 Research article
 Open Access
 Published:
Study of hadronic event shape in flavour tagged events in e^{+}e^{} annihilation at \u3008\sqrt{s}\u3009= 197 GeV
PMC Physics A volume 2, Article number: 6 (2008)
Abstract
Results are presented from a study of the structure of hadronic events in highenergy e^{+}e^{} interactions detected by the L3 detector at LEP. Various event shape distributions and their moments are measured at several energy points at and above the Zboson mass. The event flavour is tagged by using the decay characteristics of bhadrons. Measurements of distributions of event shape variables for all hadronic events, for light (u, d, s, c) and heavy (b) quark flavours are compared to several QCD models with improved leading log approximation: JETSET, HERWIG and ARIADNE. A good description of the data is provided by the models.
PACS Codes: 12.38.Qk, 13.66.Bc
1 Introduction
Hadronic events produced in e^{+}e^{} annihilation have been a powerful tool to test the predictions of Quantum Chromodynamics (QCD) [1–5]. Perturbative QCD successfully accounts for many aspects of the hadronic decays of the Z boson [6]. The primary quarks from Zboson decays first radiate gluons, which in turn may split into quark or gluon pairs. The quark and gluons then fragment into observable hadrons. Perturbative QCD itself does not describe the fragmentation process. Instead several phenomenological models have been developed to describe fragmentation. These models provide a way to correct for the effects of fragmentation in the experimental data, which can then be compared with the perturbative QCD calculations directly.
The event shape variables which characterize the global structure of hadronic events are among the simplest experimental measurements sensitive to the parameters of perturbative QCD and fragmentation models. This article reports on the measurement of event shapes for hadronic events collected at LEP by the L3 detector [7–10] at e^{+}e^{} centreofmass energies \sqrt{s} ≥ 189 GeV. Similar analyses were reported by all LEP experiments [11–15].
Heavy flavour production in e^{+}e^{} annihilation can be studied by exploiting the characteristics of heavy flavour decays. In the present study, hadronic events are separated into heavy (b) and light (u, d, s, c) flavours, and event shape variables are separately measured for these final states. This allows to test the modelling of heavy flavour mass effects. Earlier and similar measurements, at lower centreofmass energies, are reported in References [11] and [16].
2 Global event shape variables
Event shape variables, insensitive to soft and collinear radiation, are built from linear sums of measured particle momenta. They are sensitive to the amount of hardgluon radiation. Six global event shape variables are measured here, using calorimetric and tracking information measured as described in References [7–10] and [11]. They are: thrust, scaled heavy jet mass, total and wide jet broadening, the Cparameter and the jet resolution parameter. These eventshape variables are defined below.
2.0.1 Thrust
The global eventshape variable thrust, T, [17, 18] is defined as
where {\overrightarrow{p}}_{i} is the momentum vector of particle i. The thrust axis {\overrightarrow{n}}_{T} is the unit vector which maximizes the above expression. The value of the thrust can vary between 0.5 and 1.0. The plane normal to {\overrightarrow{n}}_{T} divides space into two hemispheres, S_{±}, which are used in the following definitions.
2.0.2 Scaled heavy jet mass
The heavy jet mass, M_{H}, is defined [19–21] as
M_{H} = max [M_{+}, M_{}],
where M_{±} are the invariant masses in the two hemispheres, S_{±},
where p_{ i }is the fourmomentum of particle i. The scaled heavy jet mass, ρ_{H}, is defined as
2.0.3 Jet broadening variables
These variables are defined [22, 23] by computing in each hemisphere the quantity
in terms of which the total jet broadening, B_{T}, and wide jet broadening, B_{W}, are defined as
B_{T} = B_{+} + B_{} and B_{W} = max(B_{+}, B_{}).
2.0.4 Cparameter
The Cparameter is derived from the eigenvalues of the linearized momentum tensor [24, 25]:
where a runs over final state hadrons and i, j indicate components of the momentum vectors {\overrightarrow{p}}_{a}. With λ_{1}, λ_{2} and λ_{3} the eigenvalues of Θ, the Cparameter is defined as
C = 3(λ_{1}λ_{2} + λ_{2}λ_{3} + λ_{3}λ_{1}).
