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PHYSICS LETTERS B
ELSEVIER
Physics Letters B 374 (1996) 331-340
Measurement of muon-pair production at
50 GeV < v'J < 86 GeV at LEP
L3 Collaboration
M. Acciarriab, A. Adamau, O. Adrianiq, M. Aguilar-Benitezaa, S. Ahlenk, B. Alpatai,
J. Alcaraz33, G. Alemanniw, J. Allabyr, A. Aloisioad, G. Alversonf, M.G. Alviggiad,
G. Ambrosi“1, H. Anderhubay, V.P. Andreevam, T. Angelescum, D. Antreasyan1,
A. Arefievac, T. Azemoonc, T. Aziz^, P. Bagnaiaai, L. Baksayas, R.C. Ballc, S. Banerjeej,
K. Baniczau, R. Barillère1’, L. Barone^, P. Bartaliniai, A. Baschirottoab, M. Basile1,
R. Battiston31, A. Bayw, F. Becattiniq, U. Beckerp, F. Behneray, J. Berdugoaa, P. Berges p,
B. Bertuccir, B.L. Betevay, M. Biasini1, A. Bilanday, G.M. Bileiai, J.J. Blaisingr,
S.C. Blyth^, G.J. Bobbinkb, R. Bocka, A. Böhma, B. Borgia^, A. Bouchamd,
D. Bourilkovay, M. Bourquin1, D. Boutignyd, E. Brambillap, J.G. Branson80,
V. Brigljevicay, I.C. Brock«, A. Buijsat, A. Bujak3U, J.D. Burgerp, W.J. Burger',
J. Busenitzas, A. Buytenhuijsaf, X.D. Cais, M. Campanelliay, M. Capellp, G. Cara Romeo1,
M. Caria31, G. Carlino0, A.M. Cartaceiq, J. Casaus83, G. Castellini“3, R. Castelloab,
F. Cavallariai, N. Cavallo30, C. Cecchi1, M. Cerrada33, F. Cesaronix, M. Chamizo33,
A. Chanba, Y.H. Changba, U.K. Chaturvedi\ M. Chemarinz, A. Chenba, C. Cheng,
G. Cheng, G.M. Chen«, H.F. Chen“, H.S. Chen^, M. Chenp, G. Chiefariad, C.Y. Chiene,
M.T. Choiar, L. Cifarelli“ , F. Cindolo1, C. Civininiq, I. Clarep, R. Clarep, H.O. Cohn3*5,
G. Coignetd, A.P. Colijnb, N. Colino33, V. Commichau3, S. Costantini3^, F. Cotorobai"1,
B. de la Cruzaa, T.S. D aip, R. D ’A le ssa n d r o R. de Asmundisad, H. De Boeckaf,
A. Degréd, K. Deitersav, P. Denesak, F. DeNotaristefania/', D. DiBitontoas, M. Diemoz^,
D. van Dierendonckb, F. Di Lodovicoay, C. Dionisia£, M. Dittmar3y, A. Dominguez30,
A. Doria3d, I. Dorned, M.T. Dova“’4, E. Dragoad, D. Duchesneaud, P. Duinkerb, I. Duranap,
S. Dutta-i, S. Easo31, Yu. Efremenkoag, H. El Mamouni2, A. EngleraJ, F.J. Epplingp,
F.C. Ernéb, J.P. Ernenweinz, P. Extermann1, M. Fabreav, R. Facciniaf, S. Falciano^,
A. Favaraq, J. Fayz, M. Felciniay, T. Fergusonaj, D. Fernandez33, F. Ferroniai,
H. Fesefeldt3, E. Fiandrini31, J.H. Field1, F. Filthaut^, P.H. Fisherp, G. Forconi13, L. Fredj\
K. Freudenreichay, Yu. Galaktionovac,p, S.N. Ganguli-*, S.S. Gauf, S. Gentileat, J. Gerald6,
N. Gheordanescum, S. Giaguai, S. Goldfarbw, J. Goldsteink, Z.F. Gong“, A. Gougase,
G. Grattaah. M.W. Gruenewaldh. V.K. Guotaak. A. Gurtuj, LJ. Gutay3“, K. Hangarter3,
0370-2693/96/$ 12.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved
PII S 0 3 7 0 - 2 6 9 3 ( 9 6 ) 0 0 2 5 7 - 2
332
L3 Collaboration /Physics Letters B 374 (1996) 33Î -340
B. H artm an n “, A. H a sa n ae, J.T. H e g, T. H ebbekerh, A. H e rv é r, W.C. van H o e k af,
H. H o fe ray, H. H oorani', S.R. H o u b\ G. H u s, M.M. Ily a s 5, V. In nocente1, H. J a n s s e n d,
B.N. J in g, L.W. Jo n e sc, R de J o n g p, I. Josa-M utuberriaaa, A. K asserw, R.A. K h a n \
Yu. K am yshkovag, R K apinosaw, J.S. K apustinskyy, Y. K aryotakisd, M. K a u r s,s,
M .N. K ienzle-Focacci1, D. K im e, J.K. K im ar, S.C. K im ar, Y.G. K im ar, W.W. K in n iso n y,
A. K irk b y ah, D. K irk b y ah, J. K irk b y r, W. K ittelaf, A. Klim entov p-ac, A.C. K ö n ig af,
A. K ö n g e te r\ I. K orolkoac, V. K outsenkop,ac, A. K oulbardisam, R.W. K raem erai,
T. K ram erp, W. Ki'enza, H. K uijten3*, A. K u ninp,ac, P. Ladrón de G uevaraaa, G. L a n d iq,
C. L ap o in tp, K. L assila-Periniay, M. L eb eau r, A. L eb ed ev p, P. L e b ru n 7, P. L e c o m te ay,
P. L e c o q r, P. Le C oultreay, J.S. L e e ar, K.Y. L e e ar, C. L eg g ettc, J.M. Le G o ff1, R. L e is te aw,
