A measurement of the Z0 leptonic partial widths and the
vector and axial vector coupling constants
Citation for published version (APA):
L3 Collaboration, & Leytens, X. (1990). A measurement of the Z0 leptonic partial widths and the vector and axial
vector coupling constants. Physics Letters B, 238(1), 122-130. https://doi.org/10.1016/0370-2693(90)92111-U
DOI:
10.1016/0370-2693(90)92111-U
Document status and date:
Published: 29/03/1990
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Volume 238, number 1 PHYSICS LETTERS B 29 March 1990 A M E A S U R E M E N T O F T H E Z ° L E P T O N I C P A R T I A L W I D T H S A N D T H E V E C T O R A N D A X I A L V E C T O R C O U P L I N G C O N S T A N T S L3 C o l l a b o r a t i o n B. A D E V A a, O. A D R I A N I
b
M. A G U I L A R - B E N I T E Z ~, H. A K B A R I a, j. A L C A R A Z c, A. A L O I S I O e, G. A L V E R S O N f, M. G. A L V I G G I e, Q. A N g, H. A N D E R H U B h, A. L. A N D E R S O N i, V. P. A N D R E E V J, T. A N G E L O V i, L. A N T O N O V k, D. A N T R E A S Y A N ~, A. A R E F I E V m, T. A Z E M O O N n, T. A Z I Z o, p. V. K. S. BABA g, P. B A G N A I A P, J. A. B A K K E N q, L. B A K S A Y r, R. C. B A L L n, S. B A N E R J E E o.g, j. B A O d, L. B A R O N E P, A. BAY s, U. B E C K E R i,,,S. B E I N G E S S N E R t, Gy. L. B E N C Z E u.r, j. B E R D U G O c, p. B E R G E S i, B. B E R T U C C I P, B. L. B E T E V k, A. B I L A N D h, R. B I Z Z A R R I P, J. J. B L A I S I N G t, p. B L ( ) M E K E v, B. B L U M E N F E L D '~, G. J. B O B B I N K w, M. B O C C I O L I N I b, W. B O H L E N ", A. B O H M v, T. B O H R I N G E R Y, B. B O R G I A P, D. B O U R I L K O V k, M. B O U R Q U I N ~, D. B O U T I G N Y t, J. G. B R A N S O N z, I. C. B R O C K '~, F. B R U Y A N T a, C. B U I S S O N ~, J. D. B U R G E R i, j. p. B U R Q ~, X. D. C A I h, D. C A M P A N A ~, C. C A M P S v, M. C A P E L L n, F. C A R B O N A R A e, F. C A R M I N A T I b, A. M. C A R T A C C I b, M. C E R R A D A c, F. C E S A R O N I P, Y. H. C H A N G i, U. K. C H A T U R V E D I g, M. C H E M A R I N I~, A. C H E N v, C. C H E N ~, G. M. C H E N ~, H. F. C H E N ~, H. S. C H E N 5, M. C H E N ~, M. L. C H E N n, G. C H I E F A R I e, C. Y. C H I E N d, C. C I V I N I N I b, I. C L A R E i, R. C L A R E i, G. C O I G N E T ~, N. C O L I N O a, V. C O M M I C H A U v, G. C O N F O R T O b, A. C O N T I N a, F. C R I J N S w, X. Y. C U I g, T. S. D A I i, R. D ' A L E S S A N D R O b, A. D E G R I ~ t, K. D E I T E R S r, E. D E N E S u P. D E N E S q, F. D E N O T A R I S T E F A N I v, M. D H I N A h, M. D I E M O Z v, H. R. D I M I T R O V k, C. D I O N I S I P, F. D I T T U S ~, R. D O L I N i, E. D R A G O e, T. D R I E V E R w, p. D U I N K E R w.~, I. D U R A N ax, M. E L K A C I M I ~, A. E N G L E R '~, F. J. E P P L I N G i, F. C. E R N E w, p. E X T E R M A N N ~, R. F A B B R E T T I u, G. F A B E R i, S. F A L C I A N O a,p, S. J. F A N 0, M. F A B R E h, j. FAY ta,
J. F E H L M A N N h, H. F E N K E R f, T. F E R G U S O N '~, G. F E R N A N D E Z ~, F. F E R R O N I P, H. F E S E F E L D T v, j. F I E L D ~, G. F O R C O N I ~, T. F O R E M A N w, K. F R E U D E N R E I C H h, W. F R I E B E L ~, M. F U K U S H I M A i, M. G A I L L O U D Y, Yu. G A L A K T I O N O V m, E. G A L L O b, S. N. G A N G U L I o, S. S. G A U v, S. G E N T I L E P, M. G E T T N E R f, M. G L A U B M A N f, S. G O L D F A R B n, Z. F. G O N G g'~, E. G O N Z A L E Z ~, A. G O R D E E V m, p. G O T T L I C H E R ", D. G O U J O N ~, C. G O Y t, G. G R A T T A '1, A. G R I M E S r, C. G R I N N E L L i, M. G R U E N E W A L D n, M. G U A N Z I R O L I g, A. G U R T U o, D. G O S E W E L L ", H. H A A N ", S. H A N C K E "t, K. H A N G A R T E R v, M. H A R R I S a, D. H A R T I N G w, F. G. H A R T J E S w, C. F. H E 0, A. H E A V E Y q, T. H E B B E K E R "/, M. H E B E R T ~, G. H E R T E N i, U. H E R T E N v, A. H E R V E a, K. H I L G E R S v, H. H O F E R h, L. S. H S U v, G. H U g, G. Q. H U e, B. I L L E 13, M. M. ILYAS g, V. I N N O C E N T E e, E. I S I K S A L h, E. J A G E L g, B. N. J I N ~, L. W. J O N E S n, p. K A A R E T q, R. A. K H A N g, Yu. K A M Y S H K O V ~, D. K A P L A N f, Y. K A R Y O T A K I S ~,a, V. K H O Z E J, D. K I R K B Y n, W. K I T T E L w, A. K L