Article
Reference
Measurement of hadron and lepton-pair production at 130
L3 Collaboration
ACHARD, Pablo (Collab.), et al.
Abstract
We report on measurements of e+e− annihilation into hadrons and lepton pairs. The data have been collected with the L3 detector at LEP at centre-of-mass energies between 130 and 189 GeV. Using a total integrated luminosity of 243.7 pb−1, 25864 hadronic and 8573 lepton-pair events are selected for the measurement of cross sections and leptonic forward-backward asymmetries. The results are in good agreement with Standard Model predictions.
L3 Collaboration, ACHARD, Pablo (Collab.), et al . Measurement of hadron and lepton-pair production at 130
DOI : 10.1016/S0370-2693(00)00280-X
Available at:
http://archive-ouverte.unige.ch/unige:47331
Disclaimer: layout of this document may differ from the published version.
1 / 1
Ž . Physics Letters B 479 2000 101–117
Measurement of hadron and lepton-pair production at 130 - ( s - 189 GeV at LEP
L3 Collaboration
M. Acciarri
z, P. Achard
s, O. Adriani
p, M. Aguilar-Benitez
y, J. Alcaraz
y, G. Alemanni
v, J. Allaby
q, A. Aloisio
ab, M.G. Alviggi
ab, G. Ambrosi
s, H. Anderhub
au, V.P. Andreev
f,aj, T. Angelescu
l, F. Anselmo
i, A. Arefiev
aa, T. Azemoon
c, T. Aziz
j, P. Bagnaia
ai, L. Baksay
ap, A. Balandras
d,
R.C. Ball
c, S. Banerjee
j, Sw. Banerjee
j, A. Barczyk
au,as, R. Barillere `
q, L. Barone
ai, P. Bartalini
v, M. Basile
i, R. Battiston
af, A. Bay
v, F. Becattini
p, U. Becker
n, F. Behner
au, L. Bellucci
p, J. Berdugo
y, P. Berges
n, B. Bertucci
af,
B.L. Betev
au, S. Bhattacharya
j, M. Biasini
af, A. Biland
au, J.J. Blaising
d, S.C. Blyth
ag, G.J. Bobbink
b, A. Bohm ¨
a, L. Boldizsar
m, B. Borgia
ai, D. Bourilkov
au, M. Bourquin
s, S. Braccini
s, J.G. Branson
al, V. Brigljevic
au, F. Brochu
d, A. Buffini
p, A. Buijs
aq, J.D. Burger
n, W.J. Burger
af, A. Button
c,
X.D. Cai
n, M. Campanelli
au, M. Capell
n, G. Cara Romeo
i, G. Carlino
ab, A.M. Cartacci
p, J. Casaus
y, G. Castellini
p, F. Cavallari
ai, N. Cavallo
ab,
C. Cecchi
af, M. Cerrada
y, F. Cesaroni
w, M. Chamizo
s, Y.H. Chang
aw, U.K. Chaturvedi
r, M. Chemarin
x, A. Chen
aw, G. Chen
g, G.M. Chen
g, H.F. Chen
t, H.S. Chen
g, G. Chiefari
ab, L. Cifarelli
ak, F. Cindolo
i, C. Civinini
p,
I. Clare
n, R. Clare
n, G. Coignet
d, A.P. Colijn
b, N. Colino
y, S. Costantini
e, F. Cotorobai
l, B. Cozzoni
i, B. de la Cruz
y, A. Csilling
m, S. Cucciarelli
af, T.S. Dai
n, J.A. van Dalen
ad, R. D’Alessandro
p, R. de Asmundis
ab, P. Deglon ´
s,
A. Degre ´
d, K. Deiters
as, D. della Volpe
ab, P. Denes
ah, F. DeNotaristefani
ai, A. De Salvo
au, M. Diemoz
ai, D. van Dierendonck
b, F. Di Lodovico
au, C. Dionisi
ai, M. Dittmar
au, A. Dominguez
al, A. Doria
ab, M.T. Dova
r,1, D. Duchesneau
d, D. Dufournaud
d, P. Duinker
b, I. Duran
am, H. El Mamouni
x,
A. Engler
ag, F.J. Eppling
n, F.C. Erne ´
b, P. Extermann
s, M. Fabre
as, R. Faccini
ai, M.A. Falagan
y, S. Falciano
ai,q, A. Favara
q, J. Fay
x, O. Fedin
aj,
M. Felcini
au, T. Ferguson
ag, F. Ferroni
ai, H. Fesefeldt
a, E. Fiandrini
af, J.H. Field
s, F. Filthaut
q, P.H. Fisher
n, I. Fisk
al, G. Forconi
n, L. Fredj
s,
0370-2693r00r$ - see front matterq2000 Published by Elsevier Science B.V. All rights reserved.
Ž .