M. L en tiq, E. L eonardiai, P. L evtchenkoam, C. L i u, E. L ie b aw, W.T. L in ba, F.L. Linde b-r,
B. L indem anna, L. L ista ad, Z.A. L iu g, W. L o h m an n aw, E. L o n g o a£, W. L u ah, Y.S. L u g,
K. L übelsm eyer“, C. L u c iaí, D. L u ck ey p, L. L udoviciaí, L. L u m in aria/, W. L u sterm an n av,
W.G. M a u, A. M acch io lo q, M. M aityj, G. Majumder-i, L. M a lg e ri“*, A. M alin in ac,
C. M a ñ a “3, S. Mangla-i, P. M archesini“y, A. M arin k, J.P. M a rtin z, R M a rz a n o “/;,
G.G.G. M assaro b, K. M azum darJ, D. M cN allyr, S. M e le ad, L. M e ro la ad, M. M esch in iq,
W.J. M etzgeraf, M. von der M e y a, Y. M i w, A. M ih u lm, A.J.W. van M ilaf, G. M irab ellia/>,
J. M n ic h r, M. M ö ller“, B. M onteleoniq, R. M o o re c, S. M o rg an ti^ , R. M o u n tah,
S. M ü lle r“, F. Muheim*, E. N agy", S. N a h n p, M. N ap o litan o ad, F. N essi-Tedaldiay,
H. N ew m an ah, A. N ip p e “, H. N o w a k aw, G. O rg an tin i^, R. O sto n en v, D. P an d o u las3,
S. Paolettiai, P. P ao lu cciad, H.K. P a rk ^ , G. P ascale1^, G. Passalevaq, S. P atricelliad,
T. P a u lai, M. P au lu zziai, C. P au s“, F. P a u ssay, D. P e a c h r, Y J. P e i“, S. P en so ttiab,
D. Perret-G allixd, S. P e tra k h, A. P evsnere, D. P icco lo ad, M. P ieriq, J.C. Pinto a\
P.A. P iro u é ak, E. P isto lesiq, V. P lyask inac, M. P o h lay, V. P o jid aev ac,q, H. P o ste m a p,
N. P ro d u it1, R. R aghavan', G. R ahal-C allotay, P.G. R an co ita“b, M. R attaggiab, G. R a v e n “0,
P. R a z isae, K. R e ad ag, M. R ed aelliab, D. R e n ay, M. R escig n o “£, S. Reucroft^, A. R ic k e ra,
S. R iem an n aw, B.C. R iem ersau, K. R ile s0, O. R in d 0, S. R o “r, A. R o b o h m ay, J. R o d in p,
W
F J . R odriguezaa, B.P. R o e c, S. Röhner “, L. R o m ero aa, S. R osier-L eesd, Ph. Rosselet
W. van R o ssu m “1, S. R o th “, J.A. R u b io r, H. R ykaczew skiay, J. S alicio1', E. S an ch ezaa,
A. S antocchia“1, M.E. S arakinosv, S. Sarkarj , M. S assow sky“, G. Sauvaged, C. S c h ä fe r“,
V. Schegelsky“m, S. Schm idt-K aerst“, D. S chm itz“, P. S ch m itz“, M. S chneegansd,
B. S choeneichaw, N. S ch o lzay, H. S chopperaz, D J . S ch otanu s“f, R. S chulte“, K. S c h u ltz e “,
J. S chw enke3, G. S chw ering“, C. S ciaccaad, D. Sciarrino', J.C. S e n sba, L. S erv o liai,
S. Shevchenkoah, N. Shivarovaq, V. S houtkoac, J. S h u k lay, E. S hum ilov“0, T. S ied en b u rg 3,
D. S o n “r, A. S opczakaw, V. S oulim ov“d, B. S m ith p, P. Spillantiniq, M. S te u e rp,
D.P. S tick land“k, F. S ticozzip, H. S to n e “k, B. S toyanov“q, A. Straessner“, K. S tra u c h 0,
K. Sudhakai'j, G. S u ltan o v s, L.Z. S u n “, G.F. S usinn o1, H. S u teray, J.D. S w a in s,
X.W. T an g g, L. T auscherf, L. Taylor^, Samuel C.C. T in g p, S.M. T in g p, O. T o k erai,
F. T onischaw, M. T onutti“, S.C. Tonw ar■*, J. T ó th n, A. T saregorodtsev“m, C. T u lly ak,
H. T uchschereras, K.L. T u n g g, J. U lbrichtay, U. U w e rr, E. V alentea<?, R.T. Van de W a lle af,
L3 Collaboration /Physics Letters B 374 (1996) 331-340
333
I. V etlitskyac, G. V ierte!“*, M. Vivargentd, R. V òlkertaw, H. V o g e P , H. V ogtaw,
I. V orobievac, A.A. V orobyov3™, An.A. V orobyov301, A. Vorvolakosae, M. W ad h w af,
W. W allraff3, J.C. W a n g p, X.L. W a a g u, Y.F. WangP, Z.M. W an g u, A. W eb er3,
F. W ittg en stein r, S.X. W u s, S. W ynhoff3, J. X u k, Z.Z. X u u, B.Z. Y an g “, C.G. Yang®,
X.Y. Y ao g, J.B. Y e u, S.C. Y eh ba, J.M. You aJ, C. Z accardelli3h, An. Z a lite am, P. Z e m p ay,
J.Y. Z e n g g, Y. Z e n g a, Z. Zhang«, Z.P. Z h a n g u, B. Z h o u \ G.J. Zhou®, Y. Z h o u c,
G.Y. Zhu s, R.Y. Z h u ah, A. Zichichi iJ-s
a I. Physikalisches ¡nsiitut, RWTH, D-52056 Aachen, F R G 1