I M E N T O V m, p. F. K L O K w, A. C. K O N I G ,,i, O. K O R N A D T v, V. K O U T S E N K O m, R. W. K R A E M E R ~, T. K R A M E R i, V. R. K R A S T E V k, W. K R E N Z v, A. K U H N x, V. K U M A R g, A. K U N I N m, S. K W A N f, A. V A N L A A K v, V. L A L I E U ~, G. L A N D I b, K. L A N I U S ~, D. L A N S K E ", S. L A N Z A N O ~, P. L E B R U N 13, p. L E C O M T E h, p. L E C O Q ~, P. LE C O U L T R E h, I. L E E D O M f, J. M. LE G O F F a, L. L E I S T A M a, R. L E I S T E ~, J. L E T T R Y h, p. M. L E V C H E N K O J, X. L E Y T E N S w, C. LI ~, H. T. LI 5, J. F. LI g, L. LI h, p. j. LI 0, X. G. LI 8, j. y . L I A O e, R. L I U g, Y. L I U g, Z. Y. L I N ~, F. L. L I N D E ~, D. L I N N H O F E R a, W. L O H M A N N r,, S. L O K O S ~, E. L O N G O P, Y. S. L U ~, J. M. L U B B E R S w,
K. L U B E L S M E Y E R v, C. L U C I a, D. L U C K E Y ~.i, L. L U D O V I C I P, X. L U E ~, L. L U M 1 N A R I P, W. G. MA ~, M. M A C D E R M O T T h, R. M A G A H I Z r M. M A I R E t, p. K. M A L H O T R A o, A. M A L I N I N m, C. MAIqA ax, D. N. M A O n, y . F. M A O 5, M. M A O L I N B A Y r,, p. M A R C H E S I N I ~, A. M A R C H I O N N I b, j. p. M A R T I N Is, L. M A R T I N E Z c, F. M A R Z A N O P, G. G. G. MASSARO w, T. M A T S U D A i, K. M A Z U M D A R o, p. M c B R I D E ", Th. M E I N H O L Z v, M. M E R K w, L. M E R O L A e, M. M E S C H I N 1 b, W. J. M E T Z G E R ", Y. M1 g, M. M I C K E v, U. M I C K E "~, G. B. M I L L S ", Y. M I R g, G. M I R A B E L L I P, J. M N I C H ", L. M O N T A N E T a, B. M O N T E L E O N I b, G. M O R A N D s, R. M O R A N D t, S. M O R G A N T I P, V. M O R G U N O V m, R. M O U N T q, E. N A G Y ,.a, M. N A P O L I T A N O e H. N E W M A N q, L. N I E S S E N ", W. D. N O W A K ¢, J. O N V L E E w D. P A N D O U L A S v, G. P A T E R N O S T E R e, S. P A T R I C E L L I e, Y. J. PEI v, y . P E N G w, D. P E R R E T - G A L L I X t, j. P E R R I E R s, E. P E R R I N s, A. P E V S N E R d M. P I E R I b, p. A. PIROUt~ q, V. P L Y A S K I N m, M. P O H L r,, V. P O J I D A E V m, C. L. A. POLS w, N. P R O D U I T s, J. M. Q I A N i.g, K. N. QURESHI g, R. RAGHAVAN o G. R A H A L - C A L L O T h, j. V O N R A N G O 'I, P. R A Z I S h,
K. R E A D q, D. R E N h, Z. R E N g, S. R E U C R O F T ~ T. R I E M A N N ;, C. R I P P I C H '~, S. R O D R I G U E Z ~, B. P. R O E n, M. R O H N E R 'I, Th. R O M B A C H v, L. R O M E R O c, j. ROSE "¢, S. R O S I E R - L E E S ~, Ph. R O S S E L E T Y, J. A. R U B I O a.c, W. R U C K S T U H L s, H. R Y K A C Z E W S K I h, M. S A C H W 1 T Z ~, J. S A L I C I O c, G. S A U V A G E t A. SAVIN m, V. S C H E G E L S K Y J, P. S C H M I T T K, D. S C H M I T Z v, P. S C H M I T Z v M. S C H N E E G A N S ~, M. S C H O N T A G v, H. S C H O P P E R ~', D. J. S C H O T A N U S w, H. J. S C H R E I B E R ;, R. S C H U L T E ", S. S C H U L T E v, K. S C H U L T Z E v j. S C H U T T E ",
J. S C H W E N K E v, G. S C H W E R I N G v, C. SCIACCA e, p. G. SEILER h, j. C. SENS w, I. S H E E R ~, V. S H E V C H E N K O m, S. S H E V C H E N K O m, X. R. S H I '~, K. S H M A K O V m, V. S H O U T K O '~, E. S H U M I L O V m, N. S M I R N O V J, A. S O P C Z A K z, C. S O U Y R I t, T. S P I C K E R M A N N v, B. SPIESS x, P. S P I L L A N T I N I b, R. S T A R O S T A v M. S T E U E R ~,i, D. P. S T I C K L A N D q, B. S T O H R h, H. STONE s, K. S T R A U C H '~, K. S U D H A K A R o.v, G. S U L T A N O V a R. L. S U M N E R q, H. S U T E R ", R. B. S U T T O N '~, A. A. SYED g, X. W. T A N G ~, E. T A R K O V S K Y m, j. M. T H E N A R D t, E. T H O M A S g, C. T I M M E R M A N S '", Samuel C. C. T I N G i, S. M. T I N G i, y . p. T O N G v, M. T O N U T T I v, S. C. T O N W A R °, J. T O T H u, K. L. T U N G ~, J. U L B R I C H T x, L. URB,~N u, U. U W E R v, E. V A L E N T E P, R. T. VAN DE WALLE w, H. VAN D E R G R A A F w, I. V E T L I T S K Y m, G. V I E R T E L ", P. VIKAS g, M. V I V A R G E N T t,i, H. V O G E L '~, H. V O G T ~, M. V O L L M A R v G. V O N D A R D E L a, I. V O R O B I E V m, A. A. V O R O B Y O V J, An. A. V O R O B Y O V J, L. V U I L L E U M I E R Y, W. W A L K a, W. W A L L R A F F v C. R. W A N G ~, G. H. W A N G '~, J. H. W A N G ~, Q. F. W A N G ", X. L. W A N G ~, Y. F. W A N G b, Z. M. W A N G g'~, J. W E B E R h, R. WE1LL Y, T. J. W E N A U S i, j. W E N N I N G E R ~, M. W H I T E i R. W I L H E L M w, C. W I L L M O T T c F. W I T T G E N S T E I N a, D. W R I G H T q, R. J. W U 5, S. L. W U g, S. X. W U g, Y. G. W U ~, B. W Y S L O U C H i,a Z. Z. X U e, Z. t . X U E 0, D. S. YAN o, B. Z. Y A N G ~, C. G. Y A N G ~, G. Y A N G g, K. S. Y A N G ~, Q. Y. Y A N G ~, Z. Q. Y A N G 0, Q. YE g, C. H. YE i, S. C. Y E H ~', Z. W. Y I N 0, J. M. Y O U g, C. Z A B O U N I D I S f L. Z E H N D E R h, M. Z E N G g, Y. Z E N G v D. Z H A N G ~,
