Article
Reference
Measurement of hadron and lepton-pair production at 161 GeV < √s <
172 GeV at LEP
L3 Collaboration
AMBROSI, Giovanni (Collab.), et al.
Abstract
We report on measurements of e⁺e⁻ annihilation into hadrons and lepton pairs. The data have been taken with the L3 detector at LEP at center-of-mass energies between 161 GeV and 172 GeV. In a data sample corresponding to 21.2 pb⁻¹ of integrated luminosity 2728 hadronic and 868 lepton-pair events are selected. The measured cross sections and leptonic forward-backward asymmetries agree well with the Standard Model predictions.
L3 Collaboration, AMBROSI, Giovanni (Collab.), et al . Measurement of hadron and lepton-pair production at 161 GeV Physics Letters. B, 1997, vol. 407, p. 361-376
DOI : 10.1016/S0370-2693(97)00863-0
Available at:
http://archive-ouverte.unige.ch/unige:113059
Disclaimer: layout of this document may differ from the published version.
1 / 1
4 September 1997
PHYSICS LETTERS B
ELSEVIER Physics Letters B 407 ( 1997) 361-376
Measurement of hadron and lepton-pair production at 161 GeV < J;; < 172 GeV‘at LEP
L3 Collaboration
M. Acciarriac, 0. Adriani’, M. Aguilar-Benitez”b, S. Ahlen e, J. Alcarazab, G. Alemanni”, J. Allaby s, A. Aloisio ae, G. Alverson m, M.G. Alviggi”, G. Ambrosi “, H. Anderhub=,
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0370-2693/97/$17.00 6 1997 Elsevier Science B.V. AI1 rights reserved.
PIISO370-~693(97)00863-0
A. Herve”, W.C. van Hoekag, H. Hofer”“, S.J. HongaS, H. Hoorani*,
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*Kittel as, A. Klimentov q,ad, A.C. K&rig ag, A. Kopp ‘Y, I. Korolkoad, V. Koutsenkoq*ad, R.W. Kraemer jk, W. Krenz a9 A. Kunin q,ad, P Ladron de Guevaraab, I. Laktineh aa, G. Landir, C. Lapointq, K. Lassila-PeriniaZ, P. Laurikainen”, M. LebeauS, A. Lebedevq,
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R. Moorec, S. Morgantiam, T. Moulikk, R. Mount ai, S. Miiller a, F. Muheim”,
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Samuel CC.
Ting9, S.M. Ting 4, M. Tonutti a, S.C. Tonwar k, J. T&h’, C. Tully &,
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W Collaboration /Physics Letters B 407 (1997) 361-376 363
M. Wadhwaf, W. Wallraff”, J.C. Wangq, X.L. Wang”, Z.M. Wang”, A. Weber”, F. Wittgenstein ‘, S.X. Wu’, S. Wynhoff”, J. Xue, Z.Z. Xu”, B.Z. Yang”, C.G. Yang h,
X.Y.
Yao h, J.B. Ye “, S.C. Yeh bb, J.M. You A, An. Zalite an, Yu. Zalite an, P Zemp az, Y. Zeng”, Z. Zhang h, Z.P. Zhang “, B. Zhou ‘, G.Y. Zhu h, R.Y. Zhu ai, A.
Zichichij+y’,
F. Ziegler ay
a I. Physikalisches Institut, RWTH, D-52056 Auchen, FRG ’ 111. Physikalisches Institut, RWTH, D-52056 Aachen, FRG ’
h National Institute for High Energy Physics, NIKHEF and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands c University of Michigan, Ann Arbor, MI 48109, USA
Laboratoire d’Annecy-le-Vieu.x de Physique des Particules, LAPPIN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux CEDEX, France e Johns Hopkins University, Bultimore, MD 21218, USA
f Institute of Physics, University of Basel. CH-4056 Basel, Switzerland s Louisiana State University, Baton Rouge, LA 70803, USA h Institute of High Energy Physics, IHEP 100039 Beijing, China6
i Humboldt University, D-10099 Berlin, FRG ’
i University of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italy k Tata Institute of Fundamental Research, Bombay 400 005. India
t Boston University, Boston, MA 02215, USA m Northeastern University, Boston, MA 02115, USA
n Institute of Atomic Physics and University of Bucharest. R-76900 Bucharest, Romania
l’ Central Research Institute for Physics of the Hungarian Acudemy of Sciences, H-1525 Budapest 114, Hungary2 v Harvard University. Cumbridge, MA 02139, USA
9 Mussachusetts Institute of Technology, Cambridge, MA 02139. USA t INFN Sezione di Firenze and University of Florence, I-50125 Florence. Italy s European laboratory for Particle Physics, CERN* CH-121 I Geneva 23, Switzerland
L World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland
’ University of Geneva, CH-1211 Geneva 4, Switzerland
’ Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029. China 6 w SEF7: Research Institute for High Energy Physics, PO. Box 9, SF-00014 Helsinki, Finland
x University of Lausanne, CH- IO15 Lausanne, Switzerland
Y INFN-Sezione di Lecce and Universitd Degli Studi di Lecce, I-73100 Lecce, Italy Z Los Alamos National Laborutory, Los Alamos. NM 87544, USA
m Institut de Physique Nucleaire de Lyon, IN2P3-CNRSUniversite Claude Bernard, F-69622 Villeurbanne, France ah Centro de Investiguciones Energeticas, Medioambientales y Tecnologicas, CIEMAT E-28040 Madrid, Spain3