III Physikalisches Instituí, RWTH, D-52056 Aachen, FRG 1
h National Institute fo r High Energy Physics. NIKHEF, and University o f Amsterdam, N L -I009 DD Amsterdam, The Netherlands
c University o f Michigan, Ann Arbor, M l 48109, USA
J Uiboratoire d ’Annecy-le-Vieux de Physique des Partkules, LAPP, IN2P3-CNRS, BP I IO, F-7494I Annecy-le-Vieux CEDEX, France
c Johns Hopkins University, Baltimore, MD 21218, USA
1 Institute o f Physics, University o f Basel, CH-4056 Basel, Switzerland
£ Institute o f High Energy Physics, IHEP, 100039 Beijing, China
h Humboldt University, D-10099 Berlin, FRG 1
1 INFN-Sezione di Bologna, 1-40126 Bologna, Italy
1 Tata Institute o f Fundamental Research, Bombay 400 005, India
k Boston University; Boston, MA 02215, USA
t Northeastern University, Boston, MA 02115, USA
m Institute o f Atomic Physics and University o f Bucharest, R-76900 Bucharest, Romania
n Central Research Institute fo r Physics o f the Hungarian Academy o f Sciences, H-1525 Budapest 114, Hungary2
0
Harvard University, Cambridge, MA 02139, USA
P Massachusetts Institute o f Technology, Cambridge, MA 02139, USA
4
INFN Sezione di Firenze and University o f Florence, 1-50125 Florence, Italy
r European Laboratory fo r Particle Physics, CERN, CH-1211 Geneva 23, Switzerland
s World Laboratory, FBUA Project, CH-1211 Geneva 23, Switzerland
1 University o f Geneva, CH-1211 Geneva 4, Switzerland
u Chinese University o f Science and Technology, USTC, Hefei, Anhui 230 029, China
v SE FT, Research Institute fo r High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland
■w University o f Lausanne, CH-1015 Lausanne, Switzerland
x INFN-Sezione di Lecce and Università Degli Studi di Lecce, 1-73100 Lecce, Italy
y Los Alamos National Laboratory, Los Alamos, NM 87544, USA
'• Instituí de Physique Nucléaire de Lyon, IN2P3-CNRS, Università Claude Bernard, F-69622 Villeurbanne, France
aa Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040 Madrid, Spain 1
ab INFN-Sezione di Milano, 1-20133 Milan, Italy
ac Institute o f Theoretical and Experimental Physics, ITEP, Moscow, Russia
ad INFN-Sezione di Napoli and University o f Naples, 1-80125 Naples, Italy
ae Department o f Natural Sciences, University o f Cyprus, Nicosia, Cyprus
al University o f Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands
Oak Ridge National Laboratoty, Oak Ridge, TN 37831, USA
ah California Institute o f Technology, Pasadena, CA 91125, USA
ai INFN-Sezione di Perugia and Università Degli Studi di Perugia, 1-06100 Perugia, Italy
ai Carnegie Mellon University; Pittsburgh, PA 15213, USA
ak Princeton University, Princeton, NJ 08544, USA
ai INFN-Sezione di Roma and University o f Rome, “La Sapienza ”, 1-00185 Rome, Italy
um Nuclear Physics Institute, St. Petersburg, Russia
an University and INFN, Salerno, 1-84100 Salerno, Italy
a0 University o f California, San Diego, CA 92093, USA
ap Dept, de Fisica de Partículas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain
at| Bulgarian Academy o f Sciences, Central Laboratory o f Mechatronics and Instrumentation, BU -1U 3 Sofia, Bulgaria
ur Center fo r High Energy Physics, Korea Advanced Inst, o f Sciences and Technology, 305-701 Taejon, South Korea
as University o f Alabama, Tuscaloosa, AL 35486, USA
*
334
L3 Collaboration / Physics Letters B 374 (1996) 331-340
al Utrecht University and NIKHEF, NL-3584 CB Utrecht, The Netherlands
au Purdue University, West Lafayette, IN 47907, USA
av Paul Seltener Institut, PSI, CH-5232 Villigen, Switzerland
aw DESY-Instifut fü r Hochenergiephysik, D-15738 Zeuthen, FRG
uy Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland
u/ University o f Hamburg, D -22761 Hamburg, FRG
ba High Energy Physics Group, Taiwan, ROC
Received 16 February 1996
Editor: K. Winter
Abstract