D. H. Z H A N G w, S. Y. Z H A N G ~, Z. P. Z H A N G ~, J. F. Z H O U v R. Y. Z H U ,i, A. Z I C H I C H I a,g and J. Z O L L a
a EuropeanLaboratoryforParticlePhysics, CERN, CH-1211 Geneva23, Switzerland
b INFN - Sezione di Firenze and University of Firenze, 1-50125 Florence, Italy
c CentrodelnvestigacionesEnergeticas. Medioambientalesy Tecnologicas, CIEMAT, Madrid, Spain d Johns Hopkins University, Baltimore, MD 21218, USA
I N F N - Sezione di Napoli and University of Naples, 1-80125 Naples, Italy f Northeastern University, Boston, MA 02115, USA
World Laboratory, FBLJA Project, CH-1211 Geneva, Switzerland
h EidgenOssische Technische Hochschule, ETH Ziirich, CH-8093 Zurich, Switzerland Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Volume 238, number 1 PHYSICS LETTERS B 29 March 1990
k Central Laboratory o f Automation and Instrumentation, CLANP, Sofia, Bulgaria INFN - Sezione di Bologna, 1-40126 Bologna, Italy
m Institute of Theoretical and Experimental Physics, ITEP, SU- 117 259 Moscow, USSR " UniversityofMichigan, AnnArbor, M148109, USA
° Tata Institute o f Fundamental Research, Bombay 400 005, India
P I N F N - Sezione di Roma and University ofRoma "La Sapienza'" 1-00185 Rome, Italy q Princeton University, Princeton, NJ 08544, USA
r Union College, Schenectady, N Y 12308, USA s University o f Geneva, CH-1211 Geneva 4, Switzerland
t Laboratoire de Physique des Particules, LAPP, F-74519 Annecy-le-Vieux, France
u Central Research Institute for Physics o f the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary v I. Physikalisches Institut, RWTH, D-51OOAachen, FRG 1
and lll. Physikalisches lnstitut, RWTH, D-51OO Aachen, FRG 1
w National Institute for High Energy Physics, NIKHEF, NL-IO09 DB Amsterdam, The Netherlands and NIKHEF-H and University o f Nijmegen, NL-6525 ED Nijmegen, The Netherlands
x PaulScherrer lnstitut ,PSI, Wiirenlingen, Switzerland Y University o f Lausanne, CH-IOI5 Lausanne, Switzerland z University o f California, San Diego, CA 92182, USA " CarnegieMellon University, Pittsburgh, PA 15213, USA
Institut de Physique Nuclbaire de Lyon, IN2P3-CNRS/Universitb Claude Bernard, F-69622 Villeurbanne Cedex, France High Energy Physics Group, Taiwan, ROC
Institute of High Energy Physics, IHEP, Beijing, P.R. China
Chinese University o f Science and Technology, USTC, Hefei, Anhui 230 029, P.R. China High Energy Physics Institute, DDR-1615 Zeuthen-Berlin, GDR
n California Institute o f Technology, Pasadena, CA 91125, USA o Shanghai Institute o f Ceramics, SIC, Shanghai, P.R. China
Harvard University, Cambridge, MA 02139, USA University o f Hamburg, D-2000 Hamburg, FRG
Received 7 February 1990
We have measured the partial widths of the Z ° into lepton pairs, and the forward-backward charge asymmetry for the process e+e- --. g + g - using the L3 detector at LEP. We obtain an average F~ of 83.0 + 2.1 _+ 1.1 MeV. From this result and the asymmetry
+ 0 , 0 4 6
measurement, we extract the values of the vector and axial vector couplings of the Z ° to leptons: gv = -0.066_o.027 and gA = 0 49 ~ +°'°°7 - - • J - - 0 . 0 0 7 ' 1. Introduction T h e m a s s a n d w i d t h o f t h e Z ° h a v e b e e n a c c u r a t e l y d e t e r m i n e d at L E P [ 1,2 ], u s i n g d a t a f r o m t h e reac- t i o n e + e - - ~ h a d r o n s . Precise m e a s u r e m e n t s o f F ~ , t h e p a r t i a l w i d t h o f t h e Z ° i n t o c h a r g e d l e p t o n s , a n d o f t h e l e p t o n c h a r g e a s y m m e t r i e s c a n b e u s e d to d e t e r - m i n e p a r a m e t e r s w i t h i n t h e s t a n d a r d m o d e l [ 3 ] a n d to test t h e v a l i d i t y o f t h a t m o d e l . I n this p a p e r we p r e s e n t o u r d e t e r m i n a t i o n o f F ~ a n d o f t h e Z ° v e c t o r a n d axial v e c t o r couplingg, g v a n d gA, tO c h a r g e d lep- tons. T h e results a r e b a s e d o n o u r m e a s u r e m e n t s o f 1 Supported by the German Bundesministerium f'tir Forschung
