Balandin, M P

Grebenyuk, V M

Konin, A D

Ponormarev, A N

Zinov, V G

CERN Document Server

CERN LIBRARIES, GENEVA CM-P00100725 JOINT INSTITUTE FOR NUCLEAR RESEARCH, DUBNA Report P1 - 7892 MEASUREMENT OF THE POSITIVE MUON'S LIFETIME M.P. Balandin , V.M. Grebenyuk, V.G. Zinov A.D. Konin and A.N. Ponomarev Dubna 1974 Trans l a t ed a t CERN by R. Luther (Or ig ina l : Russian) Not r ev i s ed by the T r a n s l a t i o n Serv ice (CERN Trans. 74-9) Geneva September 1974 - 1 -Sent t o JETP I n t r o d u c t i o n The f i r s t r e l a t i v e l y a c c u r a t e measurements of t h e p o s i t i v e muon 's l i f e t i m e ( o . l ± 0 . 0 5 ) % were c a r r i e d ou t i n 1962-1963 / 1 - 4 / b u t no f u r t h e r p r o g r e s s was made f o r a l o n g t i m e . The pape r by R.W. and D.L. Wi l l i ams added l i t t l e t o t h e e x p e r i m e n t a l a c c u r a c y a l r e a d y a c h i e v e d , and i t was on ly t h e change i n m e a s u r i n g t e c h n i q u e proposed by Duelos et al./6/ that pushed research forward. All the papers reveal certain substantial systematic limitations to the accuracy with which the muon's lifetime is measured. The c o n v e n t i o n a l a p p a r a t u s used f o r d e t e c t i n g p o s i t r o n s from muon decay has a s m a l l s o l i d a n g l e . T h i s r e d u c e s the d a t a a c q u i s i t i o n r a t e and makes i t d i f f i c u l t t o s e l e c t u s e f u l e v e n t s by comparing t h e p o s i t r o n s which a r e d e t e c t e d w i t h t h e muon a t r e s t . Background e v e n t s can s l i p i n i n many ways . The s m a l l s o l i d a n g l e a l s o c r e a t e s a n o t h e r d i f f i c u l t y . Allowance has t o be made f o r t h e p o s s i b l e e f f e d of asymmetry i n t h e o u t g o i n g p o s i t r o n s . T h e r e f o r e , t h e r e s i d u a l magnetic field where the muon is stopped must be reduced to hundredths or thousandths of an oersted. Moreover , t h e f a c t t h a t t h e decay p o s i t r o n s a r e v e r y e n e r g e t i c has n o t y e t been s u f f i c i e n t l y e x p l o i t e d . Method of measurement The method used by us i s based on t h e i d e a of 4 π - p o s i t r o n detection using a Cherenkov detector. In this way the data acquisition rate was increased, the background reduced and the effect caused by t h e a s y m m e t r i c a l emergence of t h e p o s i t r o n s i s s u p p r e s s e d . Device The measurements were c a r r i e d ou t i n t h e meson b e a m - l i n e of t h e JINR s y n c h r o c y c l o t r o n . A pure beam of 130 MeV/c muons was u s e d . The muons were s e l e c t e d from t h e backward decay of p i o n s c a p t u r e d i n t h e beam l i n e . - 2 -F i g . 1 shows a b l o c k d iagram of t h e e x p e r i m e n t . S c i n t i l l a t i o n c o u n t e r s 1 and 2 , measu r ing 10 x 10 x 1 cm, a r e used to r e c o r d the i n c i d e n t muons. A w a t e r t h r e s h o l d Cherenkov c o u n t e r i s used to r e c o r d t h e p o s i t r o n s o n l y . The muons' energy was s e l e c t e d so t h a t t h e y remained i n t h e c e n t r e of t h e Cherenkov d e t e c t o r ' s vo lume. The s o l i d a n g l e f o r p o s i t r o n d e t e c t i o n i s t h u s 4 π. The d imens ions of t h e r a d i a t o r (Ø 30 × 30 cm) a r e s e l e c t e d so t h a t t h e i n c i d e n t muons do n o t r a d i a t e Cherenkov l i g h t and t h e p o s i t r o n r e c o r d i n g e f f i c i e n c y r ema ins h i g h . Th i s p r e v e n t s t h e muon stop signal from affecting the time position of the outgoing positron's signal. Two FEU-49 photomultipliers scan the entire volume of t h e w a t e r r a d i a t o r w i t h i t s d i f f u s e l y r e f l e c t i n g l a y e r of MgO ( f i g . 