2.0.5 Jet resolution parameter
Jets are reconstructed using the JADE algorithm [26, 27]. The value of the "closeness variable" at which the classification of an event changes from 2jet to 3jet is called the 3jet resolution parameter {y}_{23}^{\text{J}}.
3 Monte Carlo models
The measured global event shape variables are compared below with the predictions of three Monte Carlo parton shower models JETSET[28], ARIADNE[29] and HERWIG[30–32]. In these models parton showers are generated perturbatively according to a recursive algorithm down to energy scales of 1–2 GeV defining a boundary between perturbative and nonperturbative regions of phase space. In the nonperturbative region, hadrons are generated according to phenomenological fragmentation models. In the perturbative phase of all the models, the parton branching energy fractions are distributed according to the leading order DGLAP [33–36] splitting functions. The basic Leading Logarithmic Approximation (LLA) [37–41] of the models is modified, in the framework of the Modified Leading Logarithmic Approximation (MLLA) [42–44], to take into account certain interference effects first occurring in the NexttoLeading Logarithmic Approximation (NLLA) [45–48].
The JETSET parton shower Monte Carlo program uses, as evolution variable in the parton shower, the mass squared of the (timelike virtual) branching parton. Angular ordering to describe NLLA interference effects is implemented in an ad hoc manner and the distributions of the first generated gluon are reweighted to match those of the treelevel O(α_{ s }) matrix element. Partons are hadronized according to a string fragmentation model. For light quarks (u, d, s) the Lund symmetric fragmentation function [49] is used and for b and c quarks the Peterson fragmentation function [50]. The transverse momenta of hadrons are described by Gaussian functions.
The parton cascade of ARIADNE evolves via twoparton colourdipole systems. Gluon radiation splits a primary dipole into two independent dipoles, the evolution variable being the square of the transverse momentum of the radiated gluon. This procedure incorporates, to MLLA accuracy, the NLLA interference effects that give angular ordering in the parton shower. Hadrons are generated according to the same string fragmentation model as used in JETSET.
The HERWIG Monte Carlo program uses a coherent parton branching algorithm with phase space restricted to an angleordered region. The evolution variable is E^{2}(1  cos θ) where E is the energy of the initial parton and θ the angle between the branching partons. This choice incorporates NLLA interference effects within the MLLA framework. As in JETSET the distributions of the most energetic gluon are improved by matching them to those given by the \mathcal{O}(α_{ s }) matrix element. Hadronization is described by a cluster model based on perturbativelevel QCD preconfinement.
The parameters of the models, which are detailed in Reference [11], are tuned, using Zpeak data, by fitting the models to the following distributions:
jet resolution parameter {y}_{23}^{\text{J}} of the JADE algorithm [26, 27];
FoxWolfram moment H_{4} [51–53];
narrowside minor {T}_{minor}^{NS}[54];
charged particle multiplicity N_{ch}.
The variable {y}_{23}^{\text{J}} is particularly sensitive to the 3jet rate, H_{4} to the interjet angles, {T}_{minor}^{NS} to the lateral size of quark jets and so to the transverse momentum distribution of hadrons relative to a jet axis, and N_{ch} to parameters of the fragmentation models. The tuning was performed independently for all and udsc quark flavours.
More details on the Monte Carlo models and the tuning procedure can be found in Reference [11].
4 Data and Monte Carlo samples
The data discussed in this analysis correspond to an integrated luminosity of 602.2 pb^{1}, collected during the years 1998–2000 at \sqrt{s} ≥ 189–207 GeV as detailed in Table 1. Only data corresponding to datataking periods where all subdetectors were fully operational are retained in this analysis.
The primary trigger for hadronic events requires a total energy greater than 15 GeV in the calorimeters. This trigger is in logical OR with a trigger using the barrel scintillation counters and with a chargedtrack trigger. The combined trigger efficiency for the selected hadronic events exceeds 99.9%.