a’ INFN-Sezione di Milano, I-20133 Milan, Italy
‘e Institute of Theoretical and Experimental Physics, STEP Moscow, Russia ar: INFN-Sezione di Nupoli and University of Naples, I-80125 Naples, Italy nt Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus
‘s University of Nijmegen and NlKHEF NL-6525 ED Nijmegen, The Netherlands nh Oak Ridge National Laboratory, Ouk Ridge, TN 37831, USA ai California Institute of Technology? Pasadena, CA 91125, USA
‘i INFN-Sezione di Perugia und Universita Degli Studi di Perugia, I-06100 Perugia, Italy
;Ik Carnegie Mellon University, Pittsburgh, PA 15213, USA
‘t’ Princeton University, Princeton, NJ 08544, USA
pm INFN-Sezione di Roma and University of Rome, “La Sapienza”, t-00185 Rome, Italy
” Nuclear Physics Institute. St. Petersburg, Russia a’ University and INFN, Salerno, l-84100 Salerno, Italy
‘v University of California San Diego, CA 92093, USA
“q Dept. de Fisica de Purticulas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain w Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria
as Center for High Energy Physics, Korea Adv. Inst. of Sciences and Technology, 305-701 Taejon, South Korea 81 University of Alabama, Tuscaloosa. AL 35486, USA
” Utrecht University and NIKHEF NL-3584 CB Utrecht, The Netherlands ily Purdue University, West Lafayette, IN 47907, USA
364 L.3 Collaboration/Physics Letters B 407 (19971 361-376 w Paul Scherrer Institut. PSI, CH-5232 Vii&en, Switzerland
‘y DESY-~n.~l~tut fir H~)chener~iep~~ys~~, D-15138 ~athen* FRG
a’ Eidgeniissische Technische Hochschule, ETH Zirich, CH-8093 Ziirich, Switzerland
‘a University of Hamburg, D-22761 Hamburg, FRG hh High Energy Physics Group, Taiwan, ROC
Received 7 May 1997 Editor: K. Winter
Abstract
We report on measurements of efe- annihilation into hadrons and lepton pairs. The data have been taken with the L3 detector at LEP at center-of-mass energies between 161 GeV and 172 GeV. In a data sample corresponding to 21.2 pb-’
of integrated luminosity 2728 hadronic and 868 fepton-pair events are selected. The measured cross sections and leptonic forward-backward asymmetries agree well with the Standard Model predictions. @ 1997 Elsevier Science B.V.
1. Introduction
In 1996 LEP was operated for the first time at center-of-mass energies above the W-pair production threshold. In July and August 10.9 pb-’ were col- lected at fi = 161.3 GeV. In October and November the center-of-mass energy was increased and 1 .O pb-
’
and 9.3 pb-’ were recorded at fi = 170.3 GeV and fi = 172.3 GeV, respectively. The small data sample taken at 170.3 GeV is combined with the data taken at 172.3 GeV for the me~uremen~ of muon and tau-pair production and the Bhabha asymmetry measurements.
In this article we report on measurements of the fermion pair production reactions:
e+e- --+ hadrons(y) , e+e- + ,u+,u- (y) , e+e- --+ 7+7-(y), e+e- --+ e+e-(y) . 11) In these reactions, the (7) indicates the possible pres- ence of additional photons. Cross sections are mea- sured for all processes and forward-backward asym- metries for the lepton channels.
’ Supported by the German Bundesministerium fiir Bildung, Wis- senschaft, Forschung und Technologie.
2 Supported by the Hungarian OTKA fund under contract num- bers T14459 and T24011.
3 Supported also by the Comisi6n Interministerial de Ciencia y Technologia.
4 Also supported by CONICET and Unive~idad National de La Piata, CC 67, 1900 ta Plata, Argentina.
5 Also supported by Panjab University, Chandigarh- 1600 14, India.
6 Supported by the National Natural Science Foundation of China.
For a substantial fraction of the events initial-state radiation, ISR, photons are emitted. They lower the initiai center-of-mass energy to an effective center-of- mass energy of the annihilation process, &?. When
fi is close to the 2 mass, mz, the events are classed as radiative returns to the Z. A cut on & allows a separation between events at high effective center- of-mass energies, high energy events, and radiative returns to the Z.
For the total and the high energy event samples cross sections and symmetries are measured and compared to the predictions of the Standard Model [ 11. Combin- ing the new results with our measurements at center- of-mass energies around the Z-pole [ 21 and between 130 GeV and 140 GeV [ 31, the yZ interference and the Z-boson mass are determined with improved pre- cision in the framework of the S-matrix ansatz [4].
Similar studies have been presented for the data taken at 161 GeV by the OPAL collaboration [ 51.
