Pellet, D. Potter, L. yon Lindern, E. Lorenz, G. LIltjens, U. Stierlin and P. W e i l h a m m e r , Phys. L e t t e r s 29B (1969) 128. 2. B.D. Hyams, W. Koch, D.C. Potter, J . D . Wilson, L. yon Lindern, E. Lorenz, G. Liltjens, U. Stierlin and P. W e i l h a m m e r , Nuclear Phys. B7 (1968) 1. 3. M. Bott-Bodenhausen, X. de Bouard, D.G. Cassel, D. Dekkers, R. F e l s t , R. Mermod, I. Savin, P. Scharff, M. Vivargent, T. R. Willits and K. Winter, Phys. L e t t e r s 24B (1967) 194. 4. L.M. Sehgal, On the e l e c t r o m a g n e t i c contribution to the decays KS-* / [ a n d KL-*/Z", P r e p r i n t , Tata Institute of Fundamental R e s e a r c h , Bombay, India, April 1969. 5. B.R. M a r t i n and E. de Rafael, Nuclear Phys. B8 (1968) 131. 6. N. Cabibbo and E. F e r r a r i , Nuovo Cimento 18 (1960) 928. 7. V. B a r g e r , Nuovo Cimento 32 (1964) 127. 8. M. L. Good, L. Michel and E. de Rafael, Phys. Rev. 151 (1966) 1194. 9. E. de Rafael, BNL Report 10879, 1966. 10. S. Okubo, University of R o c h e s t e r Report, UR 875-231, 1968.
* * * * *
523
AN
PHYSICS
UPPER
LIMIT
ON
THE
LETTERS
K ° -" ~ -
21 July 1969
bL+ D E C A Y
RATE
B. D. HYAMS, W. K O C H * a n d D. C. P O T T E R * * CERN and L. V o n L I N D E R N , E. L O R E N Z , G. L O T J E N S , U. S T I E R L I N a n d P . W E I L H A M M E R Max-Planck-lnstitut Jar Physik und .4 strophysik, Munich, Germany Received 4 June 1969
F r o m an e x p e r i m e n t , studying ~ p a i r and ?r pair production under s i m i l a r e x p e r i m e n t a l conditions in ~'-p collisions at 11 G e V / c b e a m momentum, we drive an upper limit for the decay mode K~ -~ - T. We find the b r a n c h i n g r a t i o F(K ° ~ ~ - ~ + ) / F ( K ~ ~ all) ~< 7.3 × 10 -6 at 90% confidence. S
We present here a determination limit on the branching ratio B
of a n u p p e r
(z)
B = F ( K ~ --* b L - / l + ) / r ( I ~ ~ a l l ) obtained from a measurement (2) a n d (3)
A d e t a i l e d d e s c r i p t i o n of t h e e x p e r i m e n t m e a s u r i n g r e a c t i o n (2) i s g i v e n i n a n e a r l i e r p u b l i c a t i o n [1]. T h e m e a s u r e m e n t of r e a c t i o n (3) w a s m a d e w i t h a n a p p a r a t u s s i m i l a r to t h a t u s e d i n t h e ~ p a i r experiment. Details on the experimental arrangement, the film measurement and the event reconstruction can be obtained from paragraphs 2 a n d 3 of a p r e v i o u s p u b l i c a t i o n [2]. O n l y t h e
of t h e r e a c t i o n s
(2) (3)
y - p -~ ~ - ~ + + (1 o r m o r e p a r t i c l e s ) y - p -~ y - ~ + + (1 o r m o r e p a r t i c l e s )
* Now at the M a x - P l a n c k - I n s t i t u t fur Physik und A s t r o physik, Munich, Germany. ** Now at the Physics Department, University of Pennsylvania, Philadelphia, USA.
a t 11 G e V / c ~ - m e s o n m o m e n t u m .