PII: S 0 3 7 0 - 2 6 9 3 0 0 0 0 2 8 0 - X
K. Freudenreich
au, C. Furetta
z, Yu. Galaktionov
aa,n, S.N. Ganguli
j, P. Garcia-Abia
e, M. Gataullin
ae, S.S. Gau
k, S. Gentile
ai,q, N. Gheordanescu
l, S. Giagu
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t, G. Grenier
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h, M. Guida
ak, R. van Gulik
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ah, A. Gurtu
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ar, D. Haas
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ac, D. Hatzifotiadou
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ag, H. Hofer
au, G. Holzner
au, H. Hoorani
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at, B.N. Jin
g, L.W. Jones
c, P. de Jong
b,
I. Josa-Mutuberrıa ´
y, R.A. Khan
r, M. Kaur
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s, D. Kim
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M. Kraber ¨
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ag, W. Krenz
a, A. Kruger ¨
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t, S. Likhoded
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k, M. Pauluzzi
af, C. Paus
q, F. Pauss
au, M. Pedace
ai, S. Pensotti
z, D. Perret-Gallix
d,
B. Petersen
ad, D. Piccolo
ab, F. Pierella
i, M. Pieri
p, P.A. Piroue ´
ah, E. Pistolesi
z, V. Plyaskin
aa, M. Pohl
s, V. Pojidaev
aa,p, H. Postema
n, J. Pothier
q, N. Produit
s,
D.O. Prokofiev
ar, D. Prokofiev
aj, J. Quartieri
ak, G. Rahal-Callot
au,q, M.A. Rahaman
j, P. Raics
o, N. Raja
j, R. Ramelli
au, P.G. Rancoita
z, A. Raspereza
at, G. Raven
al, P. Razis
ac, D. Ren
au, M. Rescigno
ai, S. Reucroft
k,
T. van Rhee
aq, S. Riemann
at, K. Riles
c, A. Robohm
au, J. Rodin
ap, B.P. Roe
c, L. Romero
y, A. Rosca
h, S. Rosier-Lees
d, J.A. Rubio
q, D. Ruschmeier
h,
H. Rykaczewski
au, S. Saremi
f, S. Sarkar
ai, J. Salicio
q, E. Sanchez
q,
M.P. Sanders
ad, M.E. Sarakinos
u, C. Schafer ¨
q, V. Schegelsky
aj,
S. Schmidt-Kaerst
a, D. Schmitz
a, H. Schopper
av, D.J. Schotanus
ad,
G. Schwering
a, C. Sciacca
ab, D. Sciarrino
s, A. Seganti
i, L. Servoli
af,
S. Shevchenko
ae, N. Shivarov
an, V. Shoutko
aa, E. Shumilov
aa, A. Shvorob
ae, T. Siedenburg
a, D. Son
ao, B. Smith
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p, M. Steuer
n, D.P. Stickland
ah, A. Stone
f, H. Stone
ah,3, B. Stoyanov
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a, K. Sudhakar
j, G. Sultanov
r, L.Z. Sun
t, H. Suter
au, J.D. Swain
r, Z. Szillasi
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T. Sztaricskai
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e, L. Taylor
k, C. Timmermans
ad, Samuel C.C. Ting
n, S.M. Ting
n, S.C. Tonwar
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m, C. Tully
q, K.L. Tung
g,
Y. Uchida
n, J. Ulbricht
au, E. Valente
ai, G. Vesztergombi
m, I. Vetlitsky
aa, D. Vicinanza
ak, G. Viertel
au, S. Villa
k, M. Vivargent
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e, I. Vodopianov
aj, H. Vogel
ag, H. Vogt
at, I. Vorobiev
aa, A.A. Vorobyov
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ac, M. Wadhwa
e, W. Wallraff
a, M. Wang
n, X.L. Wang
t, Z.M. Wang
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a, M. Weber
a, P. Wienemann
a, H. Wilkens
ad, S.X. Wu
n,
S. Wynhoff
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ae, Z.Z. Xu
t, B.Z. Yang
t, C.G. Yang
g, H.J. Yang
g, M. Yang
g, J.B. Ye
t, S.C. Yeh
ax, An. Zalite
aj, Yu. Zalite
aj, Z.P. Zhang
t,
G.Y. Zhu
g, R.Y. Zhu
ae, A. Zichichi
i,q,r, G. Zilizi
ap,4, M. Zoller ¨
aaI. Physikalisches Institut, RWTH, D-52056 Aachen, Germany, and III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany5
bNational Institute for High Energy Physics, NIKHEF, and UniÕersity of Amsterdam, NL-1009 DB Amsterdam, The Netherlands
cUniÕersity of Michigan, Ann Arbor, MI 48109, USA
dLaboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux CEDEX, France
eInstitute of Physics, UniÕersity of Basel, CH-4056 Basel, Switzerland
fLouisiana State UniÕersity, Baton Rouge, LA 70803, USA
gInstitute of High Energy Physics, IHEP, 100039 Beijing, China6
hHumboldt UniÕersity, D-10099 Berlin, Germany5
iUniÕersity of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italy
jTata Institute of Fundamental Research, Bombay 400 005, India
kNortheastern UniÕersity, Boston, MA 02115, USA
lInstitute of Atomic Physics and UniÕersity of Bucharest, R-76900 Bucharest, Romania
m Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary7
nMassachusetts Institute of Technology, Cambridge, MA 02139, USA
