arXiv:hep-ex/0504015v1 8 Apr 2005
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
February 23, 2005
Z-boson production with
two unobserved, back-to-back, hard photons at LEP
The double-radiative process e+e−→ Zγγ → q¯ qγγ where the two hard photons
escape detection at low polar angles into opposite directions, is studied in 0.62fb−1
of data collected with the L3 detector at LEP at centre-of-mass energies between
188.6 GeV and 209.2 GeV. The cross sections are measured and found to be con-
sistent with the Standard Model expectations.
Submitted to Phys. Lett. B
One of the most copious sources of events in e+e−collisions at LEP above the Z resonance
is the process e+e−→ q¯ q, with a cross section of about 100 pb. The effective centre-of-mass
the centre-of-mass energy of the LEP machine,√s, owing to the emission of one or more hard
initial-state-radiation (ISR) photons by the incoming electrons or positrons. These photons are
most likely emitted along the beam line, in the low polar-angle regions of the detectors which
are not instrumented and, therefore, escape detection.
The cross section of the e+e−→ q¯ q process was measured [1,2] and found to be in agreement
with the Standard Model predictions for both a subsample of events with values of
to√s and a more inclusive sample extending to lower values of
photons often implies
phenomenon is commonly called “radiative return to the Z”. The process e+e−→ Zγ → q¯ qγ,
where a hard ISR photon is responsible for such radiative return to the Z, was studied in
detail [4,5]. Events in which the photon was visible in the detector, were used to constrain
possible anomalous triple-couplings between neutral gauge bosons . Events with either a
detected photon or a low-angle undetected photon were used to reconstruct the mass of the Z
boson and validate the analysis tools used in the measurement of the mass of the W boson .
The e+e−→ Zγγ → q¯ qγγ process, where both ISR photons were visible in the detector, was
first observed by the L3 collaboration . The cross section of this process was then measured
for√s = 130 − 209 GeV and found to be in agreement with the predictions .
This Letter extends the study of the e+e−→ Zγγ → q¯ qγγ process to the case in which
both ISR photons are emitted at low polar angles and are therefore not detected. In particular,
the case is considered in which the two photons are emitted on opposite sides of the detector,
with comparable transverse momenta. In this topology, the two jets originating from the Z-
boson decay are back-to-back. In the following, this process is denoted as “double-radiative
return to the Z”. This study complements the previous studies of the e+e−→ q¯ q process in
a very specific phase-space region and allows further tests of Monte Carlo simulations of ISR
photons in hadronic events. Moreover, final states with two back-to-back hadronic jets and
missing energy are a signature of the near-threshold production of the Standard Model Higgs
boson, H, at LEP in the reaction e+e−→ ZH. In this case, the missing energy is due to a Z
boson decaying into neutrinos and the jets to the Higgs boson. In addition, manifestations of
New Physics in the production of an invisibly-decaying Higgs boson in association with a Z
boson decaying into hadrons would also give rise to the same final state. Finally, similar event
topologies are predicted by Supersymmetry. Therefore, a study of double-radiative return to
the Z with unobserved photons validates the background Monte Carlo simulations for those
This analysis selects e+e−→ q¯ q events with two or more hard ISR photons satisfying the
following phase-space criteria:
Eγ1,2> 5 GeV
√s′, at which this hadron production takes place does not necessarily correspond to
√s′. The emission of ISR
√s′≈ mZ, where mZ = 91.19 GeV is the mass of the Z boson. This
|cosθγ1,2| ≥ 0.96
|√s′− mZ| < 2ΓZ
cosθγ1× cosθγ2< 0
??? < 0.1√s,(5)
where Eγi, θγiand pT
beams of the photon i, respectively. ΓZdenotes the width of the Z boson, 2.49 GeV . If more
than two ISR photons are present in the event, this signal definition is applied to the two most
energetic ones. These criteria select about 6% of the phase space of the e+e−→ q¯ q process,
corresponding to a cross section of about 5.5 pb in the√s range explored at LEP. Figure 1
illustrates the complementarity of this phase space with those covered by the analyses of the
e+e−→ q¯ q, e+e−→ Zγ → q¯ qγ and e+e−→ Zγγ → q¯ qγγ processes described in References 1, 4
γiare the energy, polar angle and momentum in the plane transverse to the
2 Data and Monte Carlo Samples
This measurement is based on 0.62 fb−1of data collected with the L3 detector  at LEP
in the years from 1998 through 2000 at centre-of-mass energies between√s = 188.6 GeV and
√s = 209.2 GeV, as detailed in Table 1. In the last year of data taking, the LEP centre-of-mass
energy was routinely increased while the beams were colliding in order to enhance the sensitivity
of the search for the Standard Model Higgs boson, exploring the range√s = 202.5−209.2 GeV.