Using the data recorded with the L3 detector at LEP, we study the process e+ e ~ —►
for events with hard
initial-state photon radiation. The effective centre-of-mass energies o f the muons range from 50 GeV to 86 GeV. The data
sample corresponds to an integrated luminosity o f 103.5 pb “ 1 and yields 293 muon-pair events with a hard photon along
the beam direction. The events are used to determine the cross sections and the forward-backward charge asymmetries at
centre-of-mass energies below the Z resonance.
1, Introduction
At LEP, the cross sections and forward-backward
charge asymmetries for the process e+e~ —>
/x+/a"“(y) are measured at centre-of-mass energies,
\ f s s between 88 GeV and 136 GeV [1,2]. Data from
experiments at PEP, PETRA and TRISTAN cover
the energy range from 12 GeV to 60 GeV [3]. The
energy region between 60 GeV and 88 GeV is not
explored by direct measurements, but can be accessed
at LEP using events with hard initial-state photon ra
diation in which the fermion pair is produced at lower
centre-of-mass energies [4].
The following analysis uses 93000 muon-pair
events collected with the L3 detector in the years
1991 to 1994. The data correspond to an integrated
luminosity of 103,5 pb“ 1. Events with high missing
momentum along the beam direction are interpreted
as events with hard initial-state photon radiation.
They are used to measure cross sections and forward1 Supported by the German Bundesministerium für Bildung, Wis
senschaft, Forschung und Technologie.
*■Supported by Lhe Hungarian OTKA Fund under contract number
TI 4459.
* Supported also by the Comisión Interministerial de Ciencia y
Technologia.
4 Also supported by CONICET and Universidad Nacional de La
Plata, CC 67, 1900 La Plata, Argentina.
5 Also supported by Panjab University, Chandigarh-160014, India.
backward asymmetries at effective centre-of-mass
energies between 50 GeV and 86 GeV.
2. Photon radiation in fermion-pair production
Radiative corrections to the fermion-pair production
process e+e- —» f f ( y ) at the Z resonance can be
separated into electroweak and QED bremsstrahlung
contributions. The electroweak corrections are the sum
of propagator, vertex and box corrections, including
the effect of the energy dependence of the fine struc
ture constant a, QED bremsstrahlung corrections are
present in the initial state (ISR) and final state (F S R ).
At the Z pole, the interference between initial and
final-state radiation is small [5] and allows a separate
treatment of both corrections.
In interactions with initial-state bremsstrahlung, a
fraction of the beam energy is taken by the photon
and the fermion pair is produced at a lower effective
centre-of-mass energy, y/s*. The visible cross section
is described by a convolution of the cross section in
cluding electroweak corrections, <xew, with a radiator
function, G ( z ,i) ,
l
é
cr(s) = ƒ
4mj. / s
dz G (z ,s ) crew( z s ) ( \ + SrsR) ,
(1)
L3 Collaboration / Physics Letters B 374 (1996) 331-340
where z = sf/ s [ 6 ]. The correction <5,,su is small, e.g.
0.17% for fJL+iJL~ [ 6 ], and accounts for the effect of
final-state radiation. Measuring the differential cross
section of initial-state radiation thus allows to extract
the cross section at lower centre-of-mass energies,
dcr
dz
( 2)
G( z , s ) crewizs) ,
since Lhe radiator function G( z , s ) is calculable in
QED. A first-order calculation [7] fo rG (z , s) gives
G( z, x) =
a
77*
In
s
m
1
(3)
In the analysis presented here the KORALZ Monte
Carlo generator [ 8 ] is used to take into account
higher-order bremsstrahlung corrections. The gener
ator treats the radiation of hard photons in the initial
and final state to 0 ( a 2) . The radiation of soft photons
is considered in all orders by exponentiation.