oKLTE-ATOMKI, H-4010 Debrecen, Hungary4
pINFN Sezione di Firenze and UniÕersity of Florence, I-50125 Florence, Italy
qEuropean Laboratory for Particle Physics, CERN, CH-1211 GeneÕa 23, Switzerland
rWorld Laboratory, FBLJA Project, CH-1211 GeneÕa 23, Switzerland
sUniÕersity of GeneÕa, CH-1211 GeneÕa 4, Switzerland
tChinese UniÕersity of Science and Technology, USTC, Hefei, Anhui 230 029, China6
uSEFT, Research Institute for High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland
vUniÕersity of Lausanne, CH-1015 Lausanne, Switzerland
wINFN-Sezione di Lecce and UniÕersita Degli Studi di Lecce, I-73100 Lecce, Italy´
xInstitut de Physique Nucleaire de Lyon, IN2P3-CNRS, UniÕersite Claude Bernard, F-69622 Villeurbanne, France´ ´
yCentro de InÕestigaciones Energeticas, Medioambientales y Tecnologıcas, CIEMAT, E-28040 Madrid, Spain´ ´ 8
zINFN-Sezione di Milano, I-20133 Milan, Italy
aaInstitute of Theoretical and Experimental Physics, ITEP, Moscow, Russia
abINFN-Sezione di Napoli and UniÕersity of Naples, I-80125 Naples, Italy
ac Department of Natural Sciences, UniÕersity of Cyprus, Nicosia, Cyprus
adUniÕersity of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands
aeCalifornia Institute of Technology, Pasadena, CA 91125, USA
afINFN-Sezione di Perugia and UniÕersita Degli Studi di Perugia, I-06100 Perugia, Italy´
agCarnegie Mellon UniÕersity, Pittsburgh, PA 15213, USA
ahPrinceton UniÕersity, Princeton, NJ 08544, USA
aiINFN-Sezione di Roma and UniÕersity of Rome, ‘‘La Sapienza’’, I-00185 Rome, Italy
ajNuclear Physics Institute, St. Petersburg, Russia
akUniÕersity and INFN, Salerno, I-84100 Salerno, Italy
alUniÕersity of California, San Diego, CA 92093, USA
am Dept. de Fisica de Particulas Elementales, UniÕ. de Santiago, E-15706 Santiago de Compostela, Spain
anBulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria
aoCenter for High Energy Physics, AdÕ. Inst. of Sciences and Technology, 305-701 Taejon, South Korea
apUniÕersity of Alabama, Tuscaloosa, AL 35486, USA
aqUtrecht UniÕersity and NIKHEF, NL-3584 CB Utrecht, The Netherlands
arPurdue UniÕersity, West Lafayette, IN 47907, USA
asPaul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland
atDESY, D-15738 Zeuthen, Germany
auEidgenossische Technische Hochschule, ETH Zurich, CH-8093 Zurich, Switzerland¨ ¨ ¨
avUniÕersity of Hamburg, D-22761 Hamburg, Germany
awNational Central UniÕersity, Chung-Li, Taiwan, ROC
axDepartment of Physics, National Tsing Hua UniÕersity, Taiwan, ROC Received 16 December 1999; accepted 25 February 2000
Editor: K. Winter
Abstract
We report on measurements of eqeyannihilation into hadrons and lepton pairs. The data have been collected with the L3 detector at LEP at centre-of-mass energies between 130 and 189 GeV. Using a total integrated luminosity of 243.7 pby1, 25864 hadronic and 8573 lepton-pair events are selected for the measurement of cross sections and leptonic forward-back- ward asymmetries. The results are in good agreement with Standard Model predictions. q2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction
We report on the results of measurements of fermion-pair production above the Z pole, based on data collected using the L3 detector at LEP in 1997 and 1998 at centre-of-mass energies s
'
s182.7 GeV and'
ss188.7 GeV, respectively. Data correspond- ing to integrated luminosities of 55.5 pby1 and 176.21Also supported by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina.
2Also supported by Panjab University, Chandigarh-160014, India.
3Deceased.
4Also supported by the Hungarian OTKA fund under contract numbers T22238 and T026178.
5Supported by the German Bundesministerium fur Bildung,¨ Wissenschaft, Forschung und Technologie.
6Supported by the National Natural Science Foundation of China.
7Supported by the Hungarian OTKA fund under contract num- bers T019181, F023259 and T024011.
8Supported also by the Comision Interministerial de Ciencia y´ Tecnologıa.´
pby1 were collected, leading to much improved w x statistics compared to our previous publications 1,2 based on data from 1995 and 1996. In addition, in 1997, small amounts of data, 3.4 pby1 and 3.6 pby1, were collected at the same centre-of-mass energies as in 1995, 130.0 GeV and 136.1 GeV, respectively.
The measurements made on these data samples are combined with those resulting from a re-analysis of the previous data, superseding the results obtained in Ref. 1 .w x
In this article we report on measurements of the fermion pair production reactions:
eqey™hadronsŽg., eqey™mqmyŽg., eqey™tqtyŽg., eqey™eqeyŽg..
