University of Pennsylvania, Philadelphia, Pensylvania. Received 28 March 1966.
The momentum spectrum of positrons from K +-~ ~o + e + + v was measured.
Volume 21, number 3
POSITRON
PHYSICS LETTERS
MOMENTUM
SPECTRUM
AND
BRANCHING
15 May L966
RATIO
OF K+e3 *
R. CESTER**, P . T . ESCHSTRUTH, G . K . O'NEILL, B. QUASSIATI** and D. YOUNT *** Princeton University, Princeton, New Jersey
and J . M . D O B B S , A.K. MANN, W . K . M c F A R L A N E and D . H . W H I T E ~ University of Pennsylvania, Philadelphia, Pensylvania
R e c e i v e d 28 March 1966
The momentum spectrum of positrons from K+-~ ~o + e+ + v was measured. The observed spectrum, containing 1679 events, is consistent with vector coupling with upper limits of 18 and 4 percent of scalar and tensor admixtures, respectively. The K~e3 branching ratio was measured to be 0.0498 -~0.002.
T h i s l e t t e r d e s c r i b e s an e x p e r i m e n t designed to obtain p r e c i s e m e a s u r e m e n t s of the m o m e n tum d i s t r i b u t i o n of the p o s i t r o n s from K+e3 decay, and of the K+e3 b r a n c h i n g ratio. The e x p e r i m e n t a l a p p a r a t u s is shown in fig. 1. A 525 MeV//c p o s i t i v e beam from the P r i n c e t o n P e n n s y l v a n i a A c c e l e r a t o r , taken at 46 ° to the i n t e r n a l proton beam, was m o d e r a t e d with copper a b s o r b e r s of a t h i c k n e s s such that kaons would stop in the following s c i n t i l l a t i o n counter 3. Using t i m e - o f - f l i g h t [1] and r a n g e to identify kaons, the n u m b e r of p a r t i c l e s in the incident b e a m m i s i d e n t i f i e d a s stopped K ' s was about 5% of the stopped K + r a t e , which was about 200 per second, at the t i m e of this e x p e r i m e n t . Six t h i n plate s p a r k c h a m b e r s in a magnetic field were used to d e t e r m i n e the m o m e n t a of the charged decay products. A p a i r of thin s c i n t i l l a t i o n c o u n t e r s (5 and 6) and a l a r g e a p e r t u r e gas ~ e r e n k o v counter (with threshold set at ~, ~ 10) were placed behind the spark c h a m b e r s . The c h a m b e r s w e r e pulsed when a K + had stopped and a decay e l e c t r o n had p a s s e d through all of the c o u n t e r s at the end of the c h a m b e r s (desc r i b e d a s "Co3 t r i g g e r " ) . Also, r u n s w e r e made with the ~ e r e n k o v counter r e m o v e d from * Work supported in part by the US Atomic Energy Commission.
** Permanent address: Istituto di Fisica, Universita di Torino, Italy. *** Now at Stanford Linear Accelerator Center, Stanford, California. t Now at Cornell University, Ithaca, New York.