200
16C c~ ~12C
40
o~.Jo'.3
I
0k
0:s
0!6
07
0:8
INVARIANT MASS(lI-~*) -
08
G,v
I
+
Fig. 1. I n v a r i a n t m a s s s p e c t r u m of all y p a i r s f r o m the r e a c t i o n y-p--* ~ y + (1 or m o r e p a r t i c l e s ) . Unweighted data. 521
Volume 29B. number 8
PHYSICS LETTERS
21[
i
200
21 July 1969
EVENTSIlmm
EVENTSIlmm
rT;-q
150
(o}
t~ 1
100
50
0[
i 10
16
20
30
40
50 mm
12
o
10
20
30
40
50 mm
DISTANCE BEAM-VERTEX
DISTANCE BEAM-VERTEX J J i EVE NTSI002 GeV
EVENTS/0.02 GeV ~'~
(C)
8
t
J
[
12 1( ,
(d)
8
4 0
0.2
0.3
0.6 0.5 0.6 0.7 GeV INVARIANT MASS (p+jJ')
o
0.2
0.3
- - I I-I
0.4 0.5 0.6 0.7 GeV INVARIANTMASS(1'I+'n")
Fig. 2. Distribution of beam vertex distance for /~ pair events (a) and ?rpair events (b), respectively, with F_,gg(Eyr~)>i 10.0 GeV. The invariant mass of all events, which lie to the right side of the dotted line drawn in (a) and (b) is shown in (c) and (d) for p pairs and 7r pairs, respectively. t a r g e t position and the t r i g g e r condition in this e x p e r i m e n t w e r e different f r o m that d e s c r i b e d in ref. [2]. Here the t a r g e t was in the s a m e p o s i tion as in the ~t p a i r e x p e r i m e n t , and in the t r i g ger not only a neutron, but also m o r e than one p a r t i c l e a c c o m p a n y i n g the 7r p a i r w e r e admitted. About 45 000 photographs w e r e r e c o r d e d a t t e m p t ing to s e l e c t r e a c t i o n (3). Among these 6 396 were found to be ~ p a i r events of this type. Fig. 1 shows the lr p a i r i n v a r i a n t m a s s d i s t r i bution f r o m r e a c t i o n (3). A c l e a r signal of about 130 I ~ events, with M = 497 MeV, is s e e n above a smooth background. We m a y obtain an upper l i m i t B < 2 × 10 - ° at 90% confidence u s i n g these
K?
1
/i Y
Fig. 3. Feynman diagram for the weak X electromagnetic transition K~ -*y-y*.
522
data for K~ p r o d u c t i o n and the /~ p a i r i n v a r i a n t m a s s s p e c t r u m f r o m r e a c t i o n (2). However, the s e n s i t i v i t y of this e x p e r i m e n t i s i m p r o v e d if we make u s e of the fact that the K~ decay v e r t e x is not coincident with the b e a m t r a j e c t o r y . Our ~r p a i r data show, that the have a m e a n t r a n s v e r s e m o m e n t u m of 300 l~eV/c and thus the a v e r a g e t r a n s v e r s e d i s t a n c e f r o m the decay v e r t e x to the b e a m t r a j e c t o r y is 15 m m for a K~ with 10 GeV/c m o m e n t u m . To d e t e r m i n e the b e a m v e r t e x d i s t a n c e d we applied the s a m e m e a s u r e m e n t p r o c e d u r e t ° g p a i r s and rr p a i r s . Fig. 2a and 2b show the d i s t r i b u t i o n of d all g p a i r s and lr p a i r s r e p s e c t i v e l y , with an e n e r g y of the p a i r >/10.0 GeV. The i n v a r i a n t m a s s s p e c t r u m of those e v e n t s , which have d >/10 m m , is depicted i n fig. 2c for g p a i r s and fi T. 3d for Ir p a i r s . No e n h a n c e m e n t is s e e n in the K~ m a s s r e g i o n of the g p a i r d i s t r i b u t i o n , wher e a s in the ~ p a i r d i s t r i b u t i o n a s h a r p ~ peak on top of p r a c t i c a l l y no b a c k g r o u n d i s visibTe. N o r m a l i z i n g these two m a s s d i s t r i b u t i o n s to each other, we can give a n o t h e r upper l i m i t for the b r a n c h i n g r a t i o B. A . ~ i n t e r v a l I ~ of ~-20 MeV a r o u n d the K~ m a s s is chosen, which c o n t a i n s m o r e than 70% of all p o s s i b l e K~ -~ y - g + decays [the g p a i r
Volume 29B, n u m b e r 8
PHYSICS
LETTERS
m a s s r e s o l u t i o n i s A M = ± 1 7 M e V [2]]. T h e n u m b e r of e v e n t s o b s e r v e d i n t h i s i n t e r v a l i s n = 1. T h e n u m b e r of b a c k g r o u n d e v e n t s ~, e x p e c t e d i n lwR, i s d e t e r m i n e d f r o m t w o 4 0 M e V w i d e t e s t . ~ . O . . m t e r v a i s o n b o t h s i d e s of I K ~ , a s s u m i n g a u r n form distribution for the background in these int e r v a l s . F r o m fig. 2c o n e f i n d s ~ = 2. T h e n u m b e r of o b s e r v e d b a c k g r o u n d e v e n t s b and signal events s, are individually samples f r o m P o i s s o n d i s t r i b u t i o n s w i t h m e a n s b a n d ~, t h e r e f o r e a l s o t h e i r s u m n = b+s i s a s a m p l e f r o m a Poisson distribution with mean g = b+~. On t h e b a s i s of t h e o n e s a m p l e p o i n t n = 1, which we have available from the over-all dis t r i b u t i o n , w e c a n c a l c u l a t e t h e u p p e r l i m i t ~o o n t h e m e a n g to b e "< So = 1.9
at 90~ confidence.