Ž .
In these reactions, the g indicates the possible presence of additional photons or low invariant-mass fermion pairs.
For a substantial fraction of the events initial-state radiation, ISR, lowers the initial centre-of-mass en- ergy to an effectiÕe centre-of-mass energy of the
X X
' '
annihilation process, s . When s is close to the Z mass, m , the events are classified as radiative re-Z
'
Xturns to the Z. A cut on s allows a separation between events at high effective centre-of-mass ener-
Ž .
gies so-called high-energy events , and radiative returns to the Z. Cross sections are measured for all processes and forward-backward asymmetries are measured for the lepton channels and are compared
w x
to predictions of the Standard Model 3,4 , both for the high-energy sample and for a larger, inclusiÕe sample including also the radiative returns to the Z.
Kinematic cuts have been changed with respect to our previous publication 2 . The corresponding re-w x sults of the cross section and forward-backward asymmetry measurements have been included, with corrections for these changes applied.
Similar studies on the data taken at centre-of-mass energies between 182.7 GeV and 188.7 GeV have
w x been published by other LEP collaborations 5–7 .
2. Analysis method
The data were collected using the L3 detector
w x
described in Refs. 8–13 . For the s-channel pro- cesses, the inclusive event sample is defined by
'
Xrequiring s )60 GeV for hadronic events and
'
sX)75 GeV for lepton-pair events, to reduce uncer- tainties on radiative corrections in extrapolating to'
Xlow s values. The high-energy sample is defined
'
X'
by requiring s )0.85 s .
Using the sum of all ISR photon or pair energies, E , and momentum vectors, P , the sg g X value is given by:
X
'
2 2sssy2 Eg sqEgyP .g Ž .1 For most of the events initial-state radiation is along the beam pipe and is not detected. In this case a single photon is assumed to be emitted along the beam axis; its energy is determined from the event
'
X Ž .kinematics. The s value is estimated using Eq. 1 . The effect of multiple photon and final-state radia-
'
Xtion on the s calculation has been studied using Monte Carlo programs and is corrected for. The treatment of photons observed in the detector is addressed in the sections describing the individual analyses. Mis-reconstruction of the effective centre- of-mass energy induces a migration of events be- tween the kinematic regions allowed and excluded
'
Xby the cut on s . This is taken into account in the
efficiency determination and as an additional back- ground, denominated as ISR contamination.
Bhabha scattering at high energies is dominated by t-channel photon exchange, and hence a cut on sX is less natural. Instead, a cut is applied on the acollinearity angle, z, of the final-state eq and ey. In this case, the inclusive and high-energy samples are defined by requiring z-1208 and z-258, re- spectively.
w x With respect to our previous analyses 1,2 the systematic errors in all channels have been improved substantially. The greater amount of Z calibration data in 1997 and 1998 leads to a better detector calibration. In addition, with the increased statistics, expecially in 1998, systematic effects have been studied with higher precision leading to a reduction in the estimated systematic errors.
Selection efficiencies and backgrounds are deter- mined by Monte Carlo simulations for each centre- of-mass energy using the following event generators:
w x Ž .
BHLUMI 14 small-angle Bhabha scattering ; PY-
w x Ž q y Ž . Ž . Ž .
THIA 15 e e ™hadrons g , ZZg , Zee g ,
Ž .. w xŽ q y q yŽ . q y
Wen g ; KORALZ 16 e e ™m m g , e e
q y
Ž .. w x w x
™t t g ; BHAGENE 17 and BHWIDE 18 Žlarge-angle Bhabha scattering ; TEEGG 19. w xŽe eq y
q y
Ž .. w x Ž q y Ž ..
™e e g g ; GGG 20 e e ™gg g ; PHO-
w x Ž .
JET 21 hadronic two-photon collisions ; DIAG36 w22x Že eq y™e eq ym mq y, e eq yt tq y, e e e eq y q y.;
q y q y
w x Ž . w x
FERMISV 23 e e ™e e ff ; KORALW 24 Že eq y™W Wq yŽg..; and EXCALIBUR 25 e ew xŽ q y
X q y q y q y
Ž . .
™qq en g , e e ™e e e e .
The measurements are compared to the predic- tions of the Standard Model as calculated using the
w x w x
ZFITTER 26 and TOPAZ0 27 programs with the
w x
following parameters 28–35 : mZs91.190 GeV,
Ž 2. Ž5.
as mZ s0.119, mts173.8 GeV, Dahads0.02804, and mHs150 GeV. The theoretical uncertainties on the Standard Model predictions are estimated to be
w x
below 1% 36 except for the predictions for large angle Bhabha scattering which have an uncertainty
w x of 2% 37 .
2.1. Initial-final state interference in s-channel pro- cesses
In the presence of interference between initial- and final-state radiative corrections, the effective centre-of-mass energy, in contrast to the acollinearity
angle, is not well-defined. Moreover, for the s-chan- nel processes, unlike for Bhabha scattering, these contributions are not included in the Monte Carlo samples used to estimate efficiencies. Their effect is expected to be largest for the high-energy mqmy andtqty samples, affecting cross sections by up to 2% and forward-backward asymmetries by up to 0.02. The following approach is used in the analysis of the s-channel processes.