2. Measurement of fermion-pair production The data were collected by the L3 detector de- scribed in [ 61. The me~urements of cross sections and forward-backward asymmetries are performed for the total and the high energy event samples. In the total event sample v’? is required to be larger than 0.1 fi to reduce uncertainties on radiative corrections in extrapolating to low X@ values. The high energy sample is defined by requiring & > 0.85&.
L3 Collaborut~on /Physics Letters B 407 11997f361-376 365
Using the sum of all ISR photon energies, E,, and momentum vectors, Pu, the fi value is given by:
s’=s-2E,J;;+E;-P;. (2)
For most of the events the ISR photons are radiated along the beam pipe and are not detected. In this case the photon energy is determined assuming that a sin- gle photon is emitted along the beam axis. The &
value is estimated using Eq. (2). The effect of multi- ple and final-state photon radiation on the fi catcu- lation has been studied using Monte Carlo programs and is corrected for.
For the dete~ination of selection efficiencies and backgrounds, Monte Carlo simulations are per- formed for each center-of-mass energy using the following event generators: BHL~I [7] (smaI1 angle Bhabha scattering) ; PYTHIA [ 81 (e+e- -+
hadrons( y) , ZZ(y), Zee(y), Wev(y> ); KG- RALZ [9] (e+e- --+ ~+~-(~),?+~-(~)); BHA- GENE [IO] (e+e- --+ e+e-(7)); PHOJET [ll]
(hadronic two-photon collisions) ; DIAG36 [ 121 (e’e- -+ e+e-p”+fiu-, e+e-rfr-, e+e-e+e-);
KORALW [13] (e+e- -+ W+W-(y)), EX- CALIBUR [ 141 (e+e- + qq’ev( r), e+e- + e+e-e+e-); GGG [ 1.51 (e+e- + yy(y)).
The measurements are compared to the predic- tions of the Standard Model calculated using ZFIT- TER [16] and TGPAZO f 171 with the following parameters: rnz = 91.195 GeV [2], cy,(rng) = 0.123 [18], m, = 175 GeV [19], Ly(m$) = l/128.896 [ 201 and mu = 300 GeV. The theoreti- cal uncertainties of the Standard Model predictions are well below the one percent level [ 2 11 except for the predictions for the large angle Bhabha scattering which has an uncertainty of 2% [ 221,
The analyses of the different channels are similar to those performed at center-of-mass energies between 130 GeV and 140 GeV [ 31. Changes due to detector modifications and different background conditions at the increased center-of-mass energies are discussed in the descriptions of the individual analyses.
2.1. integrated Luminosity
The luminosity is measured using small-angle Bhabha scattering within a polar angular range of
35.0 mrad < 8 < 61.8 mrad7. The main systematic uncertainties originate from the event selection cri- teria, 0.4%, and from the limited knowledge of the detector geometry, 0.3%. Including the contribution from Monte Carlo statistics a total experimental un- certainty of 0.6% is assigned to the measurement of the integrated luminosity. The theoretical uncertainty of the BHLUMI generator is less than 0.25% for the center-of-mass energies given above [ 71.
Event selection
Events are selected by restricting the visibie energy, Evis, to 0.4 < &s/‘fi < 2.0. The longitudinal en- ergy imbalance must satisfy 1El,pl/E+ < 0.7. There must be more than 11 calorimetric clusters with an energy larger than 300 MeV. In order to reject noise and background from cosmic muons, an energy of at least 15 GeV must be deposited in the el~tromagnetic calorimeter and at least 4 tracks from the interaction point must be reconstructed in the central tracker.
At center-of-mass energies of 170 GeV and 172 GeV background from W-pair production is re- duced by applying the following cuts. Semi leptonic W-pair decays are rejected by requiring the transverse energy imbalance to be smaller than 0.3 Evi,. Events in the high energy sample with at least four jets each with energy larger than 15 GeV are rejected to de- crease the background from hadronic W-pair decays.
The jets are obtained using the JADE algorithm [ 231 with a fixed jet resolution parameter ycut = 0.01.
In Fig. 1 the most important selection variable is shown for thedifferent final states. In Fig. la thedistri- bution of the visible energy normalised to the center- of-mass energy for hadronic final state events selected at 172 GeV is shown. The double-peak structure of the signal arises from the high energy events and from the radiative returns to the Z. A good agreement be- tween data and Monte Carlo expectation is found.
To calculate the effective center-of-mass energy, all events are reclustered into two jets using the JADE
’ The analysis follows [2] with a tight fiducial volume on one side restricting the radial coordinate to 99.6 mm < R <: 176.2 mm and the azimuthal angle to /90° - (b] > 11.6”, /270° - $1 >
1 1.6”. The loose fiducial volume on the opposite side is given by:
92.0 mm < R < 183.8 mm and 190° -41 > 4’. /270*--4) > 4O.