und Technologie. t h e e + e - ~ e + e - a n d e + e - --, g + g - cross s e c t i o n s a n d o n t h e f o r w a r d - b a c k w a r d c h a r g e a s y m m e t r y AFB in e + e - --, g + p.-. W i t h t h e i n c r e a s e d l u m i n o s i t y d e l i v - e r e d b y L E P ( ~ 1 p b - ~ ), we h a v e i n c r e a s e d t h e d a t a s a m p l e sizes by a f a c t o r o f f i v e r e l a t i v e to o u r pre- v i o u s a n a l y s i s [ 4 ] . T h e s y s t e m a t i c e r r o r s also h a v e b e e n r e d u c e d b y a c a r e f u l s t u d y o f t h e d e t e c t o r p e r f o r m a n c e . 2. Data collection T h e L3 d e t e c t o r has b e e n d e s c r i b e d in d e t a i l else- w h e r e [ 5 ]. It c o n s i s t s o f a c e n t r a l t r a c k i n g a n d v e r t e x c h a m b e r , a B G O e l e c t r o m a g n e t i c c a l o r i m e t e r , a had-
ron calorimeter m a d e o f uranium, brass and propor- tional wire chambers and a high precision m u o n c h a m b e r system. The calorimeter system covers 99% o f 4n. Luminosity is measured by detecting small an- gle Bhabha events in two forward B G O calorimeters. The e+e - data sample used in this analysis was ob- tained during O c t o b e r - D e c e m b e r 1989 at LEP. The luminosity corresponding to this data sample was measured with a systematic error o f 1.7%, as de- scribed in detail in ref. [1 ]. The ~t+p. - sample in- cludes data from the same period plus data from Sep- tember where the luminosity systematic error is 4%.
Events o f the type e+e - - , e + e - (T) were detected in the B G O barrel calorimeter. They were triggered using an "energy trigger" with a total energy require- ment o f 12 GeV, as well as clustered energy triggers [6]. The trigger efficiency has been studied using e + e - ~ e + e - (T) events selected by the off line anal- ysis. F r o m the comparison o f trigger data with the signals from the B G O readout, both o f which were digitized and recorded on tape, dead trigger channels have been located and the efficiency measured. The totally efficiency is determined to be 0.975 + 0 . 0 1 4
(stat) for the whole running period.
The principal trigger for e+e - ~ t + p - (T) events requires two or more tracks in the m u o n chambers and at least two hits in the plastic scintillators sur- rounding the B G O calorimeter. The scintillator trig- ger efficiency has been studied using a second, looser trigger, which requires at least one track in the m u o n chambers and at least one scintillator hit. The effi- ciency o f the m u o n track trigger was measured by analyzing inclusive m u o n events that are triggered by the energy trigger as well as the m u o n trigger. F r o m these studies we determine an efficiency greater than 99.5% for the di-muon trigger.
3. Event selection
Events from the process e+e - --, e+e - (T) in the an- gular region covered by the B G O electromagnetic calorimeter (42 °-138 ° ) were extracted from the data by requiring that the total energy measured in the B G O be above 0.72x/J. At least 2 clusters in the BGO, with energies between 10 and 55 GeV were required, and the two highest energy clusters were required to
have an acollinearity angle between them o f less than 90 ° .
The efficiency for selecting e+e - --,e+e - (T) events which enter the B G O angular region was obtained by Monte Carlo calculation [7]. The detector simula- tion took account o f the small n u m b e r o f inactive channels in the B G O calorimeter for each running period. We found an efficiency o f 0.961 + 0 . 0 1 0 for events within the defined angular region for the cuts described above.
For the same cuts, the background from z~ and e+e - - , h a d r o n s was found to be less than 0.3% o f the final e+e - event sample. The background due to e + e - ~ T T has been calculated according to ref. [8 ], and has been subtracted from the data at each value o f x/'s. For x / s = M z o , this background a m o u n t e d to 1.8% o f the signal cross section. The contribution o f the "two p h o t o n process" e + e - ~ e + e - e + e - to the final sample was calculated to be negligible.