The selection of e^{+}e^{} → \text{q}\overline{\text{q}} → hadrons events is based on the energy measured in the electromagnetic and hadron calorimeters, as described in Section 3 of Reference [11]. Energy clusters in the calorimeters are selected with a minimum energy of 100 MeV. The principal variables used to distinguish these hadronic events from background are the cluster multiplicity and energy imbalances. Energy clusters in the calorimeters are used to measure the total visible energy E_{vis}, and the energy imbalances parallel and perpendicular to the beam direction:
respectively, where E_{ i }is the energy of cluster i and θ_{ i }and ϕ_{ i }are its polar and azimuthal angles with respect to the beam direction.
Monte Carlo events are used to estimate the efficiency of the selection criteria and purity of the data sample. Monte Carlo events for the process e^{+}e^{} → \text{q}\overline{\text{q}} → hadrons are generated by the parton shower programs PYTHIA[55] for \sqrt{s} = 189 GeV and KK2F[56, 57], which uses PYTHIA for hadronization, for the highest energies. QCD parton shower and fragmentation process are taken from JETSET 7.4 [28]. The generated events are passed through the L3 detector simulation [58, 59]. The background events are simulated with PYTHIA and PHOJET[60, 61] for hadron production in twophoton interactions, KORALZ[62] for τ^{+}τ^{} final state, BHAGENE[63, 64] for Bhabha events, KORALW[65, 66] for Wboson pairproduction and PYTHIA for Zboson pairproduction.
5 Event selection and flavour tagging
This analysis has two main sources of background. The first is the so called "radiative return" events, where initial state radiation results in a mass of the hadronic system close to the Z boson. The second is pairproduction of W or Z bosons where one or both of the bosons decay hadronically. Additional background arises from hadron production in twophoton interactions and τ pair production. Events are first selected by requiring E_{vis}/\sqrt{s} > 0.7, E_{⊥}/E_{vis} < 0.4, number of clusters > 12, and at least one wellmeasured charged track. To reduce the radiative return background, events are rejected if they have a highenergy photon candidate, defined as a cluster in the electromagnetic calorimeter with at least 85% of its energy in a 15° cone and a total energy greater than 0.18\sqrt{s}. Radiative return events, where an unobserved photon is emitted close to the beam axis, are reduced by requiring \sqrt{{s}^{\prime}/s} > 0.85, where \sqrt{{s}^{\prime}} is given by
and the energy of the unobserved photon E_{ γ }is derived by first forcing the event into a twojet topology and then using the angles of the two jets, θ_{1} and θ_{2}, as:
To reject boson pairproduction events where one of the bosons decays into leptons, events having an electron or muon with energy greater than 40 GeV are removed. Hadronic decays of boson pair events are rejected by:

1.
forcing the event to a 4jet topology using the Durham jet algorithm [67–70],

2.
performing a kinematic fit imposing energymomentum conservation,

3.
applying cuts on the energies of the most and the leastenergetic jets and on the jet resolution parameter, {y}_{34}^{\text{D}} at which the event classification changes from 3jet to 4jet. Events are rejected if the energy of the most energetic jet is less than 0.4\sqrt{s}, the ratio of the energy of the most energetic jet to the least energetic jet is less than 5, {y}_{34}^{\text{D}} > 0.007, there are more than 40 clusters and more than 15 charged tracks, and E_{} < 0.2E_{vis} after the kinematic fit.
This selection removes 11.67 ± 0.28% of the signal events, 98.11 ± 0.02% of the radiative return events, 83.31 ± 0.03% and 80.08 ± 0.11%, respectively, of Wboson and Zboson pairproduction events. We select a total of 13913 hadronic events, with an efficiency of 88.33 ± 0.28% and with a purity of 78.19 ± 0.11%. The backgrounds due to radiative return, Wboson pairs, Zboson pairs and hadron production in twophoton interaction are 5.71 ± 0.06%, 12.28 ± 0.04%, 1.01 ± 0.01% and 2.55 ± 0.09%, respectively. The remaining backgrounds are negligible. The integrated luminosity and the number of selected events for each energy point are summarized in Table 1.