the logic, in which case the c h a m b e r s were t r i g g e r e d on all charged decay p a r t i c l e s in coi n c i d e n c e with a stopped K + ("Co2 t r i g g e r " ) . The spark c h a m b e r s w e r e photographed in 90 ° s t e r e o on 35 m m film, which was m e a s u r e d with f i l m - p l a n e d i g i t i z e r s . The a p p a r a t u s was designed to p r o v i d e p r e cise m o m e n t u m m e a s u r e m e n t s and a l s o m o m e n t u m - i n d e p e n d e n t detection efficiency over at l e a s t a t w o - t o - o n e i n t e r v a l of m o m e n t u m . The m e a s u r e m e n t and computation of m o m e n t u m were checked with K~2 and K+2 events. After c o r r e c t i o n s w e r e made for ionlzaticm l o s s in the stopping region, the c e n t e r s of the m o m e n t u m d i s t r i b u t i o n s for K~2 and K~2 were in close a g r e e m e n t with the known m o m e n t a of these p a r t i c l e s . F r o m the widths of these peaks, the s t a n d a r d deviation of the m o m e n t u m m e a s u r e m e n t was found to v a r y from 2 to 4.50/0 depending on the value of the magnetic field. In o r d e r to cover the p o s i t r o n s p e c t r u m of K+ decay from 60 M e V / c to its upper end point and to achieve a m o m e n t u m - i n d e p e n d e n t detection efficiency, r u n s were made at t h r e e different magnetic fields A weight was d e t e r m i n e d for each event which gave the likelihood that a p o s i t r o n with a given origin in the stopping r e g i o n and a given m o m e n tum would be within the fiducial r e g i o n of the app a r a t u s . These weights were constant for r a d i i ot c u r v a t u r e g r e a t e r than a c e r t a i n m i n i m u m value and only events above the c o r r e s p o n d i n g m o m e n tum value at each m a g n e t i c field (Pmin, in table 1) were used in the final r e s u l t s . 343
Volume 21, number 3
PHYSICS
LETTERS
15 May 1966
I
/
Fig. 1. Experimental apparatus.
/
COPPER / ABSORBER¢---'-
SPARK
MAGNET
/
STOPPING
/,:oum'E.
No. 5
COUNTER
No~6
VETO COUNTERNo.' /
/
/
./
\// (c) TENSOR
O0 ~
25
I
I
50
75
I00
I
I
125
150
r'P'J
200
225
MOMENTUM MWIc
Fig. 2. Combined e x p e r i m e n t a l m o m e n t u m distribution c o m p a r e d with b e s t fits of (a) vector, (b) s c a l a r , (c) t e n s o r .
(o) PURE VECTOR - - - (b)VECTOR WITH 18% SCALAR. - - - - (c) VECTOR WITH 4 % TENSOR
1.4
12.
i.o
F(X} .8 .6
0
20
4o
6o
oo
I00
120
X IdWlc Fig. 3. Experimental values of F(#), compared with predictions of (a) pure vector with censtentform factor, (b) vector with 18% scalar, (c) vector with 4% tensor. The experimental points indicatedwith a trianglecorrespond to the upper branch of curves (b) and {c). part of the positron spectra and was less than 10% of the rate at any point. Finally, the experimental spectra were corrected for bremsstrahiung production in the stopping region which
reduced the rate at high m o m e n t u m and increased it at low m o m e n t u m by about 3~. The data taken at the three magnetic fields were combined to obtain a single distribution covering the m o m e n tum range 60 to 228 MeV/c. The relative weights of the data at different fields were derived in two ways: (1) by comparing the number of events in each spectrum in the interval 150-228 M e V / c where the efficiency was m o m e n t u m and field independent; and (2) by comparing the effective number of (K~2 + K ~ 2 ) events in the Co2 trigger spectrum at each field. The weighting factors obtained by the two methods were in good agreement and average values were used to combine the spectra. The data are summarized in table 1. The final experimental distribution was compared with the prediction of the current-current, parity non-conserving, V - A theory [2] as shown* in fig. 2. The best fit distributions for scalar and tensor couplings are also given in fig. 2. Subject to the assumption of constant form factors, under which the theoretical spectra are calculated, the dominant coupling is evidently vector. An alternative analysis [4] that does not involve assumptions concerning the structure of f+(q2 ) is the following. The positron spectrum for vector coupling can be written in the form
* We have modified the t h e o r e t i c a l prediction to take into account c o r r e c t i o n s f r o m r a d i a t i v e t e r m s using the calculations of G i n s b e r g [3].
345
Volume 21, number3
N(p)dp=
[G2/2(21r) 3] MK(M K -
PHYSICS LETTERS
2p)F(x)dp (1)
w h e r e p i s the p o s i t r o n m o m e n t u m , M K i s the K m a s s and F(x)
= foXdY(~-y)l .f+(2MKY) 12.