Cross sections are first determined disregarding this effect. This allows the use of existing Monte Carlo programs without modifications. Corrections are subsequently applied using the Standard Model predictions for the interference contributions, folded with the selection efficiency, e, as a function of the fermion-pair invariant mass, m , and the scatteringff angle of the anti-fermion, cosu. This leads to an additive correction:
1 1 's
sff™sffye
H
y1dcosuH
'sX d mffeŽ
cosu, mff.
= d2sintf
, Ž .2
dcosud mff
where d2sintfrdcosud mff is the differential interfer- ence contribution to the cross section as calculated using the ZFITTER program. The corrections ap- plied range between 0.1% for the hadronic cross section and 1.3% for the leptonic cross sections.
The forward-backward asymmetries for the high- energy samples are obtained as the result of an unbinned maximum-likelihood fit to the polar angu- lar distribution in the Born approximation, to which is added a term representing the differential interfer- ence cross section:
1 dsff
3 2
s8Ž1qcosu.qA cosfb u sff dcosu
q 1
eŽcosu s. ff
=
H
''sXsd mffeŽ
cosu, mff.
= d2sintf
. Ž .3
dcosud mff
For the inclusive sample, initial-state radiation dis- torts the angular distribution, such that the Born
approximation in Eq. 3 is not appropriate. Instead,Ž . the forward-backward asymmetry is obtained di- rectly from the differential cross section and extrapo- lated to the full solid angle using the ZFITTER program. The differential cross section is corrected analogously to Eq. 2 . The correction is largest forŽ . the asymmetry of the high-energy samples, ranging between 0.004 and 0.010.
2.2. Pair corrections
Besides the emission of ISR photons, also the emission of initial-state pairs can lower the effective centre-of-mass energy of the scattering process. This gives rise to a non-negligible contribution to the inclusive cross section approximately 1.5% for allŽ s-channels as estimated using the ZFITTER pro- gram when radiative returns to the Z are included in. the signal definition. To allow for a proper compari- son between experimental measurements and theoret- ical predictions, these radiative corrections are in- cluded in the fermion-pair signal definition.
To calculate the effect of this signal contribution on the overall efficiency, and to estimate the back- ground contributions leading to the same four-ferm- ion final states, events are generated using the DIAG36 program. As this program includes only photon exchange, the events are reweighted to in- clude the effects of Z exchange using the matrix element calculation of the FERMISV program. The selection efficiencies are obtained by combining those estimated from the separate Monte Carlo samples regarded as signal, weighted with their respective cross sections as estimated using the ZFITTER pro- gram. As these Monte Carlo programs do not yield a correct description of low-mass hadronic pairs, the efficiency for events with hadronic pairs is taken to be that for the events with lepton pairs. A 20%
uncertainty is assigned to this efficiency, resulting in an uncertainty less than 0.2% on the overall effi- ciency.
Because of the large number of diagrams in- volved, this approach is less straightforward in the case of Bhabha scattering. Since the relative pair
w x
correction is estimated 38 to be significantly smaller than for the s-channel processes, its effect on the selection efficiency is neglected and no correction is applied.
3. Analysis and results 3.1. Integrated luminosity
The luminosity is measured using small-angle w x
Bhabha scattering 13 . A tight fiducial volume cut,
< <
34 mrad-u-54 mrad and 908yf )11.258,
<2708yf<)11.258, is imposed on the coordinates of the highest-energy cluster on one side. The highest- energy cluster on the opposite side should be con- tained in a looser fiducial volume, 32 mrad-u-65
< < < <
mrad and 908yf )3.758, 2708yf)3.758. This method reduces the theoretical uncertainty.
The experimental systematic uncertainties origi- nate from the event selection criteria, 0.10%, and from the detector geometry, 0.05%. The Monte Carlo statistics result in an uncertainty of 0.07%, yielding a total experimental systematic uncertainty of 0.13%.
w x In addition, a theoretical uncertainty of 0.12% 39 is assigned to the BHLUMI generator, resulting in a total uncertainty of 0.18%.
q y
3.2. e e ™hadrons( )g
3.2.1. EÕent selection
Events are selected by restricting the visible en- ergy, Evis, to 0.4-Evisr
'
s-2.0. The longitudinal< <
energy imbalance must satisfy ElongrEvis-0.7. The reconstructed energies do not include isolated elec- tromagnetic energy depositions with an energy greater than 10 GeV. These cuts reject most of the background from two-photon collision processes.
In order to reject background originating from lepton pair events, more than 18 calorimetric clusters with an energy exceeding 300 MeV each are re- quested.
The W-pair production background is reduced by applying the following cuts. Semi-leptonic W-pair decays are rejected by requiring the transverse en- ergy imbalance to be smaller than 0.3 E . Thevis background from hadronic W-pair decays is reduced by rejecting events with at least four jets each with energy greater than 15 GeV. The jets are obtained
w x
using the JADE 40 algorithm with a fixed jet resolution parameter ycuts0.01.