Heavy (b) flavour events are separated from light (u, d, s, c) flavour events by using the characteristic decay properties of the bhadrons. As the first step, the interaction vertex is estimated fillbyfill by iteratively fitting all the good tracks measured in the detector during the fill. Measurements of all n tracks in the event contribute to a probability, P^{[n]}, that all tracks in the event originate from the interaction vertex. This probability is flat for zero lifetime of all produced particles but otherwise peaks at zero. A weighted discriminant is used:
B_{n} = log P, where P={P}^{[n]}{\displaystyle {\sum}_{j=0}^{n1}{(\mathrm{log}{P}^{[n]})}^{j}/j!} and {P}^{[n]}={\displaystyle {\prod}_{j=1}^{n}{P}_{j}} and P_{ j }is the probability that track j originates from the primary vertex [71].
Figure 1 shows the distribution of the discriminant B_{n} for data as well as expectations from signal and background. A cut on this discriminant is made to distinguish events with bquarks from events without. These two samples are called "bevents" and "nonb events" in the following. The nonb events are selected using B_{n} < 1.0. The bevents are selected with a cut on B_{n} > 3.4. A total of 440 bevents are selected with an efficiency of 26.2 ± 0.4% and a purity of 75.2 ± 1.2% while 6895 nonb events are selected with a selection efficiency of 75.5 ± 0.3% and a purity of 72.7 ± 0.1%. The dominant background for the bevents are due to wrong flavour events amounting to 14.3 ± 0.5% while that due to ISR, Wboson and Zboson pair events are respectively 4.5 ± 0.3%, 4.5 ± 0.1% and 1.4 ± 0.1%. On the other hand, the dominant background for nonb events are from Wboson pair events amounting to 17.6 ± 0.1% while those due to wrong flavour type, ISR, Zboson pair and 2photon events are 3.9 ± 0.1%, 3.7 ± 0.1%, 0.6 ± 0.1% and 1.4 ± 0.1% respectively.
6 Measurements
The distributions of event shape variables are measured at each energy point listed in Table 1. The data distributions are compared to a sum of the signal and the different background Monte Carlo distributions obtained using the same selection procedure and normalized to the integrated luminosity according to the Standard Model cross sections. Figures 2 and 3 show the measured distributions for event thrust and total jet broadening for all data, bevents and nonb events. Data at the different energy points are combined at the average centreofmass energy \u3008\sqrt{s}\u3009 = 197 GeV. The distributions are compared to predictions from signal and background Monte Carlo programs. There is generally good agreement between data and Monte Carlo particularly for the entire sample thus justifying the use of the latter to obtain the correction from detector level to particle level. For Monte Carlo events, these event shape variables are calculated before (particle level) and after (detector level) detector simulation. The calculation before detector simulation takes into account all stable charged and neutral particles. The measured distributions at detector level differ from the ones at particle level because of detector effects, limited acceptance and finite resolution.
After subtracting the background events the measured distributions are corrected for detector effects, acceptance and resolution, on a binbybin basis by comparing the detector level results with the particle level results. In the extraction of flavourtagged distributions, the contribution of wrongflavour contamination is subtracted in the same way as the SM background subtraction.
The data are corrected for initial and final state photon radiation binbybin using Monte Carlo distributions at particle level with and without radiation. The comparison between data and Monte Carlo models shown in Figures 4, 5, 6, 7, 8, 9 below is made for particle level distributions.
7 Systematic uncertainties
The systematic uncertainties in the distributions of event shape variables are calculated for each bin of these distributions. The main sources of systematic are uncertainties in the estimation of the detector corrections and the background levels.
The uncertainty in from detector corrections is estimated by repeating the measurements altering several independent aspects of the event reconstruction, and taking the largest variation with respect to the original measurement. These changes are:
• the definition of reconstructed objects used to calculate the observables is changed from calorimetric clusters only to a nonlinear combination of charged tracks with calorimetric clusters;
• the effect of different particle densities in correcting the measured distributions is estimated by using a different signal Monte Carlo program, HERWIG instead of JETSET or PYTHIA;
• the acceptance is reduced by restricting the events to the central part of the detector, cos(θ_{ T }) < 0.7, where θ_{ T }is the polar angle of the thrust axis relative to the beam axis.