366 L3 Cotiaboration / Physics Letters B 407 (1997) 361-376
l Data 172 GeV 5 MC C;P-(9
&$ MC background
015
Evis : +ii
1:5 015
%,’ EtlLll
.
l Data 172 GeV 1o3 td)
i
1
1
0 Data 172 GeV MC e’e-(y) MC background
0 0.2 0.4 Ei, / g 0.6 0.8 0.4 0.6 E ’
Fig. I. (a) The total visible energy normalised to the center-of-mass energy, A, for the selection of e+e- --t hadron@?) events, (b) highest muon momentum for the selection of e+e- - p+p- (7) events, (c) Ej,,/V’? calculated from the energy of the two tau jets for the selection of e+e- - T+T- ( y) events and (d) energy of highest energy electron normalised to the beam energy for the selection of e+e- + e+e- (y) events.
I.3 Collaboration /Physics Letters B 407 (1997) 361-376
l Data 172 GeV
q
MC hadrons(y) /‘@j MC background(a)
100 150
w [GeV]
l Data 172 GeV
50 100 150
c [GeV]
80 r
* Data 172’GeV 0 MC P+P-(y)
q
MC background100 150
+F [GeV]
l Data 172 GeV
q
MC e’e-(y)(d)
100 150
@ [GeV]
367
Fig. 2. The reconstructed effective center-of-mass energy, a, for the selection of (a) e+e- -) hadrons( y) events, (b) e+e- + p+p- ( y) events, fc) e+e- -+ r+~(y) events and (d) e+e- -+ efe-(y) events.
368 13 Collaboration/Physics Letters B 401~1991~ 361-376 Table I
Selection efficiencies and background fractions for the to&d, fi > 0. I&, and the high energy. & > 0.85,.& event samples of the rea&ons e*e- ----f hadrons(y), &e- + pu4p-(y), eie- -+ cr*~-(yf and e+e- - e’c- (~3. For Bhahha scattering the selection efficiencies are given for 44’ < H < I?@. The emciencies and background fractions at 170 GeV are the same as the ones quo&d for
172 GeV.
Total I%J High energy [%I
161 GeV 172 CeV I61 GeV 1’72 GeV
efe- + hadrons(~~ Selection Efficiency 93.6 90.6 93.3 85.5
Two Photon Elackground 2.5 2.2 0.4 0.6
W+W- Background I .9 6.7 4.2 5.0
Other Background 0.9 I.0 0.7 0.6
ISR Contamination 13.0 10.9
e+e- -+ pig-(y) Selection Elciency 60.0 58.9 71.2 74. I
Two Photon Backgronnd 5.5 6.0 3.0 2.9
Cosmic Background 0.7 1.8 0.5 1.8
Other Eack~mund 1.8 4.0 2.6 3.8
1SR Contamination 7.7 6.5
e+e- -+ 7+7-(y) Selection Efficiency 31.9 30.8 44.8 44. I
Two Photon Background 12.8 13.0 5.4 7.4
Qher Background 9.9 8.2 10.2 9.3
JSR Contamination 4.1 3.9
e+e- + e+e- ( y) Selection EMiciency 96.6 94.0 92.8 90.2
Background 0.5 I.0 <O.l <o.t
ISR Contamination 0.4 0.4
algorithm. A kinematic fit is performed on the two jets and the missing energy vector imposing four- momentum conservation. The direction of the miss- ing energy vector is assumed to be parallel to the beam axis. The missing energy is attributed to a sin- gle ISR photon. For about 10% of the events, a pho- ton is detected in the electromagnetic calorimeter. It must have an el~t~magnetic shower shape, an energy larger than 20 GeV and an angular separation of more than 10” to the nearest energy cluster. The energy and momentum of this photon are added to those of the undetected ISR photon and the fi value is calcu- lated according to EQ. (2). In Fig. 2 the reconstructed Q? distribution is shown for the different final states.
Fig. 2a shows the x/? dis~bution for hadronic final state events selected at 172 GeV.
tau-pair production and e’e- t Zee(y) events. The two-photon background is estimated by adjusting the Monte Carlo to the data in a background enriched sample.
Systematic errors of 1. I % for the total and 2.0%
for the high energy event sample are assigned to the cross section measurements. They are dominated by the unce~~nty on the two-photon back~ound for the total data sample and by the uncertainty on the fl determination for the high energy sample. The uncer- tainty on the fl calculation is estimated by varying the fi cut.
The numbers of selected events and the total cross sections for the different event samples are listed in TabIe 2. In Fig. 3 the cross section measurements are shown together with our previous measurements [ 2,3]
and are compared to the Standard Model predictions.
Selection efficiencies and background contributions are listed in Table I. After application of the seIec- tion criteria the sampfe contains a background frum hadronic Tao-photon coilision processes. W-, Z- and
W Collaboration /Physics Letters 3 407 (1997) 361-376 369 Table 2
Number of sekcted events, N,t, measured cross sections, 0; statisticni errors and systematic errors and the St&ad Model ~~~~ons~
(rsM, of the z&ions e+e- h bndrons[y), e+e- - ,i~~&-(yf, e+e- --) ~+r-f~f and e+e- --P e’e-fyf, for the total fi > 0.14, and the high energy, fi > O.SS,,&, event samptes. The systematic enws do not include the uncetinty of the luminosity measurement.