Photons are emitted predominantly collinear to the
direction of the radiating particles. Initial-state pho
tons go mainly along the direction of the e+e~ beams,
while final-state photons cover the full solid angle. A
separation of the different types of radiation is there
fore possible. From the energy, Ey, of the initial-state
photon one finds for the effective centre-of-mass en
ergy squared, s':
(4)
For three-particle final states the particle momenta
follow from the measured directions using energy and
momentum conservation. Assuming that the unde
tected initial-state photon is radiated in the direction
of the beams, its energy is given by the polar angles,
01 , 02 » of the outgoing fermions:
sin ( 0 ] + 0 2 ) |
Ey — y/s
sin 0 i + sin 02 + I sin ( 0 j + 02 )
335
In this analysis events of the reaction e+e~ —»
(y) are used. The process allows a clear separa
tion between photons and outgoing leptons and hence
gives a good rejection of the final-state bremsstrahlung
events. Moreover, the polar angles of the two leptons
can be measured with good precision, which is neces
sary for the determination of s'.
3. L3 detector
The L3 detector is described in detail in Ref. [9].
The components of the detector are the central tracking
chamber, the electromagnetic calorimeter composed
of bismuth germanium oxide (BGO) crystals with a
barrel region (42° < 0 < 138°) and two endcaps
(11 ° < 0 < 37° and 143° < 0 < 169°), a layer
of scintillation counters used for time measurements,
a fine grained hadron calorimeter with uranium ab
sorbers and proportional wire chamber readout, and a
muon spectrometer consisting of three layers of pre
cise drift chambers for the measurement of the trans
verse muon momentum. The inner and outer muon
chamber layers are surrounded with additional layers
of drift chambers allowing the measurement of the
muon direction in the rz plane and thus a measure
ment of the polar angle, 0. All sub-detectors are lo
cated in a 12 m diameter magnet which provides a
uniform field of 0.5 T along the beam direction.
For muons of 45 GeV the three chamber layers al
low a momentum measurement with a resolution of
2.5%. The polar angle measurement has a precision
of 4.5 mrad which is dominated by multiple scattering
of the muon in the calorimeters. Due to the 0 resolu
tion the error on y/s' according to Eqs. (4) and (5) is
smaller than 300 MeV for v s' values between 50 GeV
and 86 GeV.
(5)
Eq. (5) cannot be applied to events with more than
one hard initial-state photon or in the presence of addi
tional final-state photons which are not collinear with
the outgoing fermions. The effect of multiple initialstate photons on the measurement of the cross sec
tions and asymmetries, as well as the final-state pho
ton contamination can be estimated from Monte Carlo
simulation.
4. Event selection
The selection of muon-pair events requires two
identified muons in the detector. At least one muon
must have a reconstructed track in the muon cham
bers. For the second muon the signature of a minimum
ionising particle in the inner detector components [ 1 ]
is accepted. One muon is restricted to the angular ac
ceptance of the muon chambers | cos 0 J < 0 , 8 , while
336
L3 Collaboration /Physics Letters B 374 (1996) 331-340
0.5
Monte Carlo
0.4 in
o
•«
o
Jß
0.3
B
T
I
i
> 4 * *
♦
»«
* ♦♦
♦
«»
CO
A
4 «
•»
c
CD
Lif 0 .2
>
»■
•
»««
•w «
* f V1
*♦
i *
» *J t
*»« ♦
« V«
(D
0.1
♦
»
««
I 4 *« f i
i • «f «I
I » m • ûa I
Ü«
Si «I ■
««
■
■
a■
B
B
B
a»
• *
o
0
exp
Pu / P
Fig. J. The measured muon momentum,
normalised to the
momentum, /?^xp, calculated from the polar angles of the muon
pair. Data and signal and background Monte Carlo are shown. All
other selection cuts are applied.
for the second a polar angle up to | cos#M| < 0.9 is
allowed. Background from cosmic rays is removed
by asking a hit in the scintillation counters within
a ±3 ns time window around the beam crossing. In
addition, at least one muon must have a track in the
inner tracking chamber with a transverse distance
of less than 5 mm to the interaction point. To reject
hadronic Z decays the calorimetric cluster multiplicity
must be less than 15.
For the accepted events we apply Eq. (5) to calcu
late the energy, Ey, of the initial-state photon. Events
with a reduced centre-of-mass energy of the muon sys
tem, y/P < 0.95 y/s t are used for further analysis.
The muon momenta can also be calculated from the
polar angles of the muons similarly to the photon en
ergy. A cut on the ratio of the highest measured muon
momentum,
and the momentum, /?^xp, expected
from the polar angles is used to reduce backgrounds
from the process e+e~ —►r +r " and from the twophoton process e+e
e+e ¡jL+fjL . The distribution
of the ratio, p ^ / p ^ is shown in Fig. 1 for data, signal
and background Monte Carlo. The cut of p ^ /p ^ >
0.8 removes most of the background.