Adding in quadrature the systematic errors in the trigger efficiency ( 1.4%), the acceptance (1.0%), the event selection (0.5%), the background subtractions (0.2%) and the luminosity measurement (1.7%), we obtain a total systematic error o f 2.5% in the e + e - ~ e + e - (T) cross section.
Events from the process e+e ---,~t+~t - (T) were se- lected by requiring:
( 1 ) two tracks in the m u o n chambers with a recon- structed m o m e n t u m greater than 2 GeV, with at least one track pointing to within 200 m m o f the vertex,
(2) total energy deposited in the h a d r o n calorim- eter less than 15 GeV,
(3) less than 15 shower peaks in the electromag- netic calorimeter, and
(4) acollinearity angle between the two muons less than 15 °.
In order to include final state radiation we define E~ as the m u o n m o m e n t u m plus the energy con- tained in a cone o f semi-aperture 15 ° around the m u o n trajectory in the B G O calorimeter. We required:
(5) 0.30x/~ < E~ < 0.70x/s, for muons measured in all three m u o n c h a m b e r planes. The sum o f the two E~ was required to be above 40 GeV.
Each m u o n track had to have a scintillator hit. Us- ing the scintillator timing, corrected for the flight path from the interaction region to the scintillator, we re- quired at least one o f the following:
Volume 238, number 1 PHYSICS LETTERS B 29 March 1990
( 6 a ) the t i m e s for b o t h m u o n s h a d to be w i t h i n
_+ 2.5 ns o f the b e a m crossing t i m e a n d t h e i r differ- ence less t h a n 2.5 ns, or
( 6 b ) the t i m e for one o f the m u o n s had to be within 2.5 ns o f the b e a m crossing, a n d b o t h m u o n s h a d to satisfy a tight vertex cut.
Cuts ( 2 ) a n d ( 3 ) were used m a i n l y to reject h a d - ron events with m u o n pairs while cuts ( 4 ) a n d ( 5 ) r e m o v e d events o f the t y p e e + e - ~ e + e - g + g - a n d
e + e - ~ z + x - ~ g + g - + v ' s . Cut ( 6 ) was a p p l i e d to
reject c o s m i c ray b a c k g r o u n d , w i t h o u t losing those e + e - -~ g + g - events where one scintillator was hit out o f t i m e due to a r a n d o m c o i n c i d e n c e with back- g r o u n d in the scintillator.
F r o m the analysis o f s i m u l a t i o n s for the process
e + e - - - , x + x - - , ~ t + g - + v ' s [ 9 ] , we e s t i m a t e a con-
t a m i n a t i o n o f (0.7 _+ 0.3 )% in the selected m u o n p a i r sample. The o t h e r b a c k g r o u n d sources m e n t i o n e d a b o v e ( c o s m i c rays, g + g - from the two p h o t o n p r o - cess) have been f o u n d to give negligible contributions.
The a c c e p t a n c e for e + e - ~ g + g - ( T ) was calcu-
lated by a p p l y i n g the same cuts on events g e n e r a t e d by a M o n t e Carlo p r o g r a m [ 9 ] a n d s i m u l a t e d in the L3 detector. We f o u n d an overall a c c e p t a n c e o f 0.505 ___ 0.009 ( M o n t e Carlo statistical e r r o r ) . A cor- rection v a r y i n g in t i m e d u r i n g the r u n n i n g p e r i o d has been a p p l i e d to the acceptance, in o r d e r to account for slight changes in the d e t e c t o r p e r f o r m a n c e . The sources o f s y s t e m a t i c error are then: 2.1% due to lu- m i n o s i t y m e a s u r e m e n t , 1.8% due to M o n t e Carlo statistics, 0.4% due to event selection, a n d 0.5% due to trigger efficiency. C o m b i n i n g the s y s t e m a t i c errors in q u a d r a t u r e we o b t a i n a total s y s t e m a t i c error in the e + e - ~ g + g - cross section o f 2.8 %.
4. Partial width for Z ° - ~ e ÷ e -
Because o f the lack o f a sufficiently accurate M o n t e Carlo g e n e r a t o r for the e+e - channel, the error on the t h e o r e t i c a l cross section c o r r e s p o n d i n g to our event sample, a n d hence on our d e t e r m i n a t i o n o f Fee could be significant. We have therefore used two m e t h o d s to d e t e r m i n e Fe~ from our electron data. In the first a n d m o s t direct m e t h o d , we s u b t r a c t e d the c o n t r i b u t i o n o f the t channel , / e x c h a n g e t e r m a n d its interference from the three d a t a p o i n t s a r o u n d the
peak. F o r these points, the s u b t r a c t i o n is only a ( 16 +_ 1.6 )% c o r r e c t i o n to the data.
In the s e c o n d m e t h o d a fit using an analytical for- m u l a given in ref. [ 10] was used. This has the a d v a n - tage o f using all o f the d a t a whether on or off the peak, b u t m a y be systematically less accurate because only s i m p l e cuts are available in the calculation. Results f r o m b o t h m e t h o d s are p r e s e n t e d below, a n d are in a g r e e m e n t within the theoretical systematic errors quoted. We consider the value o b t a i n e d using m e t h o d 1 as o u r basic result on Fee, a n d we have used it in the analysis in the following sections o f this paper.
