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MEASUREMENT OF THE τ LIFETIME Mark II Collaboration-SLAC-LBL-Harvard
J. Jaros
To cite this version:
J. Jaros. MEASUREMENT OF THE τ LIFETIME Mark II Collaboration-SLAC-LBL-Harvard.
Journal de Physique Colloques, 1982, 43 (C3), pp.C3-106-C3-109. �10.1051/jphyscol:1982324�. �jpa-
00221877�
JOURNAL DE PHYSIQUE
CoZZoque C3, supple'ment
au
n o 12, Tome 43, de'cembre 1982 page C3-106MEASUREMENT OF T H E
-ILIFETIME
Mark I1 Collaboration-SLAC-LBL-Harvard P r e s e n t e d by J . A . J a r o s
S t a n f o r d L i n e a r A c c e Z e r a t o r C e n t e r ,
P.O.
Box 4349, S t a n f o r d , C a Z i f o r n i a 94305, U.S.A.1. I n t r o d u c t i o n . I f t h e t a u l e p t o n c o u p l e s t o t h e charged weak c u r r e n t w i t h u n i - v e r s a l s t r e n g t h , i t s l i f e t i m e can be e x p r e s s e d i n t e r m s of t h e muon's l i f e t i m e , t h e r a t i o o f t h e masses o f t h e muon and t h e t a u , and t h e t a u ' s b r a n c h i n g r a t i o 1 i n t o eTevT a s
We have used a new h i g h p r e c i s i o n d r i f t chamber i n c o n j u n c t i o n w i t h t h e MarkIIdetec- t o r a t PEP t o measure t h e l i f e t i m e o f t h e t a u . T h i s p a p e r d e s c r i b e s o u r measure- ment and summarizes t h e r e s u l t s of o t h e r t a u l i f e t i m e measurements.
2. Method. Tau l e p t o n s a r e pair-produced i n e+e- a n n i h i l a t i o n s , s o e a c h t a u h a s t h e known beam energy. Thus we can measure t h e l i f e t i m e by determining, t h e a v e r a g e decay l e n g t h of t h e t a u s ; a t PEP e n e r g i e s , E c m = 2 9 GeV, i t i s e x p e c t e d t o b e about 700
u .
The decay l e n g t h c a n b e measured when t h e t a u d e c a y s i n t h e three--charged- prong t o p o l o g y . It i s simply t h e d i s t a n c e between t h e p r o d u c t i o n p o i n t , i . e . t h e beam p o s i t i o n , and t h e p o s i t i o n of t h e decay v e r t e x . T h i s same t e c h n i q u e h a s been e x p l o i t e d by s e v e r a l PEP and PETRA e ~ ~ e r i m e n t s . ~ - ~3 . Apparatus. The measurement was performed w i t h t h e Mark I1 v e r t e x d e t e c t o r 6 in c o n j u n c t i o n w i t h t h e main d r i f t chamber. The v e r t e x d e t e c t o r i s a h i g h p r e c i s i o n d r i f t chamber d e s i g n e d t o measure t r a c k s a s a c c u r a t e l y a s p o s s i b l e i n t h e v i c i n i t y o f t h e i n t e r a c t i o n p o i n t . The chamber c a p t u r e s a B e r y l l i u m beam p i p e which i s 0.6%
o f a r a d i a t i o n l e n g t h t h i c k . The chamber h a s seven a x i a l l a y e r s i n a l l , f o u r j u s t beyond t h e beam p i p e a b o u t 12 cm from t h e b e a m l i n e , and t h r e e a d d i t i o n a l l a y e r s a t about 30 cm. The measurement a c c u r a c y i s a b o u t 100
u
p e r l a y e r . I n p r a c t i c e , t r a c k s which have been e x t r a p o l a t e d t o t h e i n t e r a c t i o n p o i n t a r e measured w i t h 100u
a c c u r a c y .4 . Event S e l e c t i o n . We s e l e c t e v e n t s i n which ( a t l e a s t ) one o f t h e t a u s has decayed i n t h e t h r e e - c h a r g e d prong t o p o l o g y . Tau p r o d u c t i o n a t ?EP/PETRA e n e r g i e s i s d i s t i n c t i v e : low m u l t i p l i c i t y , low mass, back-to-back j e t s a r e produced, which a r e e a s i l y d i s t i n g u i s h e d from h i g h e r m u l t i p l i c i t y hadron p r o d u c t i o n . We r e q u i r e t h e t o t a l c h a r g e t o be z e r o and t h e t h r e e p a r t i c l e i n v a r i a n t mass t o be i n t h e r a n g e 0.7 < m < 1.5 G ~ v / c ~ . To r e j e c t t a u p a i r s produced by two-photon p r o c e s s e s , we f u r t h e r r e q u i r e t h e t o t a l energy i n t h e e v e n t t o b e a t l e a s t a f o u r t h t h e c e n t e r 3rr o f mass e n e r g y and t h e t h r e e - p i o n e n e r g y t o exceed 3 GeV. We r e q u i r e a l l t h r e e o f t h e t r a c k s b e well-measured i n b o t h t h e main d r i f t chamber and t h e v e r t e x d e t e c t o r . 5. Decay Length. The decay l e n g t h i s d e t e r m i n e d once we have measured t h e beam p o s i t i o n , t h e decay v e r t e x p o s i t i o n , and t h e t a u d i r e c t i o n .