A Monte Carlo study of the photon reconstruction
according to Eq. (5) is shown in Fig. 2. The recon
structed photon energy, Ey, is compared with the gen
erated photon energy, Eyen. Both energies are nor
malised to y/s. Events where a photon is emitted along
0.1
0.2
0.3
0.4
0.5
E®en / Vs
Fig, 2. Monte Carlo study of the reconstruction of the photon
energy. The reconstructed photon energy, Ey, using Eq. (5 ), is
compared with the generated photon energy, E f n. For the events
in the diagonal band A, a photon going along the e+ e - beams is
present. The events of band B, where no hard photon is generated,
are regarded as background. The size of the squares is proportional
to the logarithm of the number of events.
the beam axis appear in the band A. For these events
the photon energy determined from the muon angles
reproduces well the generated photon energy, Eyen.
For the events of band B a large photon energy is re
constructed, although no photon parallel to the beams
is present. A large fraction of these events have a
hard photon observed in the detector, mainly origi
nating from final-state radiation. In addition, there are
events where a mis-reconstruction of a muon polarangle leads to a wrong value of Ey, In the following,
the events of region B are considered as background to
our signal. They are suppressed by the following cuts:
- The application of Eq. (5) is only correct for initialstate photons parallel to the beam axis. Final-state
photons can only be accepted if they are collinear
with the outgoing muons. Both conditions result
in a muon pair which is back-to-back in the rcj)
plane. The muons are therefore required to have an
acoplanarity angle, £ = \4>\ — f a — 180°|, of less
than 2 ° . The distribution of the muon acoplanarity is
shown in Fig. 3 for data and Monte Carlo simulation
of signal and background.
- Events with a detected photon are only accepted if
the transverse energy component of the photon with
respect to the direction of the nearest muon is less
than 1.5 GeV.
L3 Collaboration / Physics Letters B 374 (1996) 331-340
o
337
Table 2
Expected background from tau-pair production
from fourfermion production (r je e ^ ), from muon-pair production without
hard photon radiation along the beam direction
and from
events with final-state photon radiation (7/fsr) as a fraction of the
selected events.
10
d
y/7
co
c 10
(1)
>
CD
1
0
2
4
6
8
Fig. 3. Acopianarity angle,
of the muon pair for data and signal
and background Monte Carlo. All other selection cuts are applied.
Table I
Acceptance, e, for the selection of /¿+ /i~yisn events. The values
are determined from the Monte Carlo simulation and include the
detector efficiency.
e \%\
50-60
60-70
70-75
75-80
80-83
83-86
25.2 ± 1.4
3 I . 5 ± 1.3
38.8 ± 1.4
38.7 ± 1.1
41.7 ± 0 . 9
41.9 ± 0 . 5
Vcc/ifi [%1
Vrsu [%]
6.8 ± 0.6
50-60
60-70
70-75
75-80
80-83
83-86
2.9
1.5
0.9
0.3
± 0 .3
± 0 .3
± 0 .1
± 0 .1
0.2 ± 0.1
1.7 ± 0 . 3
5.5 ± 0.5
6.4 ± 0,6
8.6 ± 0 . 5
7.9 ± 0,4
5.9 ± 0 . 2
y/7
Vtt l%]
TJ/ifl 1% 1
1.6 ± 0 . 7
0.9 ± 0.2
10
£ [degrees]
V 7 [ GeV 1
[GeV]
- To ensure the rejection of final-state photons in the
acceptance gaps of the electromagnetic calorime
ter, events with an energy cluster in the hadron
calorimeter of more than 2 GeV and more than 5°
away from the nearest muon are rejected.
- The measurement of the muon polar angle using
the muon chambers and the polar angle determined
from the calorimeters must agree within 2 °.
The acceptance, e, for events from the process
e+e “
is listed in Table 1 for different
centre-of-mass energies y/F of the muon system. The
quoted values are determined from the Monte Carlo
simulation and include the detector efficiency. A large
yfs* dependence of the acceptance is observed. For
lower y/F values the muons are produced at smaller
angles to the beam direction and thus fall outside
the detector acceptance. The errors on the acceptance
[GeV]
50-86
reflect the limited Monte Carlo event statistics. A d
ditional systematic errors from the selection cuts and
from uncertainties of the detector efficiency are small
compared to the statistical error.
The background to the jui+fi~ y lSR signal comes
from tau-pair production, e+e _ —> r +r~ , from the
process, e+e" —»■ e+e ~ /u +yL6~, from muon pairs
without hard photon radiation, and from events with
a final-state photon. The corresponding background
fractions rjTT, 77e w and
respectively are esti
mated from the Monte Carlo simulation using the
KORALZ and DIAG36 [10] generators. To deter
mine the background fraction, ?7rsR, of events where
the reconstructed photon is radiated from the final
state, the four-vector information of a large KORALZ
Monte Carlo event sample is used.
Table 2 summarises the four background contribu
tions as fractions of the accepted signal events. The
backgrounds from two-photon processes and from
events with final-state photons show a significant
y/F dependence and are given for the different
intervals separately. Within the quoted errors the the
values of rjTT and
are independent of y/F.