F o r the first m e t h o d , the cross sections m e a s u r e d in the 42 ° - 1 3 8 ° p o l a r angle range are given in table 1. The errors shown are statistical only. The back- g r o u n d f r o m e+e - ~TT has been s u b t r a c t e d in these cross sections. To m a k e the t-channel subtraction, we o b t a i n e d the cross sections into di-electrons a n d into d i - m u o n s , aMce+e- a n d a~a~ ~ - , f r o m M o n t e Carlo sim- ulations [7,9] a n d we calculated the s-channel con- t r i b u t i o n to the cross section as
-(aMc - a ~ c
).
O ' Z 0 ~ O ' e x p e + e - + g -We then find
Fee = 81.1 _+ 2.8 ( s t a t ) + 1.2 ( s y s t ) + 0.7 ( t h e o r y ) M e V .
T h e statistical error q u o t e d a b o v e includes a con- t r i b u t i o n o f 1.6 M e V from the statistical error on the m e a s u r e d total w i d t h o f the Z °, as d e t e r m i n e d from our h a d r o n d a t a ( F z = 2 . 5 3 9 + 0 . 0 5 4 GeV, M z = 9 1 . 1 6 0 + 0 . 0 3 8 G e V [11).
In the s e c o n d m e t h o d we fitted the cross section as a function o f x/s using the analytic expression [ 10] m e n t i o n e d above, which takes into account b o t h the ~, a n d the Z ° exchange d i a g r a m s in the s a n d t chan- nels with interference terms. Soft r a d i a t i o n is ac- c o u n t e d for b y e x p o n e n t i a t i o n , a n d h a r d p h o t o n s are included in the collinear a p p r o x i m a t i o n . F u r t h e r cuts h a d to be a p p l i e d to the d a t a in o r d e r to reject events
c o n t a i n i n g h a r d p h o t o n s ( o f energy k >
kmax)
emit-t e d at large angles ( ~ > ~ma×) with respect to the direc- tion o f the electrons (or p o s i t r o n s ) , since these events are not a c c o u n t e d for by the fitting function. Events with h a r d acollinear p h o t o n s in the b e a m p i p e are re-
j e c t e d by an a c o l l i n e a r i t y cut Amax on the final state
Table 1
The number of events and the measured cross sections for e+e - - , e + e -, for the selection criteria used in methods 1 and 2 described above.
. ~ (GeV) Method 1 Method 2
~ . . . ~+e- (nb) Ne ... ~+e (nb) 88.279 29 0.34 _+ 0.06 26 0.30 __+ 0.06 89.277 42 0.64 _+ 0.10 39 0.60 -+ 0.10 90.277 52 0.86 _+ 0.12 50 0.83 _+ 0.12 91.030 136 1.08 -+ 0.09 129 1.02 _+ 0.09 91.278 161 1.01 _+0.08 156 0.98__+0.08 91.529 156 0.98 _+ 0.08 153 0.96 __+ 0.08 92.277 44 0.68 _+ 0.10 44 0.68 _+ 0.10 93.276 18 0.29 _+ 0.07 15 0.24_+ 0.07 94.278 13 0.15-+0.04 11 0.12_+0.04
T h e c h o i c e o f 5ma x a n d Area x has to d o n e b e a r i n g in m i n d t h a t h i g h v a l u e s o f t h e s e cuts m a k e t h e f o r m u l a less p r e c i s e w h i l e l o w v a l u e s m a k e t h e m e a s u r e m e n t s e n s i t i v e to f i n i t e r e s o l u t i o n o f t h e d e t e c t o r . A f t e r a c a r e f u l s t u d y o f t h e p e r f o r m a n c e o f o u r c a l o r i m e t e r we c h o s e fimax = 1 0 °, a n d ZJma x : 10 °, c o r r e s p o n d i n g to kmax= 7.3 G e V . We h a v e s t u d i e d t h e v a r i a t i o n in cross s e c t i o n , as m e a s u r e d u s i n g o n l y t h e t h r e e en- ergy p o i n t s close to t h e Z ° peak, a n d as p r e d i c t e d by t h e fitting f u n c t i o n c h a n g i n g t h e Z~ma x a n d 5max cuts b e t w e e n 5 ° a n d 15 °. T h e r e is a g r e e m e n t w i t h i n 1% b e t w e e n p r e d i c t i o n a n d e x p e r i m e n t . We e s t i m a t e a 2% e r r o r to t h e t h e o r e t i c a l p r e d i c t i o n o f t h e cross sec- t i o n in this s e c o n d m e t h o d .
T h e cross s e c t i o n s u s e d in t h e fit a r e also g i v e n in t a b l e 1. N o t e t h a t since s o m e w h a t m o r e r e s t r i c t i v e cuts w e r e r e q u i r e d to a l l o w use o f t h e f o r m u l a , t h e m e a s u r e d cross s e c t i o n s are s m a l l e r t h a n t h o s e u s e d in t h e p e a k s u b t r a c t i o n m e t h o d . F i t t i n g t h e d a t a w i t h M z a n d F z f i x e d to t h e v a l u e s we d e t e r m i n e d f r o m t h e h a d r o n i c cross s e c t i o n [1] we o b t a i n (fig. 1) F e e = 79.0 + 2 . 4 ( s t a t ) + 1.1 ( s y s t ) + 1 . 0 ( t h e o r y ) M e V . T h e d i f f e r e n c e b e t w e e n m e t h o d s 1 a n d 2 is par- tially statistical d u e to t h e e x c l u s i o n o f d a t a a w a y f r o m t h e p e a k in m e t h o d 1. T h e r e m a i n i n g d i f f e r e n c e is slightly larger t h a n t h e " t h e o r y e r r o r s " e s t i m a t e d . W e c o n s i d e r m e t h o d 1 to be m o r e reliable.