2 ) . The p h o t o m u l t i p l i e r s a r e s e l e c t e d so t h a t t h e i r photo-cathodes' sensitivity is both high and well-matched. Sheet Permalloy was used to screen the photomultipliers and the radiator volume from t h e m a g n e t i c f i e l d . The whole s t r u c t u r e was housed i n s i d e a s t e e l c y l i n d e r 1 m l o n g . A c o p p e r - w i r e s o l e n o i d i s wound over t h e s t e e l s c r e e n i n o r d e r t o p r o v i d e a c t i v e d . c . compensa t ion f o r t h e remanent m a g n e t i c f i e l d . The f i e l d was c o n c e n t r a t e d a t 0 . 0 1 oe by means of a b u i l t - i n P e r m a l l o y d e t e c t o r . A l e a d c o l l i m a t o r Ø 9 cm was p l a c e d a t t h e p o i n t where t h e muons e n t e r e d t h e Cherenkov c o u n t e r , and a window was c u t i n t h e s t e e l s c r e e n . S e l e c t i o n of c o n d i t i o n s f o r measurement As i n o t h e r p a p e r s , on ly t h o s e e v e n t s were s e l e c t e d i n which j u s t one muon ( t h e s t a r t muon) and one p o s i t r o n a p p e a r e d d u r i n g t h e g a t i n g p u l s e . In t h i s ca se t h e decay curve i s d e s c r i b e d by a v e r y s imp le fo rmula (A exp ( - λ t ) + B ) , where t i s t h e t i m e , λ - t h e decay r a t e , and A and Β a r e c o n s t a n t s . As t h e c a l c u l a t i o n s showed, t h e r e a r e optimum c o n d i t i o n s f o r measurements depend ing on the i n t e n s i t y of t h e muon s t o p s and t h e l e n g t h of the i n t e r v a l d u r i n g which p o s i t r o n s a r e d e t e c t e d . F i g . 3 shows t h e r e s u l t s of t h e c a l c u l a t i o n s i n g raph form. - 3 -I t i s i n t e r e s t i n g to n o t e t h a t w i t h t h i s method t h e a c c u r a c y w i t h which the muon 's l i f e t i m e can be measured i s l i m i t e d t o a b o u t 10-5. The method must be changed in order to improve on this. At a muon intensity of 7.103 sec-1, not allowing for the duty f a c t o r , t h e f u l l g a t e w i d t h was 20 µsec. The ze ro moment f o r the a p p e a r a n c e of p o s i t r o n s i n r e l a t i o n to the muon s t o p i s s h i f t e d 5 µsec on the t ime s c a l e . Th i s r e d u c e s the p o s s i b l e e f f e c t of transient processes caused by signals from particles passing through the detectors before the gates are opened. E l e c t r o n i c s F i g . 4 shows a s i m p l i f i e d b l o c k d iagram of t h e e l e c t r o n i c s system. Counters 1 and 2 picked out the incoming muon (C1 coincidences). Counters 3 and 4 identified the decay positron. The a m p l i f i e r s i n c o u n t e r c h a n n e l s 3 and 4 were a d j u s t e d so t h a t s i g n a l s from t h e same f l a s h were e q u a l i n h e i g h t . Dur ing r u n s t h e c o u n t i n g r a t e i n t h e s e c h a n n e l s was a l s o t h e same. The f o l l o w i n g a c t i o n was t a k e n i n o r d e r t o improve t h e u n i f o r m i t y of