The systematic uncertainties on the background levels are assessed by varying the procedure used for the background evaluations and taking the the difference with the original measurements. These changes are:
• an alternative criterion is applied to reject radiative return events based on a cut in the two dimensional plane of E_{}/E_{vis} and E_{vis}/\sqrt{s};
• the estimated background from twophoton interaction is varied by ± 30% and is simulated by using the PHOJET instead of the PYTHIA Monte Carlo program;
• the Wboson pairproduction background is estimated from the KORALW Monte Carlo and subtracted from the data, while releasing the cut on 4jet events which are no longer removed from the data;
• the contamination from wrongflavour events is estimated by varying the cut on the B_{n} discriminant used to tag b events from 3.4 to 3.0 or 3.8 and the cut used to tag nonb events from 1.0 to 0.9 or 1.1. An additional lower cut at 0.2 is also introduced.
The binaveraged systematic uncertainties due to different sources are summarized in Table 2 for the six event shape variables. Uncertainties due to detector corrections are between 4.8% and 6.0%, roughly 2–3 times larger than the uncertainty due to background estimation. The latter are dominated in equal parts by uncertainties due to radiative return and Wboson pairproduction. In the flavourtagged cases, the background uncertainty contains a significant contribution due to contamination from the wrong flavour and sometimes become the dominant source of systematic uncertainty. This uncertainty is between 2%–3% for the nonb events and 3%–10% for bevents.
The statistical component of the systematic uncertainty is negligible as the size of the Monte Carlo samples is at least 4 times, and sometimes even 10 times, larger than the size of the data sample. The final systematic uncertainty is taken as the sum in quadrature of all the contributions. Table 2 shows for each distribution the bin averaged systematic uncertainty as well as their contributions from different sources.
8 Results
The corrected distributions for the six chosen event shape distributions, thrust, scaled heavy jet mass, total and wide jet broadening, Cparameter and 3jet resolution parameter for the JADE algorithm, are summarized in Tables 3, 4, 5, 6, 7, 8 for \u3008\sqrt{s}\u3009 = 197 GeV. These tables also show the first and second moments of these distributions. The same six event shape distributions at \sqrt{s} = 91.2 GeV were previously measured as reported in Reference [11].
Figures 4, 5, 6, 7, 8, 9 show comparisons between data at \u3008\sqrt{s}\u3009 = 197 GeV and predictions of the JETSET, ARIADNE and HERWIG models for distributions of thrust, scaled heavy jet mass, total and wide jet broadening, Cparameter and the 3jet JADE resolution parameter for all hadronic events, bevents and nonb events. The error bars shown in these figures are the quadratic sum of statistical and systematic uncertainties. The ratios of the event shape distributions for b and nonb events are also shown together with predictions from parton shower models. For the bevents in the twojet region, the model predictions seem to overestimate the data, in particular for the thrust (Figure 4a), wide jet broadening (Figure 7a) and Cparameter (Figure 8a) distributions.
The agreement between the three models with the data is quantified in Table 9 which summarizes the χ^{2} and the confidence level of a comparison of these models with the data for the six eventshape variables for the three data samples. An overall good agreement between data and the model predictions is observed. All three models describe equally well the data, the minimum confidence level being 0.11 for the HERWIG comparison with B_{W} for nonb events. The overall agreement obtained for the three distributions singled out above presenting local discrepancies for bevents in the twojet region is found to be quite satisfactory.
Since the models were tuned only on low energy data and on all, or only udsc, quark flavours, the agreement observed shows that the energy evolution of QCD processes in the range between 90 GeV and 200 GeV, as well as the production of b quarks, is correctly described by the models considered. The event shape variables considered are, however, not very sensitive to differences between heavy and light quarks. Only in the distributions of B_{T}, at low values (Figure 6d) does the ratio of b to nonb events depart markedly from unity, a feature that is correctly described by the models.
9 Summary
Event shape distributions for hadronic events are studied from e^{+}e^{} annihilation data collected by the L3 detector at LEP at \u3008\sqrt{s}\u3009 = 197 GeV. Flavour tagging is used to separate a bquark enriched sample from a sample of lighter flavours.
The event shape distributions are well described by all the parton shower models JETSET, HERWIG and ARIADNE.