In the following, this last data sample is split into two energy ranges.
The KK2f  Monte Carlo program is used, with default options, to generate a total of 1.9
million e+e−→ q¯ q events which can contain one or more hard ISR photons, at the centre-of-
mass energies listed in Table 1. These events correspond to about 35 times the luminosity of
the data and cover a phase space much larger than that of the criteria (1)−(5). If at least two
ISR photons which satisfy the criteria (1)−(5) are present in an event this is treated as signal,
otherwise it is considered as background. This distinction between signal and background is
performed on generated variables, before any event simulation and any application of detector
Other background processes are generated with the Monte Carlo programs PYTHIA  for
e+e−→ Ze+e−and e+e−→ ZZ, KK2f for e+e−→ τ+τ−, PHOJET  for hadron production
in two-photon collisions and KORALW  for W-boson pair production except for eνeq¯ q′final
states, generated with EXCALIBUR . The hadronisation process for signal and background
events is modelled with the JETSET  program.
The L3 detector response is simulated using the GEANT  and GHEISHA  programs,
which model the effects of energy loss, multiple scattering and showering in the detector. Time-
dependent detector efficiencies, as monitored during data-taking periods, are also simulated.
3 Event Selection
The event selection proceeds from a sample of high-multiplicity events. Events containing
photons, electrons or muons with energies above 20 GeV are removed in order to reduce the
backgrounds from e+e−→ q¯ q events with ISR photons in the detector and events containing
W bosons which decay into leptons. The visible mass, Mvis, and the visible energy, Evis, of
these events are required to satisfy 50 GeV < Mvis< 140 GeV and 0.4 < Evis/√s < 0.65, to
reduce both e+e−→ q¯ q events without missing energy due to ISR photons and most events
from two-photon collisions. The latter cut is illustrated in Figure 2a. Events from two-photon
collisions are further suppressed by requiring |cosθthrust| < 0.96, where θthrust is the angle
between the thrust axis and the beam line. Events are then reconstructed into two jets by
means of the DURHAM algorithm  and the signal signature of two back-to-back jets is
enforced by requiring the angle between the two jets, θjj, to satisfy θjj> 1.5 rad. Finally, the
sum of the momenta of the two jets in the plane transverse to the beams, pT, must be less
than 0.2Evis. This cut, shown in Figure 2b, accounts for the fact that all missing momentum
in signal events is due to the two ISR photons nearly collinear with the beam particles and
therefore directed along the beam line. After this pre-selection, 17208 events are selected in
data, well consistent with the 17151 events expected from Monte Carlo simulations, of which
13% are from signal and 87% from background. The background is almost entirely composed
by e+e−→ q¯ q events which do not satisfy the signal definition (1)−(5). Small contributions
arise from four-fermion production and hadron production in two-photon collisions. The signal
efficiency at this stage of the analysis is 68%.
Three additional cuts are devised to reduce the residual background and enhance the signal
component in this sample. The energy of the most energetic jet must be greater than 0.4√s;
the angle between the two jets in the plane transverse to the beams, θT
should be such that |cosθjet
θjj> 1.95 rad and 70 GeV < Mvis< 110 GeV, as shown in Figures 2d and 3, respectively. The
former criterion is extremely efficient in removing the background from one-photon radiative
return to the Z boson, which is characterised by a larger boost than the signal and therefore a
smaller jet opening-angle.
After these selection criteria, 1672 events are selected in data while 1684 are expected from
Monte Carlo simulations, of which 61% are from signal, and 39% from background, as detailed
in Table 2. Three quarters of the background are due to e+e−→ q¯ q events which do not satisfy
the signal definition (1)−(5). The remaining background is due to four-fermion production and
hadron production in two-photon collisions. The average signal efficiency is 31%.