t h e p o s i t r o n d e t e c t i o n e f f i c i e n c y . F i r s t l y , c o i n c i d e n c e s 3 and 4 were s e l e c t e d ( c i r c u i t C3) so t h a t t h e ene rgy t h r e s h o l d f o r p o s i t r o n d e t e c t i o n could be r educed w i t h o u t i n t e r f e r e n c e from t h e p h o t o m u l t i p l i e r s . Second ly , d i s c r i m i n a t o r D 5 f o l l o w i n g l i n e a r a d d e r LA was used t o s e l e c t t h o s e e v e n t s i n which , f o r i n s t a n c e , one of t h e p u l s e s from p h o t o m u l t i p l i e r s 3 and 4 was l a r g e . T h i s may o c c u r when t h e p o s i t r o n emerges i n t h e d i r e c t i o n of one of t h e p h o t o m u l t i p l i e r s , and a l a r g e p a r t of t h e l i g h t cone f a l l s on i t s p h o t o c a t h o d e . The m u l t i p l e e v e n t d e t e c t i o n c i r c u i t s (ME1 and ME2) a l lowed t h e t ime -code c o n v e r t e r (TC) t o s e l e c t e v e n t s when a second muon o r p o s i t r o n d id n o t a p p e a r w h i l s t t h e g a t e was open . Delay l i n e DL-2 s h i f t e d t h e p o s i t r o n s i g n a l ( " S t o p " ) 5 µ s e c . i n r e l a t i o n t o t h e muon s t o p s i g n a l ( " S t a r t " ) , i . e . i t s h i f t e d t h e b e g i n n i n g of t h e e x p o n e n t i a l . Delay l i n e DL-1 ( a l s o 5 µ s e c . ) was used i n t h e same way t o r e j e c t e v e n t s where a second muon a r r i v e d d u r i n g t h e g a t i n g p u l s e . - 4 -In o r d e r t o e x c l u d e t r a n s i e n t e f f e c t s caused by t h e i n t e n s i t y -r e l a t e d s h i f t i n t h e d . c . l e v e l , a l l e l e c t r o n i c c o n n e c t i o n s were g a l v a n i c . Where t h i s was i m p o s s i b l e , b i p o l a r s i g n a l s were p r o d u c e d . Time-code c o n v e r t e r The t i m e - c o d e c o n v e r t e r forms a major p a r t of t h e a p p a r a t u s . I t was s p e c i a l l y d e s i g n e d f o r t h e e x p e r i m e n t . I t t h e r e f o r e i n c l u d e s c e r t a i n s p e c i a l f e a t u r e s . F i g . 5 shows a s i m p l i f i e d b l o c k d iagram of t h e c o n v e r t e r . The s t a r t p u l s e ( s t o p p e d muon) t r i g g e r s f l i p -f l o p s F1 and F 2 . S i g n a l s from t h e c r y s t a l o s c i l l a t o r CO p a s s t o r e g i s t e r s Rl and R2a v i a g a t i n g c i r c u i t s C1 and C2 r e s p e c t i v e l y . The " s t o p " p u l s e (decay p o s i t r o n ) r e t u r n s f l i p - f l o p F2 t o i t s o r i g i n a l s t a t e , and t h e d i g i t a l code of t h e t ime i n t e r v a l i s r e c o r d e d on r e g i s t e r R2a. F l i p - f l o p F1 r e t u r n s t o i t s o r i g i n a l s t a t e on ly a f t e r a g i v e n number of p u l s e s has been accumula t ed i n r e g i s t e r R l , i . e . i t s e t s t h e g a t e w i d t h by d i g i t a l means . During t h e g a t e i n t e r v a l , event pulses (arrival of second muon, second positron) may be transmitted via gating circuit C3 to register R2b at any time. In the e v e n t code 10 b i t s (R2a) a r e a s s i g n e d t o t ime and 2 b i t s (R2b) t o c h a r a c t e r i s t i c s . At t h e end of t h e g a t i n g p u l s e , t h e e v e n t code i s t r a n s m i t t e d t o t h e AI-4096 memory i n t h e measu r ing c e n t r e of t h e L a b o r a t o r y f o r N u c