The r m s beam s i z e a t PEP is 500
u
h o r i z o n t a l l y and a b o u t 50u
v e r t i c a l l y . The a v e r a g e beam p o s i t i o n i s remarkably s t a b l e from one f i l l t o t h e n e x t . Over t h e c o u r s e of t h e e n t i r e experiment t h e h o r i z o n t a l beam p o s i t i o n v a r i e d l e s s t h a n 2 mm and t h e v e r t i c a l beam p o s i t i o n , 0.5 mm. We measured it by f i n d i n g t h e a v e r a g e i n t e r s e c t i o n p o i n t f o r a n ensemble o f well-measured t r a c k s . A s a c r o s s c h e c k , we have compared t h i s d e t e r m i n a t i o n o f t h e beam p o s i t i o n t o t h e v e r t e x p o s i t i o nArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982324
J.A. J a r o s C3- 107
measured i n hadronic e v e n t s . Fig. 1 shows t h a t t h e s e methods a g r e e . The width of t h e bx d i s t r i b u t t o n i s c o n s i s t e n t with t h e known beam s i z e , and t h e width of t h e Ay d i s t r i b u t i o n i s c o n s i s t e n t with our v e r t e x r e s o l u t i o n . This demonstrates t h a t t h e beams a r e s t a b l e .
7-82
,,,,,,
DECAY LENGTH ERROR (mm)Fig. 1 : H o r i z o n t a l and v e r t i c a l had- Fig. 2 : C a l c u l a t e d e r r o r i n t h e decay r o n i c v e r t e x p o s i t i o n s r e l a t i v e t o t h e l e n g t h .
beam p o s i t i o n . Only t h o s e r u n s with t a u decays a r e shown.
The decay v e r t e x p o s i t i o n and i t s e r r o r e l l i p s e a r e determined from t h e t h r e e pion t r a j e c t o r i e s and t h e i r a s s o c i a t e d e r r o r s with a chi-square minimization pro- cedure. We exclude e v e n t s with a v e r t e x chi-squared per degree of freedom g r e a t e r t h a n 6 . The b e s t e s t i m a t e f o r t h e p r o j e c t e d decay l e n g t h i s t h e n given i n terms of t h e decay v e r t e x p o s i t i o n r e l a t i v e t o t h e beam p o s i t i o n ( x v , y v ) , t h e sum of t h e beam and v e r t e x e r r o r m a t r i c e s ( u . . ) , and t h e T d i r e c t i o n c o s i n e s ( t x , t y ) by t h e
1 3 f o l l o w i n g e x p r e s s i o n :
The t a u d i r e c t i o n i s a c c u r a t e l y approximated by t h e d i r e c t i o n of t h e 371 system.
Then t h e decay l e n g t h i s
R =
l%dIp ,
P3n
where p3, i s t h e t o t a l momentum of t h e t h r e e pion system. -
F i g u r e 2 shows t h e c a l c u l a t e d e r r o r i n t h e decay l e n g t h , which depends on t h e opening a n g l e s and o r i e n t a t i o n of t h e decay. I n c o n t r a s t t o p r e v i o u s experiments, t h e average u n c e r t a i n t y i n t h e decay l e n g t h i s comparable t o , not f i v e t o t e n times g r e a t e r t h a n , t h e expected decay l e n g t h . Consequently, t h e s t a t i s t i c a l power of t h e experiment i s improved by roughly t h i s same f a c t o r , and t h e measurement b i a s i s s i g n i f i c a n t l y reduced.
JOURNAL DE PHYSIQUE
Fig. 3 : Measured decay l e n g t h s .