Fig. 1a shows the distribution of the visible en- ergy normalised to the centre-of-mass energy for hadronic final state events selected at 189 GeV. The
observed peak structure of the signal arises from the high-energy events and from the radiative returns to the Z.
As an additional cross-check, an alternative selec- tion is performed using an artificial neural network
w x
technique 41 instead of the cuts described above.
The results obtained using the two selection methods are compatible with each other.
To reconstruct the effective centre-of-mass en- ergy, two different methods are used. In the first method, all events are reclustered into two jets using the JADE algorithm. A single photon is assumed to be emitted along the beam axis and to result in a missing momentum vector. From the polar angles of the jets, u1 and u2, the photon energy is then estimated as:
<sinŽu1qu2.<
Egs
'
sPsinu1qsinu2q<sinŽu1qu2.<. Ž .4The second method uses the clustered jets obtained using the JADE algorithm with a fixed cut, ycuts 0.01. A kinematic fit is performed assuming the emission of either zero, one, or two photons along the beam axis. The hypothesis of the smallest num- ber of photons yielding a probability of the kine- matic fit larger than 8.5% is used. The cross sections are estimated as the average of the results obtained using the two methods. A systematic uncertainty on
'
Xthe s reconstruction, equal to half their difference, is assigned.
For about 10% of the events, a high-energy clus- ter is detected in the electromagnetic calorimeter. It is selected as described above and is assumed to be a photon. Its energy and momentum are added to the undetected ISR photons. The effective centre-of-mass energy is then calculated using Eq. 1 .Ž .
'
XFig. 2a shows the reconstructed s distribution, based on the reconstruction using the jet angles, for hadronic final state events.
3.2.2. Cross section
Selection efficiencies and background contribu-
'
Xtions are listed, for the s reconstruction method using the jet angles, in Table 1. The selected sample contains a background from hadronic two-photon collision processes, W-, Z- and tau-pair production
q y q y
Ž .
and e e ™Ze e g events. The two-photon
q y
'
Ž . Ž . Ž .
Fig. 1. a The total visible energy normalised to the centre-of-mass energy, s , for the selection of e e ™hadronsg events, b highest
q y q y
Ž . Ž .
muon momentum normalised to the beam energy for the selection of e e ™m m g events, c highest tau jet energy normalised to the
q y q y
Ž . Ž .
beam energy for the selection of e e ™t t g events, and d highest electron energy normalised to the beam energy for the selection
q y q y
Ž . of e e ™e e g events.
background is estimated by adjusting the Monte Carlo to the data in a two-photon enriched sample.
The numbers of selected events, the total cross sections for the different event samples, and the corresponding statistical and systematic uncertainties are listed in Table 2, together with our previous
published measurements 2 . The systematic uncer-w x
'
Xtainties are dominated by the uncertainty on the s determination and are correlated between different centre-of-mass energies. In Fig. 3 the cross section measurements are shown and compared to the Stan- dard Model predictions.
X q y q y q y
' Ž . Ž . Ž . Ž .
Fig. 2. The reconstructed effective centre-of-mass energy, s , for the selection of a e e ™hadronsg events, b e e ™m m g
Ž . q y q yŽ . Ž . q y q yŽ .
events, c e e ™t t g events, and the reconstructed acollinearity angle for d e e ™e e g events.
q y q y
3.3. e e ™m m ( )g
3.3.1. EÕent selection
The event selection for the process eqey™
q y
Ž . w x
m m g follows that of Ref. 2 . Two muons are
< <
required within the polar angular range cosu -0.9.
For the data taken at 183 GeV the angular range is
< <
restricted to cosu -0.81. At least one muon must be measured in the muon spectrometer, and have a momentum greater than 35 GeV. This reduces sub-
Table 1
q y
Ž . Selection efficiencies and background fractions for the inclusive and the high-energy event samples of the reactions e e ™hadronsg ,
q y q y
Ž . q y q yŽ . q y q yŽ .
e e ™m m g, e e ™t t g and e e ™e e g . For Bhabha scattering the selection efficiencies are given for 448-u-1368
Ž . Ž .
inclusive % high energy %
's GeVŽ . 130.0 136.1 182.7 188.7 130.0 136.1 182.7 188.7
q y
Ž .
e e ™hadronsg Selection Efficiency 97.4 97.2 90.0 89.2 93.7 93.8 88.2 88.1
Two Photon Background 1.8 1.8 2.5 2.8 1.4 1.8 1.8 1.9
q y
W W Background – – 4.4 5.2 – – 6.9 8.1
Other Background 0.2 0.2 1.3 1.4 0.3 0.4 0.9 1.1
ISR Contamination 0.2 0.1 0.2 0.2 17.7 17.0 11.4 11.2
q y q y
Ž .