The cross sections are quoted far the full solid angle except for the Bhabha scattering, given for 44’ < B < 136O.
e+e- -+ hadrons(yf
Total High energy
fi ICeV] C Ipb-‘1 AI,,\ flhild IPbl USM 1 @I N,I flhad 1 pbl QM bbl
261.3 10.0 1542 fS5.O zk 4.2 147.2 423 37.3 + 2.2 34.9
170.3 i.0 122 I23 i I2 126.6 39 39.5 It 7.5 29.8
I-72.3 8.5 1064 LFf.2 i 4.2 122.7 24& 28.2 + 2.2 28.9
Systematic error 1.1% 2.0%
fi [@VI L [pb-*l N,ei c~~l;li~- [phi WSM kpbl %xt rptp- I‘pbl crs~ [pbl
161.3 10.9 94 13.4 f 1.5 11.1 41 4.59 f. 0.84 4.4
172,l 10.2 67 9.9 f 1.4 9.5 32 3.40 f 0.15 3.8
Systematic error 4% 4%
fi lCeVl L: !@-‘I N,i ‘T$.$ .r- Ipbl CSM t$t f&2 @+- fpbl KsM fpbf
161.3 9.8 45 I I.2 i 2.1 Il.1 25 4.6 f I.1 4.5
172.1 9.7 45 I I.8 zk 2.2 9.5 23 4.3 f 1.1 3.9
Systematic error 7% 7%
fi [GeVl c Lpb-‘I N,I CT~Q-- tpbl f?iM [@I &I a,+,- [pbl asp Ipb]
e’+e- _f eie-(yf 161.3 10.2 337
170.3 1.0 24
172.3 8.8 256
Systematic error
34.0 f 1.9 35.2 289 30.5 f 1.8 28.4
25.t f 5.4 31.3 21 24.1 f 5.3 25.4
30.8 i L.9 30.3 207 26.2 i k.8 24.8
3% 3%
2.3. e+e- -4 p+p-(y)
The event sefcztion for the process e+e- -+
g+fi-fy) follows that of 131 with minor moditi- cations. The fouler cut on the highest momentum measured in the muon chambers, pmax, is set to a fixed value of 35 GeV to ensure high acceptance for events with hard ISR photons.
Background from cosmic muons is reduced by using scintillation counter time information. The number of accepted cosmic muon events is found to be 0.6 i 0.2 at 161 GeV and 1.2 It 0.3 at 172 GeV. In Fig_ lb the dist~bution of the m~imum muon momentum nor- malised to I&,,,, for events selected at 172 GeV is shown.
The @ value for each event is determined using
IQ. (2) assuming the emission of a single ISR pho- ton. In case the photon is found in the detector it is required to have an energy, E,, larger than 10 GeV in the e~~troma~netic cdorimeter and an angular sepa- ration 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, 61 and 62, of the outgoing muons:
The distribution of the reconstructed fi for events selected at 172 GeV is shown in Fig. 2b. A good agreement between data and Monte Carlo expectation is found.
370 L3 Collaborarion /Physics Letters B 407 (1997) 361-376
10 - 1 “b
“Q.()
-SM:&%>O.l
. . . . . . . .-... SM: &%> 0.85
“‘%Q +
“‘..o...
1 ” ” I ” ” I ” ” I,, I 75 100 125 150 175
6 [GeV]
Fig. 3. Cross sections of the process e+e- -+ hadrons(y), total (solid dots) and the high energy sample (open dots). The Standard Model predictions are shown as a solid line for the total sample and as a dashed line for the high energy sample. The measurements at center-of-mass energies below I61 GeV have been corrected to correspond to fl > 0.16 for the total and fi > 0.854 for the high energy event samples. Measurements at the Z peak which arc close in center-of-mass energies have been combined.
Cross section
Selection efficiencies and background contribu- tions are listed in Table 1. The main background contributions are from the reactions e+e- -+
e+e-~+~-.-,e+e- -+ ~+7-- (y) and from W-pair production. The background contributions include the contamination of the high energy event sample with events with hard ISR photons. The systematic error of the cross section measurement is estimated to be 4% for both the total and the high energy sample.
The main contributions are the uncertainties on the background and acceptance corrections.
In Table 2 the number of selected events and the resulting cross sections for the two event samples at the different center-of-mass energies are summarised.
In Fig. 4 the comparison to the Standard Model pre- diction is shown.
1.0: 4 I , ” I “I I 0.5:
?z a 0.0:
-0.5 1
75 100 125 150 17;
& [GeV]
Fig. 4. Cross sections and forward-backward asymmetries of the processes efe- -+ pcL+flcL- (y) and e+e- - 7+7-(y) for the total (solid symbols) and the high energy sample (open symbols).
The Standard Model predictions are shown as a solid line for the total sample and as a dashed line for the high energy sample. The measurements at center-of-mass energies below I61 GeV have been corrected to correspond to fi > 0.16 for the total and v’? > 0.854 for the high energy event samples. Measurements at the Z peak which are close in center-of-mass energies have been combined.
Forward-backward asymmetry
The forward-backward asymmetry is determined using events with two identified muons with opposite charge and an acollinearity angle smaller than 90’. The angular distribution of the events is parametrised by
dg
dcos0 0: f(1 fcos28) +Afbcose, (4) where 8 is the polar angle of the outgoing fermion with respect to the incoming electron.