,.a* DECAY LENGTH (mm) .2.8A,
The measured decay l e n g t h s a r e shown i n F i g u r e 3 , where we have included o n l y t h o s e e v e n t s with decay l e n g t h e r r o r s l e s s t h a n 1.5 mm. The mean of t h e d i s t r i b u - t i o n i s obviously p o s i t i v e and i t s shape is asymmetric. We f i t t h e d i s t r i b u t i o n with a maximum l i k e l i h o o d t e c h n i q u e which t a k e s t h e decay l e n g t h e r r o r i n t o account event-by-event. The f i t t i n g f u n c t i o n i s t h e c o n v o l u t i o n of t h e g a u s s i a n decay l e n g t h e r r o r and an e x p o n e n t i a l decay d i s t r i b u t i o n . We f i n d t h a t t h e average decay l e n g t h i s 7 1 0 t 120
u.
6 . Checks and C o r r e c t i o n s . We have checked our t r a c k i n g , v e r t e x i n g , and f i t t i n g programs w i t h simulated d a t a generated by Monte Carlo t e c h n i q u e s . Rou h l y 1000
H
decays were f e n e r a t e d f o r each of t h r e e l i f e t i m e s , T, = 0 , T~ = 2.8 x 10- s , and r , = 5.6 x 10- s; t h e y were t h e n analyzed with t h e same programs used f o r a c t u a l d a t a a n a l y s i s . T a b l e I summarizes t h e average decay l e n g t h s generated f o r each of t h e t h r e e l i f e t i m e s , and t h e decay l e n g t h determined by f i t t i n g t h e "measured" decay l e n g t h d i s t r i b u t i o n . T h i s demonstrates t h a t our a n a l y s i s t e c h n i q u e i s a c c u r a t e .
Table I Monte Carlo Simulation
L i f e t i m e Average Decay Length Average Decay Length
(10-13 s ) Generated (p) F i t (u)
We performed an a d d i t i o n a l check by a n a l y z i n g pseudo-tau decays i n hadronic e v e n t s . Three p a r t i c l e combinations were chosen i n h a d r o n i c e v e n t s t o mimic t h e p r o p e r t i e s of t h e t h r e e pion t a u decays a s a c c u r a t e l y a s p o s s i b l e . The average
"decay l e n g t h " f o r t h e s e combinations was 2 5 0 2 4 0 u ; our hadron Monte Carlo e v e n t s gave a decay l e n g t h of 2 7 5 t 5 0
u .
The presence of charm decays e x p l a i n s t h e f i n i t e decay l e n g t h , and t h e Monte Carlo c o r r e c t l y s i m u l a t e s t h e d a t a .We s t u d i e d s y s t e m a t i c e f f e c t s by re-analyzing t h e d a t a with d i f f e r e n t assump- t i o n s about t h e beam p o s i t i o n , beam width, r & s o l u t i o n , and f i t t i n g f u n c t i o n . The observed v a r i a t i o n s l e a d u s t o a s s i g n a s y s t e m a t i c e r r o r o f ? 150
u
t o t h e decay l e n g t h .Using a Monte Carlo c a l c u l a t i o n , we e s t i m a t e t h a t 10% of our t a u c a n d i d a t e s a r e hadrons. T h i s l e a d s t o a + 5 0
u
c o r r e c t i o n i n t h e average decay l e n g t h . I n i t i a ls t a t e r a d i a t i o n lowers t h e average t a u energy from i t s nominal 14.5 GeV t o 13.8 GeV.
I n c o r p o r a t i n g both t h e s e c o r r e c t i o n s , we f i n d r T = 3.31 +- .57
+
.60 x 10-l3 s , where t h e f i r s t e r r o r i s t h e s t a t i s t i c a l e r r o r , and t h e second i s t h e s y s t e m a t i c . T h i s v a l u e i s c o n s i s t e n t with t h e o r e t i c a l e x p e c t a t i o n . Our measurement i s compared t o t h e o t h e r measurements which have appeared i n t h e l i t e r a t u r e o r were p r e s e n t e d t o t h i s conference i n Table 11. The number of decays s t u d i e d and t h e average decay l e n g t h e r r o r a r e a l s o shown f o r comparison. A l l t h e experiments a r e c o n s i s t e n tJ.A. J a r o s
w i t h t h e e x p e c t e d l i f e t i m e . The p r e s e n t experiment c o n f i r m s t h a t t h e t a u c o u p l e s t o t h e c h a r g e d weak c u r r e n t w i t h u n i v e r s a l s t r e n g t h w i t h i n t h e 10% s t a t i s t i c a l and s y s t e m a t i c e r r o r s .
T a b l e 11
Experiment Number of Average Decay
Decays Length E r r o r
(mm)
MARK I1
V e r t e x D e t e c t o r 7 1
R e f e r e n c e s
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