5. Cross sections
The data sample used for the cross section measure
ment was recorded in the years 1991 to 1994 at the
three centre-of-mass energies, 89.5 GeV, 91.2 GeV
338
L3 Collaboration / Physics Letters B 374 (1996) 331-340
IT)
10 U
CM
O
o
<z>
c
CD
>
CD
• Data 91-94
□ Monte Carlo
<■
Q
10
10
Table 3
Number of selected e + e“ —►¿£+ ju” yLSR events, N ^ y , and the
background corrected number, N ^ y { I — r}), The correction 77 is
the sum of the backgrounds from tau-pair production, from twophoton processes, from muon pairs without photon radiation and
from events with final-state photons. Also given are the expected
number of initial-state photon events,
. The cross section, <r , is
calculated according Equation ( 6 ). The systematic error accounts
for the Monte Carlo statistics, the uncertainty on the background
subtraction and the uncertainty of the efficiency determination. The
energy { y /7 ) is the mean energy of the corresponding energy bin.
i
-
10 i
1
0.2
0.4
0.8
0.6
a/s’ /
1
Vs
Fig. 4. The y / V spectrum of all inuon-pair events for data and
Monte Carlo simulation. All selection cuts are applied. The dou
ble arrow shows the y /V range used for the cross-section and
asymmetry measurements (50 GeV < y /F < 86 GeV). In the
region y / s '/ y / s < 0.55 the background contamination from the
two-photon process, e+e~ —* e+ e ” /u.+ /A~, becomes large.
and 93.0 GeV and corresponds to a total integrated
luminosity of 103.5 pb~1.
The
s' distribution of all selected muon-pair
events is shown in Fig. 4 in comparison with the
Monte Carlo prediction. Good agreement is observed.
Out of this data sample 293 events have a recon
structed y/s* value between 50 GeV and 86 GeV and
are used to determine the cross section for six en
ergy bins. The number of selected e+e~ —> At+ya" 7 iSU
events, N ^ y , are given in Table 3 for the different bins
of effective centre-of-mass energy, yf sf. The observed
events are corrected for the expected total background,
V (v = Vtt + Vczjiii + V w + *7fsr)» according to Ta
ble 2 , and the corrected number of events are listed in
a second column.
The number of expected initial-state bremsstrahlung
events, A ^c , for the different y fp bins is determined
from the Monte Carlo simulation. The luminosity con
tribution of the three different LEP centre-of-mass en
ergies and the detector efficiency are taken into ac
count. The predictions are given in Table 3.
The cross section, cr, is determined by comparing
the background corrected number of /x+/A~y1SR can
didates in the data with the Monte Carlo prediction,
/V^{c . The ratio of the two is multiplied by the theo
retical cross section, crew, determined from a Standard
y /7
IGeVl
(V 7 )
[GeV]
50-60
60-70
70-75
75-80
80-83
83-86
55.4
65.8
73.3
77.9
81.7
84.8
mMC
( 1 —77) /vISIi
Nppy
10
17
30
37
56
143
8.9
15.3
27.2
32.6
50.6
130.7
< r± (s ta t.)± (s y s t.)
[pb]
11.8 24.9 ± 7.9 ± 1.5
19.2
18.9
32.9
47.3
20.3
37.1
30.5
47.8
121.6 87.5
± 4 .8
± 6.8
± 5.0
± 6.3
± 7.3
± 0 .9
± 1.6
± 1.0
± ( .3
± 1.7
Model calculation [11]:
cr((s/s')) = crew({v/i7)) •
A/m c
(6)
ISR
The value (Vs7) is the mean y/F value of the data
in the corresponding energy bin. The resulting cross
sections for the six different energy points are listed
in Table 3. The quoted systematic errors account for
the Monte Carlo statistics, uncertainties of the back
ground subtraction and the error on the acceptance
determination.
The results are shown in Fig. 5 compared with
the Standard Model prediction for crew« We also in
clude our results from the cross section measurements
around and above the Z-pole energy [ 1]. They are cor
rected for the effect of initial-state photon radiation.
Our measurement of the cross sections at lower y/s/
values is in good agreement with the theoretical pre
diction. For comparison the muon-pair cross sections
measured at PEP, PETRA and TRISTAN [3] are also
shown. They are corrected to include the effect of the
running of the fine structure constant, a.
6. Forward-backward asymmetries
In the centre-of-mass system of the muons, the an
gular distribution of the muon-pair production can be
L3 Collaboration / Physics Letters B 374 (1996) 331-340
Table 4
Number of forward (/Vf) and backward ( N h) produced muon
pairs, the fitted forward-back ward asymmetry, AjjJ, and the re
sulting background corrected asymmetry value, A^. The quoted
systematic error accounts for the uncertainty of the background
correction. The energy {Vs*) is the mean energy of the corre
sponding energy bin.