L3 Collaboration
P. Achard^{20}, O. Adriani^{17}, M. AguilarBenitez^{25}, J. Alcaraz^{25}, G. Alemanni^{23}, J. Allaby^{18}, A. Aloisio^{29}, M. G. Alviggi^{29}, H. Anderhub^{49}, V. P. Andreev^{6,34}, F. Anselmo^{8}, A. Arefiev^{28}, T. Azemoon^{3}, T. Aziz^{9}, P. Bagnaia^{39}, A. Bajo^{25}, G. Baksay^{26}, L. Baksay^{26}, S. V. Baldew^{2}, S. Banerjee^{9}, Sw. Banerjee^{4}, A. Barczyk^{49,47}, R. Barillère^{18}, P. Bartalini^{23}, M. Basile^{8}, N. Batalova^{46}, R. Battiston^{33}, A. Bay^{23}, U. Becker^{13}, F. Behner^{49}, L. Bellucci^{17}, R. Berbeco^{3}, J. Berdugo^{25}, P. Berges^{13}, B. Bertucci^{33}, B. L. Betev^{49}, M. Biasini^{33}, M. Biglietti^{29}, A. Biland^{49}, J. J. Blaising^{4}, S. C. Blyth^{35}, G. J. Bobbink^{2}, A. Böhm^{1}, L. Boldizsar^{12}, B. Borgia^{39}, S. Bottai^{17}, D. Bourilkov^{49}, M. Bourquin^{20}, S. Braccini^{20}, J. G. Branson^{41}, F. Brochu^{4}, J. D. Burger^{13}, W. J. Burger^{33}, X. D. Cai^{13}, M. Capell^{13}, G. Cara Romeo^{8}, G. Carlino^{29}, A. Cartacci^{17}, J. Casaus^{25}, F. Cavallari^{39}, N. Cavallo^{36}, C. Cecchi^{33}, M. Cerrada^{25}, M. Chamizo^{20}, Y. H. Chang^{44}, M. Chemarin^{24}, A. Chen^{44}, G. Chen^{7}, G. M. Chen^{7}, H. F. Chen^{22}, H. S. Chen^{7}, G. Chiefari^{29}, L. Cifarelli^{40}, F. Cindolo^{8}, I. Clare^{13}, R. Clare^{38}, G. Coignet^{4}, N. Colino^{25}, S. Costantini^{39}, B. de la Cruz^{25}, S. Cucciarelli^{33}, R. de Asmundis^{29}, P. Déglon^{20}, J. Debreczeni^{12}, A. Degré^{4}, K. Dehmelt^{26}, K. Deiters^{47}, D. della Volpe^{29}, E. Delmeire^{20}, P. Denes^{37}, F. DeNotaristefani^{39}, A. De Salvo^{49}, M. Diemoz^{39}, M. Dierckxsens^{2}, C. Dionisi^{39}, M. Dittmar^{49}, A. Doria^{29}, M. T. Dova^{10,♯}, D. Duchesneau^{4}, M. Duda^{1}, B. Echenard^{20}, A. Eline^{18}, A. El Hage^{1}, H. El Mamouni^{24}, A. Engler^{35}, F. J. Eppling^{13}, P. Extermann^{20}, M. A. Falagan^{25}, S. Falciano^{39}, A. Favara^{32}, J. Fay^{24}, O. Fedin^{34}, M. Felcini^{49}, T. Ferguson^{35}, H. 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Lecomte^{49}, P. Lecoq^{18}, P. Le Coultre^{49}, J. M. Le Goff^{18}, R. Leiste^{48}, M. Levtchenko^{27}, P. Levtchenko^{34}, C. Li^{22}, S. Likhoded^{48}, C. H. Lin^{44}, W. T. Lin^{44}, F. L. Linde^{2}, L. Lista^{29}, Z. A. Liu^{7}, W. Lohmann^{48}, E. Longo^{39}, Y. S. Lu^{7}, C. Luci^{39}, L. Luminari^{39}, W. Lustermann^{49}, W. G. Ma^{22}, L. Malgeri^{18}, A. Malinin^{28}, C. Maña^{25}, J. Mans^{37}, J. P. Martin^{24}, F. Marzano^{39}, K. Mazumdar^{9}, R. R. McNeil^{6}, S. Mele^{18,29} Salvatore.Mele@cern.ch, L. Merola^{29}, M. Meschini^{17}, W. J. Metzger^{31}