e e ™m m g Selection Efficiency 68.6 65.9 47.4 61.4 78.8 73.8 63.9 75.4
Two Photon Background 2.0 2.8 4.8 10.0 0.8 1.5 1.8 2.9
q y
W W Background – – 0.7 2.9 – – 0.5 2.5
Cosmic Background 0.9 1.1 2.0 0.5 0.9 2.4 1.8 0.4
Other Background 0.4 0.7 2.8 2.8 0.2 0.1 1.2 1.3
ISR Contamination 0.4 0.4 0.4 0.3 8.0 6.7 4.1 4.2
q y q y
Ž .
e e ™t t g Selection Efficiency 45.9 38.7 35.2 34.8 51.0 45.0 47.2 47.3
Two Photon Background 2.3 2.1 7.2 7.4 1.3 1.2 2.6 2.2
Other Background 3.0 5.5 4.8 7.2 2.2 3.7 3.7 5.8
ISR Contamination 0.5 0.5 0.5 0.4 7.6 7.3 5.2 5.2
q y q y
Ž .
e e ™e e g Selection Efficiency 97.9 97.6 96.4 97.5 98.0 97.6 95.9 97.1
q y
t t Background 1.3 1.5 1.3 1.3 1.1 1.4 1.3 1.3
Other Background 0.6 1.1 1.2 1.3 0.6 0.5 0.7 0.6
stantially the background from eqey™eqeymqmy interactions whilst ensuring a high acceptance for events with hard ISR photons.
Background from cosmic muons is reduced using both scintillation counter time information and the distance of the muon tracks from the beam axis. The number of accepted cosmic muon events is estimated by extrapolating the corresponding sideband distribu- tions to the signal region. Fig. 1b shows the distribu- tion of the maximum muon momentum normalised to Ebeam for events selected at 189 GeV.
'
XThe s value for each event is determined using Eq. 1 assuming the emission of a single ISR pho-Ž . ton. In case a photon is detected in the electromag- netic calorimeter it is required to have an energy greater than 15 GeV and an angular separation to the nearest muon of more than 10 degrees. Otherwise the photon is assumed to be emitted along the beam axis and its energy is calculated from the polar angles of the outgoing muons according to Eq. 4 . The distri-Ž .
'
Xbution of the reconstructed s for events selected at 189 GeV is shown in Fig. 2b.
3.3.2. Cross section
Selection efficiencies and background contribu- tions are listed in Table 1. The main background contributions are from the reactions eqey™
q y q y q y q y
Ž .
e e m m , e e ™t t g and from W-pair production.
Table 2 summarises the numbers of selected events, the resulting cross sections, and their statisti- cal and systematic uncertainties for the two event samples at the various centre-of-mass energies. The main contributions to the systematic uncertainties originate from the background subtraction and from the acceptance correction. Fig. 4 shows the compari- son to the Standard Model prediction.
3.3.3. Forward-backward asymmetry
The forward-backward asymmetry is determined using events with two muons with opposite charge and an acollinearity angle smaller than 90 degrees.
For the high-energy sample, the angular distribu- tion of the events is parametrised according to Eq.
Ž .3 . The asymmetry, A , is determined from anfb
Table 2
Number of selected events, N , measured cross sections,sel s, statistical errors and systematic errors and the Standard Model predictions,
q y
Ž . q y q yŽ . q y q yŽ . q y q yŽ .
sSM, of the reactions e e ™hadronsg , e e ™m m g, e e ™t t g and e e ™e e g, for the inclusive and the high-energy event samples. The systematic errors do not include the uncertainty on the luminosity measurement. In the case of Bhabha scattering, both leptons have to be inside 448-u-1368. The results for the 161–172 GeV data have been taken from Ref. 2 and correctedw x
Ž . Ž .
using ZFITTER s-channel processes and BHAGENE Bhabha scattering to correspond to the kinematic cuts described in the text
inclusive high energy
's GeVŽ . LLŽpby1. Nsel s Žpb. sSM Žpb. Nsel s Žpb. sSM Žpb.
q y
Ž .
e e ™hadronsg 130.0 6.1 1972 326.0"7.5"1.9 329.5 632 84.2"4.4"1.0 83.5 136.1 5.8 1571 274.4"7.0"1.8 272.0 460 66.6"3.9"0.8 66.9 161.3 10.0 1542 152.5"4.1"1.7 151.8 423 37.3"2.2"0.7 35.4 172.3 8.5 1064 121.2"4.1"1.3 124.5 248 28.2"2.2"0.6 28.8 182.7 54.9 5626 105.2"1.5"0.5 105.7 1505 24.7"0.8"0.4 24.3 188.7 173.4 16695 98.2"0.8"0.4 96.9 4517 23.1"0.4"0.3 22.2
q y q y
Ž .
e e ™m m g 130.1 6.1 91 21.0"2.3"1.0 20.9 44 8.2"1.4"0.2 8.5 136.1 5.9 70 17.5"2.2"0.9 17.8 33 6.9"1.4"0.3 7.3 161.3 10.9 94 12.5"1.4"0.5 10.9 41 4.59"0.84"0.18 4.70 172.1 10.2 67 9.2"1.3"0.4 9.2 32 3.60"0.75"0.14 4.00 182.7 50.5 197 7.34"0.59"0.27 7.90 111 3.09"0.33"0.14 3.47 188.7 167.4 893 7.28"0.29"0.19 7.29 420 2.92"0.16"0.06 3.22
q y q y
Ž .