1
-Q
I
+=*• 10
10
10
50
100
150
Vs [GeV]
Fig. 5. Measured cross sections of muon-pair production compared
with the Standard Model prediction. The theory (solid line) does
not include the effect of initial-state photon radiation. The results of
this analysis, e+ e “ —►¡jl+
are shown as solid squares. The
L3 results from the measurements at energies around and above
the Z pole have been corrected for the effect of initial-state photon
radiation and are shown as dots. For comparison the measurements
at lower energies from PEP, PETRA and TRISTAN are included.
parametrised using the forward-backward asymmetry,
4 n>:
da
- a [ | ( l 4- cos2 0 *) 4* Afb cos 0*] .
d cos 0
(7)
The angle 0* is the production angle of the
in
the centre-of-mass system of the muon pair. In the
presence of an initial-state photon, the event is boosted
along the beam direction and 0 * can be calculated
from the muon polar angles, 0
and 0 ^+, measured
in the laboratory;
cos 0 * =
1
sin *2 ( 0^1
V )
sin ^ ( 0 ^h + 0 ^ - )
( 8)
The forward-backward asymmetry is determined us
ing an unbinned maximum-likelihood fit, where the
likelihood, L, is defined as the product of the single
event probabilities:
L—
339
(l -{- cos2 0*) + Afb cos 0*] .
(9)
The result of the fit is shown in Table 4 for the differ
ent y/7* bins. The asymmetry measurement does not
require an accurate knowledge of the luminosity deter-
Vs*
[GeVJ
(V 7 )
50-60
60-70
70-75
75-80
80-83
83-86
55.0
Nr /vh
AjjJ ±(stat.)
± ( s ta t.) ± ( s y s t.)
[GeV]
66.0
73.3
78.0
81.8
84.8
5
7
6
10
16
51
—0.14
- 0 .2 6
24 - 0 .7 5
29 - 0 .5 2
46 - 0 .5 8
106 -0 .4 1
8
12
± 0.31
± 0.21
± 0 .1 7
± 0 .1 4
± 0 .1 0
± 0.07
—0.16
- 0 .3 0
- 0 .8 4
-0 .6 0
- 0 .6 5
- 0 .4 4
± 0.36
± 0.25
± 0 .1 9
± 0 .1 7
± 0 .1 1
± 0.08
± 0.01
± 0.01
± 0.01
± 0 .0 1
± 0 .0 1
± 0.01
mination or the trigger efficiency. Therefore, the lumi
nosity used for the asymmetry measurement is slightly
higher and leads to more events (320 events) than for
the cross section measurement. The fitted asymme
try, AfjJ, has to be corrected for the background con
tamination according to Table 2. A correction factor
is calculated by assuming a zero asymmetry for the
four-fermion production, the Standard Model asym
metry prediction for the tau-pair production, and for
the background from muon-pair events without hard
photon radiation. The influence of the final-state pho
ton contamination is computed from a high-statistics
Monte Carlo event sample by comparing the asymme
try we calculate for the initial-state photon events with
the asymmetry value we determine after the full anal
ysis. The correction accounts for the angular distribu
tion of the FSR background, mainly located in the very
forward and backward directions, and for the effect of
multiple photons. Applying the correction to the fitted asymmetry values we find the forward-backward
asymmetry, Afb, as given in Table 4. The systematic
error reflects the uncertainty of the correction factor.
The results are shown in Fig. 6 compared with the
Standard Model prediction of the electroweak cor
rected asymmetry, A ^ \ Also shown are our asymme
try measurements around and above the Z-pole energy
[ 1]. They are corrected for the effect of initial-state
photon radiation. The measurements of the asymme
try at lower centre-of-mass energies are in good agree
ment with the theoretical prediction. For comparison,
the muon-pair asymmetries measured at PEP, PETRA
and TRISTAN [3] are also shown. They are corrected
L3 Collaboration/Physics Letters B 374 (1996) 331-340
340
References
1
0.5 -
dL
t
0
H“
o
-
n
<c-0.5 -
-1
Vs [GeV]
Fig, 6 . Measured forward-backward asymmetries of muon-pair
production compared with Standard Model prediction. The theory
(solid line) does not include the effect of initial-state photon
radiation. The results of this analysis, e+e ” —) P +P yisR, are
shown as solid squares. The L3 results from the measurements
at energies around and above the Z pole have been corrected for
the effect of initial-state photon radiation and are shown as dots.
For comparison the measurements at lower energies from PEP,
PETRA and TRISTAN are included.
to include the effect of the running of the fine structure
constant, a.
7. Conclusion
The effect of initial-state radiation in the process
e+e
jul* fji~ (y) is studied using 293 events with
a hard initial-state photon and an effective centre-ofmass energy between 50 GeV and 86 GeV. The events
are used to measure the cross section and the forwardbackward asymmetry of the muon-pair production at
energies between the TRISTAN and the Z-pole en
ergy. The measurements show good agreement with
the Standard Model prediction.
Acknowledgements
We wish to express our gratitude to the CERN ac
celerator divisions for the excellent performance of the
LEP machine. We acknowledge the effort of all en
gineers and technicians who have participated in the
construction and maintenance of this experiment.
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