(2)
In eq. (2), f+(2MKY ) i s the single f o r m f a c t o r n e c e s s a r y to d e s c r i b e v i r t u a l s t r o n g i n t e r a c t i o n s in K~3 d e c a y , x = 2 P ( P m a x - P ) / ( M K - 2p), P m a x = (M 2 - m~)/2M K and 2MKY =q2 =PK-p~)2, w h e r e PK and iO~ a r e f o u r - v e c t o r s . The d i s t r i b u t i o n function (1) h a s one p a r t i c u l a r l y u s e f u l f e a t u r e . Since p i s a d o u b l e - v a l u e d function of x, and s i n c e F(x) i s an i n c r e a s i n g function of x, then N(P)/ [MK(MK - 2ib)] cc F(x} h a s the s a m e value f o r the two v a l u e s of p that c o r r e s p o n d to a p a r t i c u l a r x. T h i s f e a t u r e i s unique to v e c t o r coupling and independent of the s t r u c t u r e of the f o r m f a c t o r f + ~ z ) . In fig. 3 t h e e x p e r i m e n t a l v a l u e s of N(p)/ [MK(M K - 2p)] a r e p l o t t e d a g a i n s t x. T h e two v a l u e s of N(p)-/[MK(MK - 2ib) ] c o r r e s p o n d i n g to the s a m e v a l u e of x c o i n c i d e , within the l i m i t of e r r o r , o v e r the full r a n g e of x. To s e t l i m i t s on t h e coupling a d m i x t u r e s , we have f i r e d t h e d a t a t o a v e c t o r s p e c t r u m with an a d m i x t u r e of s c a l a r and to a v e c t o r s p e c t r u m with an a d m i x t u r e of t e n s o r . With 90% confidence, a d m i x t u r e s l a r g e r than 18% s c a l a r o r 4% t e n s o r a r e r e j e c t e d . T h e t h e o r e t i c a l d i s t r i b u t i o n s in F(x) f o r p u r e v e c t o r with c o n s t a n t f o r m f a c t o r and f o r t h e two c a s e s of a d m i x t u r e a r e shown in fig. 3. T h e s e c o n c l u s i o n s a r e in a c c o r d with t h o s e of p r e v i o u s K~3 m e a s u r e m e n t s [5] which a r e c o n s i s t e n t with p o s s i b l e a d m i x t u r e s of 4% s c s l ~ r o r 9% t e n s o r to t h e dominant v e c t o r coupling. It follows f r o m eqs. (1) and (2) that [f+(¢2)12 d e p e n d s only on t h e s e c o n d d e r i v a t i v e of t h e p o s i t r o n s p e c t r m n and t h e r e f o r e t h i s s p e c t r u m d o e s not p r o v i d e a s e n s i t i v e d e t e r m i n a t i o n of the s t r u c t u r e o f f + ( ~ ) . T h i s i s c o n f i r m e d by attemptin¢: to fit a v e c t o r s p e c t r u m with f+f@2) = A (1 + ~. q2/MK2 ) to the e x p e r i m e n t a l d i s t r i bution. W e find that the quality of fit d o e s not change a p p r e c i a b l y o v e r a l a r g e v a r i a t i o n of ;~. Branching ratio. T h e b r a n c h i n g r a t i o R of + Ke3 to (K~2 + K~2) w a s obtained a s K+e3 e v e n t s p e r Co2 count R× (K~2 + K~2) e v e n t s p e r Co2 count 1 1 × ~2 f/3 Ceff A w h e r e ~ 3 and ~22 a r e the a v e r a g e s o l i d a n g l e s of a c c e p t a n c e f o r p a r t i c l e s f r o m K~3 and (K~2 + K~2), r e s p e c t i v e l y , e e l f i s the ~ e r e n k o v c o i m t e r e f f i c i e n c y and A i s the f r a c t i o n of the 346