The asymmetry, &,, is determined from an un- binned maximum-likelihood fit of Eq. (4) to the data within 1 cos 8) < 0.9. The muon charge is measured in the muon spectrometer. The effect of a wrong charge assignment is estimated for each event and taken into account in the fit procedure. The charge confusion per track, 2 f 1%, has a negligible effect on the asymme-
l.3 Collaboration/Physics Letters B 407 (1997) 361-376 371 Table 3
Number of forward, Nr, and backward events, Nb. focal-backward ~yrn~~es, Am, statistical errors and systematic errors and the Standard Mode1 predictions, @sM, of the reactions e’e- -t /.c+~*-(y), efe- + T+T- (y) aad e+e- -+ eie- (y) for the to&I, fi >
O.i&, and the high energy, x.@ > 0.854, event samples. For the etectron pair production both leptons have to be inside 44O < B < 136O.
Total High energy
fi [GeVl NC Nh A* WM Nf Nb Alh USM
e+e- +,u+jK(y) 161.3 35 21 0.29”.‘2 II. 14 0.29 22 8 0.59;;; 0.63
172.1 23 16 0.16”.‘6 0.17 0.29 IS 9 0 . 3&s 0.21 0.61
Systematic Error 0.05 0.05
,/? IGeVl NC Nh Aib @M Nf h &I ffSM
e+e- --t 7+7-(y) 161.3 15 12 0 . 1611.19 fl.20 0.29 12 4 0.97;:2; 0.63
172.1 16 16 0.07”-‘s 0. I9 0.29 9 7 0 . 180.25 0.21 0.61
Systematic Error 0.10 0.10
fi IGeVi Nr ffh Alh WM & Nb Ant CSM
e+e- -+e+e-(y) 161.3 240 43 0.767 f 0.049 0.753 206 29 0.819 rt 0.046 0.815
172.1 203 51 0.691 f 0.058 0.769 176 31 0.796 tfr 0.056 0.816
Systematic Error 0.012 0.012
try since only events with zero total charge are used.
For the total event sample the differential cross sec- tion is distorted by hard ISR photons. For the high en- ergy sample the measured quantity, &,, directly gives the forward-backward asymmetry for the full solid angle, AB. To extract A& for the total event sample a correction, c, = A%/&, =I 0.78 hO.01, obtained from Monte Carlo is applied.
The background from e+e- ---) ?+r-(y) is small and, assuming lepton universality, has no influence on the me~urement because it has the same ~ymmet~
as the signal. The other background cont~butions are taken into account and the correction is in all cases smaller than 0.07. For the high energy sample the cor- rection includes the background from events with hard ISR photons as calculated from Monte Carlo. The sys- tematic error on the forward-backward asymmetry is estimated to be 0.05. Its main contributions are the un- certainties on background and acceptance corrections.
Table 3 summarises the numbers of forward and backward events, the background corrections, and the corrected asymmetries. In Fig. 4 the comparison of the corrected asymmetries to the Standard Model predic- tion is shown.
2.4. e+e- +7+7-(y) Event selection
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 elec- tromagnetic and hadron calorimeters with cracks in the central tracker and the muon spectrometer. Two tau jets of at least 3.5 GeV are required to lie within the polar angular range 1 cos 81 < 0.92.
The r~onst~ction of fi follows the procedure described in Section 2.3 using the polar angles of the two tau jets. Events with one-one, one-three and three-three prong topologies are accepted. To allow for reconstruction inefficiencies one tau jet may also have 2 tracks and one-four topology events are ac- cepted. One-one topology events are rejected if at least one of the tau jets lies in the region 0.72 <
/ cos 81 < 0.80, which is not completely covered by the electromagnetic calorimeter. Hadronic events are re- moved by requiring less than 13 calorimetric clusters.
Bhabha events are rejected by requiring the two high- est energy clusters in the electroma netic calorime- ter to have energies less than 0.4 Jg s’ and 0.25 fi.
Radiative Bhabha events and events from the process
e’e- + cte-e*e- are removed by rejecting events with two identified electrons. Electrons are identified as a cluster in the electromagnetic calorimeter with en- ergy larger than 3 GeV, with electromagnetic shower shape, and a matched track in the central tracker. AI1 events with more than one reconstructed track in the muon chambers are removed. The energy of a recon- structed muon has to be less than Cl.45 fi.
To reject back~ound from two-photon collisions only events with a v@ larger than 60 GeV are ac- cepted, In addition the quadratic sum of the energies of the tau jets, Ejeu = dq%, has to be larger than 0.15 a. In Fig. lc the ~~~~~~ distribution for events selected at 172 GeV is shown.
To reject leptonic final states from W-pair produc- tion the acoplanarity of the two tau jets must be less than 15”. The background from cosmic muons is re- duced by using scintillation counter time info~ation.
The total energy in the electromagnetic calorimeter has to exceed 4 GeV. Applying this selection the v’?
distribution as shown in Fig. 2c for events selected at 172 GeV is obtained. Good agreement between data and Monte Carlo expectation is found.