, A. Mihul^{11}, H. Milcent^{18}, G. Mirabelli^{39}, J. Mnich^{1}, G. B. Mohanty^{9}, G. S. Muanza^{24}, A. J. M. Muijs^{2}, M. Musy^{39}, S. Nagy^{15}, S. Natale^{20}, M. Napolitano^{29}, F. NessiTedaldi^{49}, H. Newman^{32}, A. Nisati^{39}, T. Novak^{31}, H. Nowak^{48}, R. Ofierzynski^{49}, G. Organtini^{39}, I. Pal^{46}, C. Palomares^{25}, P. Paolucci^{29}, R. Paramatti^{39}, G. Passaleva^{17}, S. Patricelli^{29}, T. Paul^{10}, M. Pauluzzi^{33}, C. Paus^{13}, F. Pauss^{49}, M. Pedace^{39}, S. Pensotti^{27}, D. PerretGallix^{4}, D. Piccolo^{29}, F. Pierella^{8}, M. Pieri^{41}, M. Pioppi^{33}, P. A. Piroué^{37}, E. Pistolesi^{27}, V. Plyaskin^{28}, M. Pohl^{20}, V. Pojidaev^{17}, J. Pothier^{18}, D. Prokofiev^{34}, G. RahalCallot^{49}, M. A. Rahaman^{9}, P. Raics^{15}, N. Raja^{9}, R. Ramelli^{49}, P. G. Rancoita^{27}, R. Ranieri^{17}, A. Raspereza^{48}, P. Razis^{30}, S. Rembeczki^{26}, D. Ren^{49}, M. Rescigno^{39}, S. Reucroft^{10}, S. Riemann^{48}, K. Riles^{3}, B. P. Roe^{3}, L. Romero^{25}, A. Rosca^{48}, C. Rosemann^{1}, C. Rosenbleck^{1}, S. RosierLees^{4}, S. Roth^{1}, J. A. Rubio^{18}, G. Ruggiero^{17}, H. Rykaczewski^{49}, A. Sakharov^{49}, S. Saremi^{6}, S. Sarkar^{39}, J. Salicio^{18}, E. Sanchez^{25}, C. Schäfer^{18}, V. Schegelsky^{34}, H. Schopper^{21}, D. J. Schotanus^{31}, C. Sciacca^{29}, L. Servoli^{33}, S. Shevchenko^{32}, N. Shivarov^{42}, V. Shoutko^{13}, E. Shumilov^{28}, A. Shvorob^{32}, D. Son^{43}, C. Souga^{24}, P. Spillantini^{17}, M. Steuer^{13}, D. P. Stickland^{37}, B. Stoyanov^{42}, A. Straessner^{20}, K. Sudhakar^{9}, G. Sultanov^{42}, L. Z. Sun^{22}, S. Sushkov^{1}, H. Suter^{49}, J. D. Swain^{10}, Z. Szillasi^{26,¶}, X. W. Tang^{7}, P. Tarjan^{15}, L. Tauscher^{5}, L. Taylor^{10}, B. Tellili^{24}, D. Teyssier^{24}, C. Timmermans^{31}, Samuel. C. C. Ting^{13}, S. M. Ting^{13}, S. C. Tonwar^{9}, J. Tóth^{12}, C. Tully^{37}, K. L. Tung^{7}, J. Ulbricht^{49}, E. Valente^{39}, R. T. Van de Walle^{31}, R. Vasquez^{46}, G. Vesztergombi^{12}, I. Vetlitsky^{28}, G. Viertel^{49}, M. Vivargent^{4}, S. Vlachos^{5}, I. Vodopianov^{26}, H. Vogel^{35}, H. Vogt^{48}, I. Vorobiev^{35,28}, A. A. Vorobyov^{34}, M. Wadhwa^{5}, Q. Wang^{31}, X. L. Wang^{22}, Z. M. Wang^{22}, M. Weber^{18}, S. Wynhoff^{37,‡}, L. Xia^{32}, Z. Z. Xu^{22}, J. Yamamoto^{3}, B. Z. Yang^{22}, C. G. Yang^{7}, H. J. Yang^{3}, M. Yang^{7}, S. C. Yeh^{45}, An. Zalite^{34}, Yu. Zalite^{34}, Z. P. Zhang^{22}, J. Zhao^{22}, G. Y. Zhu^{7}, R. Y. Zhu^{32}, H. L. Zhuang^{7}, A. Zichichi^{8,18,19}, B. Zimmermann^{49}, M. Zöller^{1}
^{1}III. Physikalisches Institut, RWTH, D52056 Aachen, Germany.