The distribution of Mvis, shown in Figure 3, presents a clear enhancement at mZ, as expected
for signal events.
jj, is required to be
jj> 2.9 rad, as shown in Figure 2c; the polar angle of the jet closest to the beam line, θjet
low| < 0.85. Finally, two of the pre-selection criteria are tightened:
4 Systematic Uncertainties
Several sources of possible systematic uncertainties are considered, and their effects are sum-
marised in Table 3.
Monte Carlo simulations might not perfectly reproduce the tails of the variables used in the
event selection owing to, for instance, non-linearity in the modelling of the calorimeter response
or a bias in the determination of jet directions close to the edge of fiducial volumes. To assess
this effect, the analysis is repeated by removing one selection criterion at a time. In addition,
a 0.5% uncertainty in the jet energy-scale and a 2% uncertainty in the determination of the jet
angles are also considered.
The signal and background events from the e+e−→ q¯ q process are generated taking into
account the interference between ISR photons and those emitted in the final state. The anal-
ysis is repeated by using a Monte Carlo sample without this interference and the difference
with the original result is used as an extreme systematic uncertainty on the modelling of this
The cross sections are measured by assuming a fixed background level, as discussed below.
Uncertainties in the background cross sections are therefore a possible source of systematic
uncertainty, which is estimated by repeating the analysis with a variation of 10% for the cross
section of the e+e−→ eνeq¯ q′process, 5% for e+e−→ q¯ q events classified as background, 5%
for the e+e−→ ZZ process, 5% for the e+e−→ Ze+e−process and 0.5% for W-boson pair
Finally, statistical uncertainties related to the limited amount of Monte Carlo events used
to describe the signal and the background processes are included as systematic uncertainties.
The total systematic uncertainty on the signal cross section varies between 5.3% and 7.7%,
depending on the centre-of-mass energy.
The signal cross sections are determined for each centre-of-mass energy by fitting the observed
distributions of Mvis. Two components are considered, both with a shape fixed to Monte Carlo
expectations: a signal component with a free normalisation, and a background component with
fixed normalisation. The results are listed in Table 2 and plotted in Figure 4, together with the
corresponding statistical and systematic uncertainties. A good agreement with the predictions
of the KK2f Monte Carlo, also given in Table 2 and Figure 4, is observed. These predictions
have an uncertainty of 3%, which includes a statistical component and the uncertainty from
higher-order corrections, estimated following the suggestions in Reference 9.
To further compare the results and the expectations, the ratio between the measured, σ,
and the expected, σth, values of the cross section is calculated for each centre-of-mass energy.
These values are then averaged, by assuming all systematic uncertainties to be fully correlated,
with the exception of those due to the limited Monte Carlo statistics. The result is:
σ/σth= 0.98 ± 0.04 ± 0.06,
where the first uncertainty is statistical and the second systematic.
In conclusion, the cross section of the process e+e−→ Zγ → q¯ qγγ, where the two photons
are emitted in the phase space defined by the criteria (1)–(5), is measured with an accuracy of
7% and is well reproduced by the current simulations of ISR in hadronic events. This finding
validates the estimate of the background from events with two back-to-back jets with mass
close to the mass of the Z boson both in the searches for Higgs bosons of the Standard Model
and beyond and for other manifestations of New Physics.