l e a r Problems where t h e e v e n t s a r e s o r t e d and s t o r e d . The f r equency of t h e c r y s t a l o s c i l l a t o r was a p p r o x i m a t e l y 50 MHz ( i t s a b s o l u t e v a l u e was known t o an a c c u r a c y of 100 H z ) . Checking t h e o p e r a t i o n of t h e a p p a r a t u s In o r d e r t o a c h i e v e h i g h measurement a c c u r a c y , t h e o p e r a t i o n of the apparatus must be checked. The main criterion is the differential non-linearity of the whole electronics system from the c o u n t e r s t h r o u g h t o the t ime -code c o n v e r t e r . N o n - l i n e a r i t y may be caused bo th by c o u p l i n g between t h e s t a r t - s t o p c h a n n e l s and by t h e s u p e r p o s i t i o n of p u l s e s i n each c h a n n e l . I f t h e mean d i f f e r e n t i a l n o n - l i n e a r i t y of t h e e l e c t r o n i c s sy s t em i s r e p r e s e n t e d i n the form - 5 -(C + D λ t ) , i t t h e n f o l l o w s from t h e e s t i m a t e s t h a t t h e D/C r a t i o i s e q u a l t o t h e r e l a t i v e e r r o r i n t h e l i f e t i m e m e a s u r e m e n t s . The d i f f e r e n t i a l n o n - l i n e a r i t y of t h e a p p a r a t u s was measured i n c o n d i t i o n s s i m i l a r t o t h e o p e r a t i n g c o n d i t i o n s . The s i g n a l s from two s c i n t i l l a t i o n c o u n t e r s , which r e c o r d e d γ - q u a n t a from r a d i o a c t i v e s o u r c e s , were t r a n s m i t t e d to the s y s t e m ' s i n p u t s . A f t e r s e v e r a l days of measu remen t s , i t was found t h a t t h e mean d i f f e r e n t i a l n o n - l i n e a r i t y of t h e whole sys tem d i s a p p e a r s a t D/C = ± 10-5. F i g . 6 shows the intermediate results from the tests which clearly demonstrate the quality of the electronics system. The t ime r e s o l u t i o n of t h e Cherenkov d e t e c t o r a t 10-4 from t h e maximum is 100 nsec. (fig. 7). According to the results from the runs, the decay positrons were detected with 90% efficiency. Measurements and p r o c e s s i n g of r e s u l t s The measurements were c a r r i e d o u t d u r i n g 4 r u n s on t h e synchrocyclotron on different days. During operation, the data were transmitted through a direct link to the computer every 2 hours. Rapid p r o c e s s i n g was t h e n c a r r i e d ou t u s i n g s i m p l i f i e d p r o g r a m s . The r e s u l t s were p r e s e n t e d i n bo th d i g i t a l and g r a p h i c form. At t h e end of t h e run t h e t ime s p e c t r a were p r o c e s s e d i n f u l l u s i n g t h e χ2 minimum method. When t h e p a r a m e t e r s were v a r i e d , b o t h t h e background p a r t and t h e u s e f u l p a r t of t h e spec t rum were t aken into account by means of the formulae(C exp (- λ t)+ B) t < 0 and (A exp (- λ t)+ B) t > 0. The results coincided when t h e background and u s e f u l p a r t s of t h e spec t rum were p r o c e s s e d s e p a r a t e l y w i t h i n t h e l i m i t s of e r r o r . The f i r s t t ime spec t rum c h a n n e l was s h i f t e d 320 n s e c . from t h e b e g i n n i n g of t h e e x p o n e n t i a l . The r e s u l t s a r e shown i n t h e t a b l e . The muon l i f e t i m e v a l u e ( 2 . 