5. Partial width for Z°-~lt+li-
The e + e - - ~ ~ + ~ t - - + (7) cross s e c t i o n a n d its statis- tical e r r o r m e a s u r e d as a f u n c t i o n of,~/~ a r e s h o w n in E v ~0 1 50 1 . 0 0 0.50 ZO__. e + e - * 8 6 88 90 92 94 96 (GeV)
Fig. 1. Measured cross sections as a function of the CM energy for the reaction e+e - - , e + e - for the polar angle region from 42 ° to 138 °. The curve is the fit to the data obtained with method 2 as described in the text.
Table 2
Number of events and cross sections for e+e ~p+~t-.
~fs (GeV) g+~t-(T) events o~+._ (nb)
88.279 5 0.12_+0.05 89.277 8 0.29_+0.10 90.277 51 1.15_+0.16 91.030 82 1.44_+0.16 91.278 147 1.44_+0.12 91.529 110 1.32_+0.13 92.309 33 0.97_+0.17 93.276 32 0.70_+0.12 94.278 16 0.38_+0.09
Volume 238, number 1 PHYSICS LETTERS B 29 March 1990 20 1.5 10 0 5 0 I I I I I I 86 88 90 92 94 96 (GeV)
also completely correlated for the two measurements. We a v e r a g e d the d a t a from the two l e p t o n i c chan- nels, a s s u m i n g universality, a n d o b t a i n e d
F ~ =83.0+_2.1_+ 1.1 M e V .
I f we do not assume universality, we f i n d F , , = 87.6 +_ 5.6 M e V using the m e a s u r e d value o f Fee. The error q u o t e d includes b o t h statistical a n d systematic errors.
7. Simultaneous fit to lepton and hadron data Fig. 2. Measured cross sections as a function of the CM energy
for the reaction e+e--~g+g -. The curve is the fit to the data to obtain F[¢~.
table 2. We f i t t e d these d a t a using an analytic f o r m for the Z ° cross section [ 11 ], a n d o b t a i n e d M z = 91.11 _+ 0.13 G e V a n d F z = 2.49 _+ 0.28 G e V which is in excellent a g r e e m e n t with our p r e v i o u s measure- m e n t s o f the h a d r o n i c final state [ 1 ] . G i v e n this agreement, we fit the d a t a by fixing the m a s s a n d width o f the Z ° to the values d e t e r m i n e d f r o m o u r fit to the h a d r o n i c cross section. T h e m e a s u r e d e+e -
~+ p - ( y ) cross sections a n d the f i t t e d function are shown in fig. 2. U s i n g the p . + g - d a t a alone, we find
F ~ = ~
= 8 4 . 3 + 2 . 4 ( s t a t ) + 1.2 ( s y s t ) M e V .
T h e statistical error q u o t e d a b o v e includes a contri- b u t i o n o f 1.4 M e V f r o m the statistical error in o u r m e a s u r e d value o f Fz.
We have m a d e a s i m u l t a n e o u s fit to our cross sec- tions for h a d r o n [ 1 ], e+e - , a n d g + g - p r o d u c t i o n . The fit is m o d e l i n d e p e n d e n t with Mz, Fhaa, F ~ a n d Fi,v as free p a r a m e t e r s . As before, we have used the analytical forms for the Z ° cross section given in ref. [ 11 ]. These include initial state r a d i a t i o n a n d a B r e i t - W i g n e r with an energy d e p e n d e n t width. We find, with a Z 2 = 17 for 18 degrees o f freedom,
M z = 91.156 +_ 0.026 +_ 0.030 G e V , Fhad = 1.744 +_ 0.053 G e V ,
F ~ = 82.8 +_ 2.4 M e V , F~nv = 537 +_ 48 M e V ,
I f we assume the p a r t i a l width o f the Z ° to n e u t r i n o pairs from the s t a n d a r d model, this value o f Finv yields the n u m b e r o f n e u t r i n o s N v = 3.23 -4-_ 0.29. T h i s value should be c o m p a r e d with our d e t e r m i n a t i o n within the s t a n d a r d m o d e l using the h a d r o n d a t a alone o f N v = 3.29 _+ (J.17.
6. Average leptonicwidth
T h e correct d e t e r m i n a t i o n o f the average l e p t o n i c width, a n d its error, requires t h a t the c o r r e l a t i o n s be- tween the errors in Fee a n d in F ~ be t a k e n into ac- count. T h e statistical errors o f 1.6 M e V on the p a r t i a l w i d t h for e + e - final states, a n d o f 1.4 M e V on the p a r t i a l w i d t h for g + g - final states, which are due to the statistical error on o u r m e a s u r e m e n t o f F z [ 1 ], are c o m p l e t e l y correlated. The s y s t e m a t i c errors on Fee a n d F~'~ b o t h c o n t a i n a 0.85% c o n t r i b u t i o n f r o m the s y s t e m a t i c e r r o r on luminosity. These errors are
8. Determination of gA and gv
U s i n g o u r e+e - - - , g + g - (~) event sample, we have also m e a s u r e d the f o r w a r d - b a c k w a r d charge asym- m e t r y AFB d e f i n e d as
a F - - a B
AFB -- -
-rYE + ~B "
By fitting d ~ / d ( c o s 0) to our d a t a s a m p l e and ex- t r a p o l a t i n g cos 0 to the full range we o b t a i n e d AFB(x/~= 89.94 G e V ) = - ( 2 5 . 0 + 1 5 . 2 ) % ,
0.6 0.4 0.2 o -0.2 -0.4 -0.6 89 L I I I 90 91 92 93 '/~ (GoV) 94
Fig. 3. Measured forward-backward charge asymmetry AFB as a function of the CM energy for the reaction e+e--~t+~t -. The curve is the prediction of the standard model.