The L3 Collaboration:
I.Clare,13R.Clare,38G.Coignet,4N.Colino,25S.Costantini,39B.de la Cruz,25S.Cucciarelli,33R.de Asmundis,29
P.D´ eglon,20J.Debreczeni,12A.Degr´ e,4K.Dehmelt,26K.Deiters,47D.della Volpe,29E.Delmeire,20P.Denes,37
D.Duchesneau,4M.Duda,1B.Echenard,20A.Eline,18A.El Hage,1H.El Mamouni,24A.Engler,35F.J.Eppling,13
B.N.Jin,7P.Jindal,14L.W.Jones,3P.de Jong,2I.Josa-Mutuberr´ ıa,25M.Kaur,14M.N.Kienzle-Focacci,20J.K.Kim,43
J.Kirkby,18W.Kittel,31A.Klimentov,13,28A.C.K¨ onig,31M.Kopal,46V.Koutsenko,13,28M.Kr¨ aber,49R.W.Kraemer,35
A.Kr¨ uger,48A.Kunin,13P.Ladron de Guevara,25I.Laktineh,24G.Landi,17M.Lebeau,18A.Lebedev,13P.Lebrun,24
P.Lecomte,49P.Lecoq,18P.Le Coultre,49J.M.Le Goff,18R.Leiste,48M.Levtchenko,27P.Levtchenko,34C.Li,22
D.Teyssier,24C.Timmermans,31Samuel C.C.Ting,13S.M.Ting,13S.C.Tonwar,9J.T´ oth,12C.Tully,37
K.L.Tung,7J.Ulbricht,49E.Valente,39R.T.Van de Walle,31R.Vasquez,46V.Veszpremi,26G.Vesztergombi,12
1 III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany§
2 National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam,
3 University of Michigan, Ann Arbor, MI 48109, USA
4 Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP,IN2P3-CNRS, BP 110, F-74941
Annecy-le-Vieux CEDEX, France
5 Institute of Physics, University of Basel, CH-4056 Basel, Switzerland
6 Louisiana State University, Baton Rouge, LA 70803, USA
7 Institute of High Energy Physics, IHEP, 100039 Beijing, China△
8 University of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italy
9 Tata Institute of Fundamental Research, Mumbai (Bombay) 400 005, India
10 Northeastern University, Boston, MA 02115, USA
11 Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania
12 Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary‡
13 Massachusetts Institute of Technology, Cambridge, MA 02139, USA
14 Panjab University, Chandigarh 160 014, India
15 KLTE-ATOMKI, H-4010 Debrecen, Hungary¶
16 Department of Experimental Physics, University College Dublin, Belfield, Dublin 4, Ireland
17 INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy
18 European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland
19 World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland
20 University of Geneva, CH-1211 Geneva 4, Switzerland
21 University of Hamburg, D-22761 Hamburg, Germany
22 Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China△
23 University of Lausanne, CH-1015 Lausanne, Switzerland
24 Institut de Physique Nucl´ eaire de Lyon, IN2P3-CNRS,Universit´ e Claude Bernard, F-69622 Villeurbanne, France
25 Centro de Investigaciones Energ´ eticas, Medioambientales y Tecnol´ ogicas, CIEMAT, E-28040 Madrid, Spain♭
26 Florida Institute of Technology, Melbourne, FL 32901, USA
27 INFN-Sezione di Milano, I-20133 Milan, Italy
28 Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia
29 INFN-Sezione di Napoli and University of Naples, I-80125 Naples, Italy
30 Department of Physics, University of Cyprus, Nicosia, Cyprus
31 Radboud University and NIKHEF, NL-6525 ED Nijmegen, The Netherlands
32 California Institute of Technology, Pasadena, CA 91125, USA
33 INFN-Sezione di Perugia and Universit` a Degli Studi di Perugia, I-06100 Perugia, Italy
34 Nuclear Physics Institute, St. Petersburg, Russia
35 Carnegie Mellon University, Pittsburgh, PA 15213, USA
36 INFN-Sezione di Napoli and University of Potenza, I-85100 Potenza, Italy
37 Princeton University, Princeton, NJ 08544, USA
38 University of Californa, Riverside, CA 92521, USA
39 INFN-Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy
40 University and INFN, Salerno, I-84100 Salerno, Italy
41 University of California, San Diego, CA 92093, USA
42 Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria
43 The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, Republic of Korea
44 National Central University, Chung-Li, Taiwan, China
45 Department of Physics, National Tsing Hua University, Taiwan, China
46 Purdue University, West Lafayette, IN 47907, USA
47 Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland
48 DESY, D-15738 Zeuthen, Germany
49 Eidgen¨ ossische Technische Hochschule, ETH Z¨ urich, CH-8093 Z¨ urich, Switzerland
§ Supported by the German Bundesministerium f¨ ur Bildung, Wissenschaft, Forschung und Technologie.
‡ Supported by the Hungarian OTKA fund under contract numbers T019181, F023259 and T037350.