Crcrss section
Selection efficiencies and backgrounds are listed in Table 1. The total systematic error which is dominated by the uncertainty on the background from two-photon collision processes is estimated to be 7% for both the total and the high energy sample.
The number of selected events and the total cross sections for the different event samples are listed in Table 2. The cross section measurements are compared to the Standard Model prediction in Fig. 4.
For the dete~ination of the forw~d-backw~d asymmetry, events with zero charge sum and an acollinearity angle between the two tau jets of less than 90° are used. The procedure to obtain the forward- backward asymmet~ is described in Section 2.3. The co~es~onding correction, cx, is 0.92 f 0.01.
The charge confusion of the events is estimated from the data to be 2.1 f 0.2% for the total and 2.5 * 0.3% for the high energy sample, and is corrected for.
The asymmetries are corrected for backgrounds and the correction is in all cases smalier than 0.07. For the
high energy sample, the correction includes the effect of the contamination from events with hard TSR pho- tons. The systematic error on the forward-backward asymmetry is estimated to be 0.10. Its contributions are the uncert~nties from the back~ound and accep- tance corrections and from the charge confusion.
In Table 3 the number of forward and backward events and the corrected asymmetries are given. In Fig. 4 the comparison of the corrected asymmetries to the Standard Model predictions is shown.
2.5. e+e- -+ e+e- (y) Event setection
Electron candidates are recognised by an energy deposition in the electromagnetic calorimeter with at least five associated hits in the central tracking cham- ber within a three degree cone. In addition only dec- trons within the polar angular range 44’ < 0 < 136”
are accepted.
Bhabha events are selected by requiring the two highest energy electrons to have an energy larger than 0.6 Eh,, and 5 GeV, respectively. The acolline~ity of the two electrons must be smaller than 90’. In Fig. Id the energy of the highest energy electron candidate, E elecrron* normalised to the beam energy for events se- lected at 172 GeV is shown,
The & value is reconstructed from the invariant mass of the two identified electrons. Its distribution is shown in Fig. 2d for events selected at 172 GeV.
The largest part of the events is from the E-channel exchange for which the fi value is close to the center- of-mass energy.
The selection efficiencies within the fiducial vol- ume and the background contributions are listed in Table 1. The background is from tau-pair production.
The total systematic error of 3% assigned to the cross section m~urements is dominated by uncertainties in the event selection.
In Table 2 the number of selected events and the resulting cross sections for the two event samples at the different center-of-mass energies are summarised. The cross sections are compared to the Standard Model prediction in Fig. 5.
i3 Collabmkm /Physics Letters B 407 (19971361-376 313
O!“i”.‘,I”‘,i.‘,‘i.“.,’
75 100 125 150 175
& [GeV]
Fig. 5. Cross sections and forward-backward asymmetries of the process e+e-‘ - efe-(y) for the total (solid symbols) and the high energy sample (open symbols). The Standard Model predictions are shown as a solid line for the total sample and as a dashed line for the high energy sample. The two electrons are required to be inside 44’ < 0 < 136’. The measurements at center-of-mass energies below 161 GeV have been corrected to correspond to & > 0.14 for the total and & > 0.85fi for the high energy event samples. Measu~men~ at the 2 peak which are close in center-of-mass energies have been combined.
Fonvaml-bachward asymmetry
The electron direction in the event is detrained using a combined fit to both tracks as described in [ 21. The average charge confusion of the events is measured from the data to be (5.0 f 0.5) % and is corrected for.
The foxed-backw~d asymme~y is measured by counting events in the forward and backward hemi- spheres. In Table 3 the numbers of forward and back- ward events and the corrected asymmetries are sum- marised. The systematic error on the measured asym- metry is estimated to be 0.012 and is dominated by the uncertainty on the charge confusion. In Fig. 5 the comparison of the measured asymmetries to the Stan- dard Model prediction is shown.
The differential cross sections for the high energy samples at the different center-of-mass energies are
moo
ie+e- + e’e-(y)
,n
l Data 161 GeV0 . &. , -. .- . : I
l Data 172 GeV
$ *?
-0.5 0 0.5J
case
Fig. 6. Differential cross section of the high energy event sample, for the process e+e- -t e’e-(y) at center-of-mass energies of 161 GeV and 172 GeV. The Iines indicate the fit results from which the s-channel asymmetry is obtained.
shown in Fig. 6. A binned maximum-likelihood fit to the cos@ dist~butions is performed to determine the s-channel ~yrnrne~ for the high energy event sam- ple in the full solid angle. The dominant f-channel and s/t interference contributions are fixed to their Stan- dard Model expectations. The resulting asymmetries are 0.3:;; and 0X$:% for the data taken at center-of- mass energies of 161 GeV and 172 GeV, respectively.
These values agree with the Standard Model expecta- tion which is 0.6 at both center-of-mass energies,
3. Determination of the yZ interfermce
The data is interpreted in the framework of the S- matrix ansatz [ 41, which makes a minimum of the- oretical ~sumptions. The programs SMATASY [ 241 together with ZFITlXR and TOPAZO, are used for the calculation of the theoretical predictions and QED radiative corrections of cross sections and forward- backward asymmetries.