A F B ( x f S = 9 1 . 0 3 G e V ) = - (9.0_+ 1 0 . 7 ) % , AVB ( X / ~ = 91.28 G e V ) = ( 17.9 _+ 8.4 ) % ,
AFB(x/SS=
9 1.53 G e V ) = (8.7 _+ 10.2 ) % , A F B ( X / ~ = 9 3 . 0 9 G e V ) = (8.2_+ 1 1 . 7 ) % , Fig. 3 shows t h e m e a s u r e d a s y m m e t r i e s c o m p a r e d w i t h v a l u e s p r e d i c t e d b y the s t a n d a r d m o d e l (Mtoo = 100 G e V a n d M H = 100 G e V ) . U s i n g t h e e q u a t i o nGuM 3
F ~ - 6x//~n (g~ +g2 ) ,
we f o u n d g ~ +g~, = 0.250_+ 0.007 . F r o m a fit to o u r a s y m m e t r y d a t a a n dF~,
i n c l u d i n g Q E D r a d i a t i v e c o r r e c t i o n s [ 12 ] a n d u s i n g the Z ° m a s s we h a v e p r e v i o u s l y m e a s u r e d [ 1 ], we o b t a i n e d : _ ~ q 4 0 ~ + 0 . 0 0 7 c~ (~KK+0.046 g A - - - - ' ~ . J J - - o . o 0 7 , gv = - - u ' u u u - - O . 0 2 7 w h e r e t h e errors i n c l u d e systematics. N o t e t h a t d a t a f r o m o t h e r e x p e r i m e n t s [ 1 3 - 1 7 ] are u s e d to deter- m i n e t h e signs. Fig. 4 c o m p a r e s o u r d e t e r m i n a t i o n o f gA a n d gv to p r e v i o u s m e a s u r e m e n t s [ 1 3 - 1 8 ] ~' -0.3 -0.4gA
-0,5 -0.6 -0.7 J ~ ~ J J ." I ." m L3 ~- ~ ~ I~ x" _._./ ________.--- -0.2 -0.1 0 0.1 0.2 gvFig. 4. Results obtained from neutrino experiments and the e+e - experiments expressed as contours in gA and gv. Area (A) is the result of the CHARM Collaboration (68% confidence level ) l 13 ], area (B) is the combined e+e - result from PETRA and PEP (95% confidence level) 114], area (C) is the reactor 9ee result (68% confidence level) l 15 ], area (D) is the BNL result (68% confi- dence level) [ 16], and area (E) is the CHARM II result (68% confidence level) [ 18 ]. The black area represents our measure- ment based on the L3 measurements of FQ~ and the asymmetry (68% confidence level). 9. C o n c l u s i o n We h a v e m e a s u r e d F ~ i n b o t h the e + e - a n d ~t+~t - c h a n n e l s . T h e average result o f F ~ = 8 3 . 0 _ + 2 . 1 + 1.1 M e V is i n g o o d a g r e e m e n t w i t h t h e e x p e c t a t i o n o f the s t a n - d a r d m o d e l . C o m b i n i n g o u r l e p t o n i c a n d h a d r o n i c m e a s u r e m e n t s , we get a m o d e l i n d e p e n d e n t deter- m i n a t i o n o f the n u m b e r o f n e u t r i n o species o f 3 . 2 3 + 0 . 2 9 . We h a v e also m e a s u r e d the f o r w a r d - b a c k w a r d charge a s y m m e t r y in ~t+~t - p r o d u c t i o n for 5 v a l u e s o f x/s. T h e a s y m m e t r y is c o n s i s t e n t w i t h t h e s t a n d a r d m o d e l a n d allows us to d e t e r m i n e the axial v e c t o r a n d v e c t o r c o u p l i n g s o f the l e p t o n s to the Z°: c~ 4 0 ~ + 0 . 0 0 7 ~ c~ (~t~K+0.046 g A ~ - - ~ J . J J - - 0 . 0 0 7 ~ ,~V -~" - - v - v u V - - O . 0 2 7 - ~l N o t e i n fig. 4, t h a t i n o r d e r t o c o m p a r e w i t h o u r r e s u l t , w e h a v e p l o t t e d t h e r e s u l t o f ref. 116 ] b y a d d i n g in q u a d r a t u r e t h e i r s t a t i s t i c a l a n d s y s t e m a t i c e r r o r s . A c k n o w l e d g e m e n t
Volume 238, number 1 PHYSICS LETTERS B 29 March 1990 W e w a n t p a r t i c u l a r l y t o e x p r e s s o u r g r a t i t u d e t o t h e L E P d i v i s i o n : it is t h e i r e x c e l l e n t a c h i e v e m e n t s w h i c h m a d e t h i s e x p e r i m e n t p o s s i b l e . W e a c k n o w l e d g e t h e s u p p o r t o f all t h e f u n d i n g a g e n c i e s w h i c h c o n t r i b u t e d t o t h i s e x p e r i m e n t . References
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