¶ Also supported by the Hungarian OTKA fund under contract number T026178.
♭ Supported also by the Comisi´ on Interministerial de Ciencia y Tecnolog´ ıa.
♯ Also supported by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina.
△ Supported by the National Natural Science Foundation of China.
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202.5 − 205.5
205.5 − 209.2
Table 1: Centre-of-mass energies and corresponding integrated luminosities, L, con-
sidered in this analysis. The last two energy ranges correspond to the average
centre-of-mass energy values <√s >= 204.8 GeV and <√s >= 206.6 GeV, re-
660.1 ± 6.9
97.3 ± 2.1
236.5 ± 4.2
196.3 ± 3.9
80.9 ± 2.1
153.2 ± 1.6
259.9 ± 2.3
372.3 ± 4.6
56.7 ± 1.5
149.7 ± 2.8
126.6 ± 2.5
52.8 ± 1.6
102.2 ± 1.0
173.5 ± 1.3
287.9 ± 5.1
40.6 ± 1.5
86.8 ± 3.1
69.6 ± 3.0
28.1 ± 1.4
50.9 ± 1.2
86.5 ± 2.0
36.1 ± 0.4
34.7 ± 0.9
32.3 ± 0.6
29.6 ± 0.6
27.8 ± 0.8
26.4 ± 0.3
25.5 ± 0.2
5.31 ± 0.39 ± 0.37
3.63 ± 0.88 ± 0.44
5.51 ± 0.55 ± 0.32
6.05 ± 0.60 ± 0.31
5.32 ± 0.87 ± 0.33
4.81 ± 0.58 ± 0.27
5.33 ± 0.46 ± 0.27
Table 2: Number of events observed in data after the final selection, NData, compared with the
total number of events expected from Monte Carlo, NMC. The number of signal events expected
from the KK2f Monte Carlo, NSign, is also given, together with the number of background
events, NBack. The selection efficiency, ε, is also listed, together with the measured, σ, and
expected, σth, signal cross sections. The uncertainties on NMC, NSign, NBackand ε correspond
to the statistical uncertainty of the Monte Carlo. The first uncertainty on σ is statistical, the
Jet energy scale
Monte Carlo statistics
1.4 − 4.4
1.2 − 3.9
5.3 − 7.7
Table 3: Systematic uncertainties on the signal cross section.
high q q
Figure 1: Distributions at generator level of the absolute difference of the two photon
polar angles versus the energy of the most energetic photon for a) the signal, b) the
e+e−→ q¯ q process for√s′/√s > 0.85 and√s′> 60 GeV, c) the e+e−→ q¯ q process
q¯ qγγ process. Only events with at least two photons with energies greater than
1 MeV are shown, for a sample at√s = 189 GeV. The histograms show the fraction
of the cross section of each process in each bin. These cross sections are, respectively,
5.8 pb, 89.7 pb, 16.1 pb, 20.3 pb and 0.4 pb.
√s′> 60 GeV, d) the e+e−→ Zγ → q¯ qγ process, and e) the e+e−→ Zγγ →
Events / 0.02
Evis / √s
0 0.1 0.20.30.4 0.5 0.6
Events / 0.025
pT / Evis
Events / 0.05 rad
Events / 0.05 rad
Figure 2: Distribution for data and Monte Carlo of a) the visible energy divided
by the centre-of-mass energy; b) the sum of the transverse momenta of the two
jets divided by the visible energy; c) the angle between the two jets in the plane
transverse to the beams and d) the angle between the jets. The distributions in
a) and b) refer to pre-selection level, those in c) and d) to the final selection. The
arrows represent the position of the cuts, once all other pre-selection or selection
cuts are applied.
Events / 5 GeV
Figure 3: Distribution of the visible mass for data and Monte Carlo after the appli-
cation of all other selection cuts.
[GeV]s Download full-text
190195 200 205
KK2f Monte Carlo
Figure 4: Measured cross sections for the various centre-of-mass energies, indicated
by the points, compared with the Standard Model predictions, indicated by the
band. The bars on the point show the sum in quadrature of the statistical and
systematic uncertainties. The inner bars represent the statistical uncertainties. The
width of the band corresponds to an uncertainty of 3% on the predictions, derived
as discussed in the text.