15 May 1966
positron spectrum actually measured assuming p u r e v e c t o r coupling and constant f o r m f a c t o r . C eft was found in s e p a r a t e t e s t s to be (97 ± 2)% o v e r the a p p r o p r i a t e f i d u c i a l r e g i o n . R was c a l c u l a t e d u s i n g the c o m b i n e d d a t a f r o m the t h r e e m a g n e t i c f i e l d s which y i e l d e d R = 0.0589 + 0.0016. The e r r o r i n c l u d e s u n c e r t a i n t i e s in a l l the f a c t o r s in the e x p r e s s i o n f o r R. Taking [6] R(K~2/K +) = 0.213 + 0.006 and R(K+2 / K +) = 0.632 + 0.006, our v a l u e of R(K+3/I~+Tis then 0.0498 ~ 0.002, in good a g r e e m e n t * with the a v e r a g e of the f o u r p r e v i o u s m e a s u r e m e n t s [6] which y i e l d R ( K ~ 3 / K +) = 0.049 + 0.003. F o r r e a l c o n s t a n t f o r m f a c t o r s , the r a t i o of the r e l a t i v e r a t e s R(K~3/K +) and R ( K ~ 3 / K +) i s r e l a t e d to the f o r m f a c t o r r a t i o ~ by [7] R(K~3----~) = 0.65 + 0.13~ + 0.019~ 2. RfK~3)
U s i n g [6] R ( K ~ 3 / S + ) = 0.034 ± 0.003 and R(K~3/ K +) above, one o b t a i n s t h ~ . ~ l u t i o n s ~ = +0 3 -HJ. + 0.26 _0:3~and ~ = - 6 . 9 1 - 0 . ~ . The l a t t e r s o l u tion i s not c o n s i s t e n t with r e c e n t r e s u l t s [8-11] on the p o l a r i z a t i o n and e n e r g y s p e c t r u m of m u o n s f r o m K~3. T h e p r e s e n t m e a s u r e m e n t of R ( K e 3 / K +) g i v e s the Cabibbo a n g l e [12] f o r the v e c t o r c o m ponent of the weak i n t e r a c t i o n c u r r e n t a s 0 v = 0.236 + 0.004, without c o r r e c t i o n s for s y m m e t r y b r e a k i n g [13], r a d i a t i v e e f f e c t s [6] o r the v a r i a t i o n [14] o f f + ( q 2 ) with q2. We would l i k e to thank the P P A o p e r a t i n g staff for t h e i r e f f o r t s on our behalf, and t h e i r unfailing c o o p e r a t i o n . We thank D r . E. B. Hughes f o r h i s a s s i s t a n c e in t h e a n a l y s i s . M r . K. E. W r i g h t and h i s staff w e r e r e s p o n s i b l e for the m e c h a n i c a l d e s i g n and c o n s t r u c t i o n of much of the a p p a r a t u s . We a l s o a c k n o w l e d g e the help of R. I m l a y , D. Bowen and D. H. R e a d i n g in running the e x p e r i m e n t .
References 1. D. Bowen et al., Princeton-Pennsylvania Accelerator Internal Report, PPAD 526 D (1964). The time structure of the primary beam has been used by other experiments at this machine (for example, V.L.Fitch, C.A.Quarles, and H.C.Wilkins, Phys. Rev. 140 (1965) 1089), since the initial observation by P. Piroue of the tight bunching of the internal proton beam.
* We have recently received a preprint of a paper by A. C. Callat~n in which is obtained the value R(K~.~/ K+) = 0.0394 * 0.OOlV. We are grateful to Dr. canYahan for providing us with his results before publication.