The lowest-order total cross section, c$$, and
374 L3 Collaboration /Physics Letters B 407 f19971361-376
forward-backward asymmetry, A& for e+e- -+
fT [4] are:
i&s) =
+Y 2 &Xfil[ s+
j$(s -ii+) +rf”s
-1
(s - fig)2 + @I-E for a = tot, fb
3 flk(s) A&) = --.
4 c&(s)
The S-matrix ansatz defines the 2 resonance using a Breit-Wigner denominator with s-independent width.
In other approaches usually a Breit-Wigner denomi- nator with s-dependent width is used which implies the following transfo~ation of the values of the 2 bo- son mass and width [ 41: rnz = fiz + 34.1 MeV and Tz = rz + 0.9 MeV. In the following the fit results are quoted after applying these transformations. The S-matrix parameters rr, jr and gr scale the Z exchange,
$7, interference and y exchange contributions. Here the y exchange contributions gf are fixed to their QED predictions.
The S-matrix parameters are determined in a ,y2 fit to the m~surements presented here and to our previ- ously published measurements [ 2,3]. The uncertain- ties on the LEP beam energy of 27 MeV and 30 MeV for the 161 GeV and 172 GeV data [ 251, respectively, have a negligible effect on the fit results.
The fitted S-matrix parameters for electrons, muons, taus and hadrons, and their correlations, are listed in Tables 4 and 5. The fits are performed with and without the assumption of lepton universality. The pa- rameters obtained for the individual ieptons are com- patible with each other and support this ~sumption.
A large correlation, -43%, is found between the mass of the Z boson and the hadronic yZ interference term, jF$. This correlation causes an increase in the error on mz with respect to fits where the hadronic
~2 interference term is fixed to its Standard Model prediction [ 26,2,27]. Under the assumption of lepton universality the fitted hadronic yZ interference term is:
j& = 0.39 f 0.29,
which agrees with the Standard Model prediction of 0.22 and improves the precision of our previous re- sult [ 3 ] significantly. The fitted value for rnz is:
mz=91193f9&3 MeV.
Table 4
Results of the fits in the S-matrix framework with and without the assumption of lepton universality.
Parameter Treatment of charged leptons Standard Model Non-universality Universality
91193f 10 91193f 10 -
2494f IO 2494 f 10 2497
2.956 f 0.029 2.955 i 0.028 2.967 0.1410 f 0.0018
0.1404 * 0.0017 0.1421 f 0.0019
0.1411 f 0.0015 0.1426 0.38 f 0.29 0.39 zt 0.29 0.22 -0.07 f 0.1 I
0.001 zt 0.064 0.040 i 0.076
_ 0.002 f 0.045 0.004
0.0016 & 0.0018
0.0030 f 0.0012 _ 0.0046 f 0.0017
_ 0.00307 f 0.00085 0.00267 0.65 f 0.19
0.736 f 0.089 0.68 f 0.12
0.706 f 0.066 0.799
100/127 103/135
Table 5
The correlation matrix for the 8 parameter S-matrix fit in Table 4.
mz 1.00 0.05 0.03 0.03
rZ 1.00 0.80 0.72
-0.43 -0.19 0.14 -0.04 -0.01 -0.01 0.04 0.04
0.02 -0.01 0.06 0.05 0.01 0.05 0.07 0.07 1.00 0.16 -0.06 0.04 1.00 0.01 0.23 I .oo 0.14 1.00
91.16 91.18 91.20 91.22 mz EGNI
Ftg. 7. Contours in the (ts~, jz) plane at 68% confidence level under the assumption of lemon u~~~e~~ity. The dashed lirre shows the Z data only; including the results from 130 GeV to 172 GeV the solid line is obtained. The Standard Model prediction for jgd is shown as the horizontal band.
The contribution of the uncertainty on the YZ interfer- ence has been separated from the total experimental error and is quoted as the second error. It is reduced by a factar of 2 with respect to our previous publica- tion [ 33. Fig. 7 shows the 68% confidence level con- tours in the (mz, jgd) plane for the data taken at the Z-pole and after including the 130-- I72 GeV measure- ments. The improvement arising from the high energy m~surements is dearly visible.
4. Summary and conclusion
Based on an integrated luminosity of 21.2 pb-’ cof- lected at center-of-mass energies between 161 GeV and 172 GeV, we select 2728 hadronic and 868 lepton-pair events. The data is used to measure cross sections and leptonic forward-backward asymmetries.
The measurements are performed for the total event sample and for the high energy sample. The results are in good agreement with the Standard Model. Our
measurements provide an improved determination of the yZ interference terms and the Z-boson mass within the S-matrix framework.
Acknowledgemeuts
We wish to congratulate the CERN accelerator di- visions for the successful upgrade of the LEP machine and to express our gratitude for the excellent perfor- mance of the machine, We a~know~~ge the effort of all engineers, technicians and support staff who have
~a~icipat~ in the construction and rn~nt~n~~~ of this experiment. Those of us who are not from mem- ber states thank CERN for its hospitality and help.
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