1 9 7 1 1 ± 0 .00008 µ s e c ) i s c o r r e c t e d once to a l l o w f o r the f i n a l r e s o l u t i o n of t h e c i r c u i t s which i d e n t i f y e v e n t s w i t h two muons o r two p o s i t r o n s . The r e l a t i v e v a l u e of t h e c o r r e c t i o n i s a p p r o x i m a t e l y 10-5. One hundred h o u r s of p h y s i c s y i e l d e d 109 u s e f u l e v e n t s . - 6 -The a c c u r a c y of t h e s e t - u p used by Duclos e t a l . / 6 / may be improved s t i l l f u r t h e r by i n c r e a s i n g t h e speed of r e s p o n s e of t h e p o s i t r o n d e t e c t o r s and by e x t e n d i n g t h e i r s o l i d a n g l e t o 4 π. In c o n c l u s i o n , t h e a u t h o r s a r e d e e p l y g r a t e f u l t o A . I . Mukhin f o r u s e f u l d i s c u s s i o n s , t o L . I . Lap idus f o r h i s c o n t i n u e d i n t e r e s t and s u p p o r t , t o S.V. Medved' f o r h e l p i n g t o p e r f e c t t h e measu r ing s y s t e m , t o V . I . Komarov, S.M. Korenchenko and V . S . Roganov f o r t h e i r helpful advice, and to M.M. Petrovskij for helping with the construction of the apparatus. - 7 -Bibl iography 1. P.J.M. Parley, T. Massam, T. Muller and A. Zichichi. Proc. 1962 Int. Conf. on High Energy Physics at CERN, p. 415. 2 . H.A. Lundy. Phys. Rev., 125, 1936 ( l962 ) . 3. M. Eckhause, T.A. Pillipas, R.B. Sutton and R.E. Welsh. Phys. Rev., 132, 422 (1963). 4. S.L. Meyer, E.W. Anderson, E. Blesér, L.M. Lederman, J.L. Rosen, J. Rothberg, I.-T. Wang. Phys. Rev., 132, 2693 (1963). 5. R.W. Williams and D.L. Wil l iams. Phys. Rev. D6, 737 (1972). 6. J . Duclos, A. Magnon and J . P ica rd , Phys. L e t t . , 47B, 491 (1973). The manuscript was received by the publ i sh ing department on 25 Apr i l 1974. Table Run Lifetime ( µ s e c ) χ2 /< χ 2> 1 2.19740 ± 0.00031 0.82 2 2.19687 ± 0.00014 1.02 3 2.19731 ± 0.00014 1.18 4 2.19709 ± 0.00013 0.87 Total spectrum P a p e r / 6 / 2.19711 ± 0.00008 0.87 2.1973 ± 0.0003 F i g . 1 . Block d iagram of t h e e x p e r i m e n t . F i g . 2 . S t r u c t u r e of t h e Cherenkov c o u n t e r : 1 . winding f o r compensat ing t h e magnet f i e l d ; 2 . s t e e l magne t i c s c r e e n ; 3 . Pe rmal loy magne t ic s c r e e n ; 4. Pe r spex r a d i a t o r w a l l s ; 5 . MgO l i g h t r e f l e c t o r ; 6 . w a t e r ; 7 . p h o t o m u l t i p l i e r . F i g . 3 . Optimum i n t e n s i t y g r a p h . t - g a t e w id th ; Τ - measur ing t ime ; I - s topped muon i n t e n s i t y . F i g . 4 . Block diagram of t h e e l e c t r o n i c sys tem; D - d i s c r i m i n a t o r , C - c o i n c i d e n c e c i r c u i t , M - mixe r , DL - d e l a y l i n e , LA - l i n e a r a d d e r , A - a m p l i f i e r , TC - t ime -code c o n v e r t e r , ME - c i r c u i t f o r d e t e c t i n g a second p u l s e i n t h e g a t e s , AI - AI4096 b u f f e r s t o r e . F i g . 5 . Block d iagram of t h e t ime -code c o n v e r t e r : F - f l i p f l o p , CO - c r y s t a l o s c i l l a t o r , C - c o i n c i d e n c e c i r c u i t , R - r e g i s t e r . Fig. 6. Time s p e c t r a : 1. 1 ' s t a r t ' pu l se and 1 ' s t o p ' p u l s e i n t h e g a t e ; 2 . 1 ' s t a r t ' , 2 ' s t o p ' ; 3 . 2 ' s t a r t ' , 1 ' s t o p ' ; 4. 2 ' s t a r t ' , 2 ' s t o p ' . F i g . 7 . Time r e s o l u t i o n of t h e a p p a r a t u s . Fig. 8. Decay curve (for one run). 

Measurement of the positiv muon's lifetime

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