Volume 21, n u m b e r 3
PHYSICS
LETTERS
15 May 1966
8. V. Bisi, G . B o r r e a n i , A . M a r z a r i - C h i e s a , G. Rinaudo, M.Vigone and A . E . Werbrouck, P h y s . Rev. 139 (1965) B1068 and F . S . S h a k l e e , G . L . Jensen, B . P . R o e a m i D . S i n c l a i r , P h y s . Rev. 136 (1964) B 1423. 9. G.Gidal, W . M . P o w e l l , R . M a r c h and S.Natali, Phys. Rev. L e t t e r s 13 (1964) 95. 10. V . A . Smiraiinki and A. O. W e i s s e n b e r g , Phys. Rev. L e t t e r s 12 (1964) 233. 11. D . C u t t s , T . E l i o f f and R.Stiening, P h y s . Rev. 138 (1965) B969. 12. N. Cabihbo, P h y s . Rev. L e t t e r s 10 (1963) 531. 13. M.Admnollo and R.Gatto, Phys. Rev. L e t t e r s 13 (1964) 264. See also H . T . N i e h , P h y s . Rev. L e t t e r s 15 (1965) 902. 14. S.Oneda and J . S u c h e r , Phys. Rev. L e t t e r s 15 (1965) 927,
2. R . P . Fey--man and M. GeH-Mann, P h y s . Rev. 109 (1958) 193, and E . C . G . S u d a r s h a n and R . E . M a r s hak, P h y s . Rev. 109 (1956) 1360. 3. E . S . G i n s b e r g , P h y s . Rev. 142 (1966) 1035. 4. M . B o l s t e r l i and D.A.Geffen, P h y s . Rev. L e t t e r s 7 (1961) 203 and S.W. McDowell, L e c t u r e s at S e m i n a t on T h e o r e t i c a l physics, T r i e s t e , 1962 (Intern. At. E n e r g y Agency, Viemm 1963) p. 619. 5. J . L . B r o w n , J . A . K a d y k , G . H . T r f l l i n g , R . T . V a n de Walle, B . P . R o e and D . S i n c l a i r , P h y s . Rev. L e t t e r s 7 (1961) 423; G. L. J e n s e n , F . S . Sh-idee, B . P . Roe and D. Sinclair, P h y s . Rev. 136 (1964) B1431; G. B o r r e a n i , G. Rinaudo and A . E . Werhrouck, Phys. L e t t e r s 12 (1964) 123 and G . E . K a l m u s , A . K e r n a n , U . C a m e r i n i and C . H e n d e r s c n , UCRL - 11553 (1964). 6. A.H. Resenfeld, A. B a r b a r o - G a l t i e r i , W.H. B a r k e s , P . C . B a s t i e n , J . K i r z and M . R o o s , Rev. Mod. Phys. 37 (1965) 633. 7. P . D e n n e r y and H . P r i m a k o f f , Phys. Rev. 131 (1963) 1334; N. B r e n e , L. E g a r d t and B. Qvist, Nuclear P h y s i c s 22 (1961) 553. * * * * *
OBSERVATION
OF
X ° PRODUCTION
IN
~+n
INTERACTIONS*
H. O. C O H N Oak Ridge National Laboratory, Oak Ridge, Tew,zessee R . D. M c C U L L O C H Central Data Processing Facility, Union Carbide Nuclear Division, Oak Ridge, Tennessee
and W . M . B U G G a n d G. T . CONDO University of Tennessee, Knoxville, Tennessee and Oak Ridge National Laboratory, Oak Ridge, Tennessee Received 1 April 1966
We have o b s e r v e d the producticm of the X° in the #+ + d interaction at 3.29 G e V / c , u n c o r r e l a t e d wiht N* formation. The X ° was found in both the 7r+~- MM and the ~r+n-#+lr-Tr° s y s t e m s .
Recently Trilling et aL,[ I] have observed the W ~ decay m o d e of the X u (959 M e V ) m e s o n in the reaction: ~+ + p -. 21r+ + ~- + p + missing mass. In this reaction the production of the X ° was restricted to those events where an asso* R e s e a r c h s p o n s o r e d by the US Atomic Energy Cc~, m i s s i o n u n d e r c o n t r a c t with the Union Carbide C o r poration.
c i a t e d N * ( 1 2 3 8 ) ++ w a s p r o d u c e d . T h e i r w o r k r e p r e s e n t s t h e o n l y o b s e r v a t i o n of X ° p r o d u c t i o n i n ~N c o l l i s i o n s , a l l p r e v i o u s o b s e r v a t i o n s having been made in the reaction: K- + p-~ A°+X ° [2-7]. We report evidence for X ° production uncorrel a t e d w i t h N * ( 1 2 3 8 ) f o r m a t i o n i n a n e x p o s u r e of t h e B N L 20 i n c h d e u t e r i u m b u b b l e c h a m b e r t o 3.29 G e V / c ~ + m e s o n s . T h e r e a c t i o n s s t u d i e d a r e : 347