T h i s n u m b e r i s o b t a i n e d b y s o l v i n g eq. (4) f o r n o
h=0 h'
exp
-
g o = 0.1,
(4)
w h i c h g i v e s g o -- 3.9 o r ~o -- g o - b o -- 1.9. N o r m a l i z i n g to t h e n u m b e r of i n c o m i n g b e a m particles and correcting for the differences in electronics efficiency, analysis efficiency and a c c e p t a n c e b e t w e e n t h e ~z p a i r a n d 7r p a i r e x p e r iments, one finds an upper limit for the branching ratio B~ B
= 7.3 x 10 - 5 a t 90°~ c o n f i d e n c e . (5) o T h i s v a l u e i s a n i m p r o v e m e n t of o n e o r d e r of m a g n i t u d e w i t h r e s p e c t to t h e p r e s e n t u p p e r l i m i t B ~< 7.3 × 10 - 5 [3].
21 July 1969
The branching ratio B expected a weak and electromagnetic transition with a Feynman diag r a m s h o w n i n fig. 3 i s e x p e c t e d t o b e B g 5 × 10 - 9 [ 4 - 7 ] . T h e a p p e a r a n c e of a b r a n c h i n g r a t i o c o n s i d e r a b l y h i g h e r t h a n 5 × 10 - 9 w o u l d t h u s b e e v i d e n c e f o r t h e e x i s t e n c e of n e u t r a l l e p t o n i c c u r r e n t s c o u p l i n g to s t r a n g e n e s s c h a n g i n g hadronic currents. Our limit B o provides an upper limit on coupling constants occuring in models on neutral leptonic currents [8-10].
References
1. B.D. Hyams, W. Koch, D. Pellet, D. Potter, L. yon Lindern, E. Lorenz, G. LIltjens, U. Stierlin and P. W e i l h a m m e r , Phys. L e t t e r s 29B (1969) 128. 2. B.D. Hyams, W. Koch, D.C. Potter, J . D . Wilson, L. yon Lindern, E. Lorenz, G. Liltjens, U. Stierlin and P. W e i l h a m m e r , Nuclear Phys. B7 (1968) 1. 3. M. Bott-Bodenhausen, X. de Bouard, D.G. Cassel, D. Dekkers, R. F e l s t , R. Mermod, I. Savin, P. Scharff, M. Vivargent, T. R. Willits and K. Winter, Phys. L e t t e r s 24B (1967) 194. 4. L.M. Sehgal, On the e l e c t r o m a g n e t i c contribution to the decays KS-* / [ a n d KL-*/Z", P r e p r i n t , Tata Institute of Fundamental R e s e a r c h , Bombay, India, April 1969. 5. B.R. M a r t i n and E. de Rafael, Nuclear Phys. B8 (1968) 131. 6. N. Cabibbo and E. F e r r a r i , Nuovo Cimento 18 (1960) 928. 7. V. B a r g e r , Nuovo Cimento 32 (1964) 127. 8. M. L. Good, L. Michel and E. de Rafael, Phys. Rev. 151 (1966) 1194. 9. E. de Rafael, BNL Report 10879, 1966. 10. S. Okubo, University of R o c h e s t e r Report, UR 875-231, 1968.
* * * * *
523