^{2}National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL1009 DB Amsterdam, The Netherlands.
^{3}University of Michigan, Ann Arbor, MI 48109, USA.
^{4}Laboratoire d'AnnecyleVieux de Physique des Particules, LAPP, IN2P3CNRS, BP 110, F74941 AnnecyleVieux CEDEX, France.
^{5}Institute of Physics, University of Basel, CH4056 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 INFNSezione di Bologna, I40126 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, R76900 Bucharest, Romania.
^{12}Central Research Institute for Physics of the Hungarian Academy of Sciences, H1525 Budapest 114, Hungary^{‡}.
^{13}Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
^{14}Panjab University, Chandigarh 160 014, India.
^{15}KLTEATOMKI, H4010 Debrecen, Hungary^{¶}.
^{16}UCD School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.
^{17}INFN Sezione di Firenze and University of Florence, I50125 Florence, Italy.
^{18}European Laboratory for Particle Physics, CERN, CH1211 Geneva 23, Switzerland.
^{19}World Laboratory, FBLJA Project, CH1211 Geneva 23, Switzerland.
^{20}University of Geneva, CH1211 Geneva 4, Switzerland.
^{21}University of Hamburg, D22761 Hamburg, Germany.
^{22}Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China^{△}.
^{23}University of Lausanne, CH1015 Lausanne, Switzerland.
^{24}Institut de Physique Nucléaire de Lyon, IN2P3CNRS, Université Claude Bernard, F69622 Villeurbanne, France.
^{25}Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E28040 Madrid, Spain^{♭}.
^{26}Florida Institute of Technology, Melbourne, FL 32901, USA.
^{27}INFNSezione di Milano, I20133 Milan, Italy.
^{28}Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia.
^{29}INFNSezione di Napoli and University of Naples, I80125 Naples, Italy.
^{30}Department of Physics, University of Cyprus, Nicosia, Cyprus.
^{31}Radboud University and NIKHEF, NL6525 ED Nijmegen, The Netherlands.
^{32}California Institute of Technology, Pasadena, CA 91125, USA.
^{33}INFNSezione di Perugia and Università Degli Studi di Perugia, I06100 Perugia, Italy .
^{34}Nuclear Physics Institute, St. Petersburg, Russia.
^{35}Carnegie Mellon University, Pittsburgh, PA 15213, USA.
^{36}INFNSezione di Napoli and University of Potenza, I85100 Potenza, Italy.
^{37}Princeton University, Princeton, NJ 08544, USA.
^{38}University of Californa, Riverside, CA 92521, USA.
^{39}INFNSezione di Roma and University of Rome, "La Sapienza", I00185 Rome, Italy.
^{40}University and INFN, Salerno, I84100 Salerno, Italy.
^{41}University of California, San Diego, CA 92093, USA.
^{42}Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU1113 Sofia, Bulgaria.
^{43}The Center for High Energy Physics, Kyungpook National University, 702701 Taegu, Republic of Korea.
^{44}National Central University, ChungLi, 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, CH5232 Villigen, Switzerland.
^{48}DESY, D15738 Zeuthen, Germany.
^{49}Eidgenössische Technische Hochschule, ETH Zürich, CH8093 Zürich, Switzerland
Note
^{§}Supported by the German Bundesministerium für 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 Comisión Interministerial de Ciencia y Tecnologia.
^{♯}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.
^{‡}Deceased.
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Mele, S., the L3 Collaboration. Study of hadronic event shape in flavour tagged events in e^{+}e^{} annihilation at \u3008\sqrt{s}\u3009= 197 GeV. PMC Phys A 2, 6 (2008). https://doi.org/10.1186/1754041026
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DOI: https://doi.org/10.1186/1754041026
Keywords
 Systematic Uncertainty
 Parton Shower
 Event Shape
 Monte Carlo Program
 Hadronic Event