e e ™t t g 130.1 6.1 66 22.1"2.9"0.5 20.9 35 9.8"1.9"0.3 8.5 136.1 5.9 43 17.1"2.8"0.5 17.8 23 7.5"1.8"0.3 7.3 161.3 9.8 45 10.4"2.0"0.7 10.9 25 4.6"1.1"0.3 4.7 172.1 9.7 45 11.0"2.0"0.8 9.2 23 4.3"1.1"0.3 4.0 182.7 55.5 174 7.77"0.68"0.17 7.89 108 3.62"0.40"0.06 3.47 188.7 176.8 527 7.27"0.37"0.17 7.28 309 3.18"0.21"0.07 3.22
q y q y
Ž .
e e ™e e g 130.1 6.1 312 51.1"2.9"0.2 56.5 274 45.0"2.7"0.2 49.7 136.1 5.8 281 49.3"2.9"0.2 50.9 248 43.6"2.8"0.2 45.4 161.3 10.2 337 34.0"1.9"1.0 35.1 289 31.1"1.8"0.9 32.4 172.3 8.8 256 30.8"1.9"0.9 30.3 207 26.7"1.8"0.8 28.3 182.7 55.3 1506 27.6"0.7"0.2 26.7 1385 25.6"0.7"0.1 25.0 188.7 175.9 4413 25.1"0.4"0.1 24.9 4097 23.5"0.4"0.1 23.4
unbinned maximum-likelihood fit of this parametri- sation to the data within the fiducial volume. The muon charge is measured as described in Ref. 2 .w x The charge confusion per event, ranging between 0.2% and 0.7%, is taken into account in the fit procedure. The asymmetries for the accepted back- ground contributions are estimated using the same method and are corrected for. The corrections range between 0.045 and 0.059.
For the inclusive event sample the differential cross section is distorted by hard ISR photons.
Therefore, Afb is computed directly from the differ- ential cross sections obtained within the fiducial volume. To obtain the asymmetry for the full solid
angle an extrapolation factor is calculated using the ZFITTER program. It ranges between 1.10 for the 183 GeV data and 1.03 for the 189 GeV data.
Table 3 summarises the numbers of forward and backward events, the forward-backward asymmetry measurements, and their statistical and systematic uncertainties. The main contributions to the system- atic uncertainty are the uncertainties on the back- grounds and on the momentum reconstruction. Fig. 4 shows the comparison of the corrected asymmetries to the Standard Model prediction. Table 4 lists the differential cross sections at 183 GeV and 189 GeV, compared to their Standard Model predictions. The 189 GeV distributions are displayed in Fig. 5.
q y
Ž . Fig. 3. Cross sections of the process e e ™hadronsg , for the
Ž . Ž
inclusive solid symbols and the high-energy sample open sym- bols . The Standard Model predictions are shown as a solid line. for the inclusive sample and as a dashed line for the high-energy sample. The lower plot shows the ratio of measured and predicted cross sections.
q y q y
3.4. e e ™t t ( )g
3.4.1. EÕent selection
The selection of tau-pair events has been modified with respect to our previous analysis 2 in order tow x reduce background from Bhabha and two-photon events.
Taus are identified as narrow, low multiplicity jets, containing at least one charged particle. Tau jets are formed by matching the energy depositions in the electromagnetic and hadron calorimeters with tracks in the central tracker and the muon spectrometer.
Events containing two jets within the polar angular
< <
range cosu -0.92 are accepted. The reconstruction
'
Xof s follows the procedure described in Section 3.3 using the polar angles of the two tau jets, requiring at least 10 GeV for observed photons.
Hadronic events are removed by requiring at most 16 calorimetric clusters with an energy exceeding
100 MeV each and at most 9 tracks in the central tracker. Events containing two electrons or two muons are rejected. Electrons are identified by a cluster in the electromagnetic calorimeter with an energy greater than 2.5 GeV and an electromagnetic shower shape, a matched track, and less than 2.5 GeV deposited in the hadron calorimeter. Muons are identified by a track in the muon spectrometer and a minimum-ionising particle signature in the calorime- ters. Bhabha events are further rejected by requiring the electromagnetic energy of the highest-energy jet
'
Xand the other jet to be less than 0.375 s and 0.25
'
s , respectively. In addition, the acoplanarity of theXtwo jets must be larger than 0.2 degrees.
To reject background from two-photon collision processes the most energetic jet must have an energy greater than 0.24 Ebeam. The distribution of this quantity is shown in Fig. 1c for the data taken at 189 GeV. The energy of reconstructed muons is required
Ž . Ž .
Fig. 4. Cross sections a and forward-backward asymmetries b
q y q y
Ž . q y q yŽ .
of the processes e e ™m m g and e e ™t t g for
Ž . Ž
the inclusive solid symbols and the high-energy sample open symbols . The Standard Model predictions are shown as a solid. line for the inclusive sample and as a dashed line for the high-en- ergy sample.
