- Research article
- Open Access
Study of hadronic event shape in flavour tagged events in e^{+}e^{-} annihilation at $\u3008\sqrt{s}\u3009$= 197 GeV
- Salvatore Mele^{1, 2}Email author and
- the L3 Collaboration^{1}
Received: 6 June 2008
Accepted: 8 December 2008
Published: 8 December 2008
Abstract
Results are presented from a study of the structure of hadronic events in high-energy 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 Z-boson mass. The event flavour is tagged by using the decay characteristics of b-hadrons. 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
Keywords
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 Z-boson 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^{-} centre-of-mass 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 centre-of-mass 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 hard-gluon 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 C-parameter and the jet resolution parameter. These event-shape variables are defined below.
2.0.1 Thrust
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_{-}],
2.0.3 Jet broadening variables
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 C-parameter
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 C-parameter 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 2-jet to 3-jet is called the 3-jet 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 non-perturbative regions of phase space. In the non-perturbative 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 Next-to-Leading 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 (time-like 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 tree-level 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 two-parton colour-dipole 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 angle-ordered 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 perturbative-level QCD pre-confinement.
The parameters of the models, which are detailed in Reference [11], are tuned, using Z-peak data, by fitting the models to the following distributions:
jet resolution parameter ${y}_{23}^{\text{J}}$ of the JADE algorithm [26, 27];
Fox-Wolfram moment H_{4} [51–53];
narrow-side minor ${T}_{minor}^{NS}$[54];
charged particle multiplicity N_{ch}.
The variable ${y}_{23}^{\text{J}}$ is particularly sensitive to the 3-jet rate, H_{4} to the inter-jet 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
Summary of integrated luminosity and number of selected hadronic events at the different energies.
$\sqrt{s}$ (GeV) | Integrated Luminosity (pb^{-1}) | Selection Efficiency (%) | Sample Purity (%) | Selected events |
---|---|---|---|---|
188.6 | 175.1 | 87.72 ± 0.62 | 80.92 ± 0.25 | 4473 |
191.6 | 29.4 | 87.77 ± 0.62 | 80.11 ± 0.26 | 720 |
195.5 | 83.4 | 88.41 ± 0.63 | 78.60 ± 0.27 | 1884 |
199.5 | 81.2 | 88.51 ± 0.62 | 77.54 ± 0.25 | 1835 |
201.7 | 36.5 | 89.02 ± 0.63 | 76.98 ± 0.25 | 817 |
205.1 | 70.5 | 88.77 ± 0.64 | 75.65 ± 0.22 | 1496 |
206.5 | 126.2 | 88.93 ± 0.63 | 75.26 ± 0.22 | 2688 |
197.0 | 602.2 | 88.33 ± 0.28 | 78.19 ± 0.11 | 13913 |
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 charged-track trigger. The combined trigger efficiency for the selected hadronic events exceeds 99.9%.
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 two-photon interactions, KORALZ[62] for τ^{+}τ^{-} final state, BHAGENE[63, 64] for Bhabha events, KORALW[65, 66] for W-boson pair-production and PYTHIA for Z-boson pair-production.
5 Event selection and flavour tagging
- 1.
- 2.
performing a kinematic fit imposing energy-momentum conservation,
- 3.
applying cuts on the energies of the most- and the least-energetic jets and on the jet resolution parameter, ${y}_{34}^{\text{D}}$ at which the event classification changes from 3-jet to 4-jet. 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 W-boson and Z-boson pair-production 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, W-boson pairs, Z-boson pairs and hadron production in two-photon 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 b-hadrons. As the first step, the interaction vertex is estimated fill-by-fill 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 $P={P}^{[n]}{\displaystyle {\sum}_{j=0}^{n-1}{(-\mathrm{log}{P}^{[n]})}^{j}/j!}$ 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].
6 Measurements
After subtracting the background events the measured distributions are corrected for detector effects, acceptance and resolution, on a bin-by-bin basis by comparing the detector level results with the particle level results. In the extraction of flavour-tagged distributions, the contribution of wrong-flavour contamination is subtracted in the same way as the SM background subtraction.
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 non-linear 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 two-photon interaction is varied by ± 30% and is simulated by using the PHOJET instead of the PYTHIA Monte Carlo program;
• the W-boson pair-production background is estimated from the KORALW Monte Carlo and subtracted from the data, while releasing the cut on 4-jet events which are no longer removed from the data;
• the contamination from wrong-flavour 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 non-b events from 1.0 to 0.9 or 1.1. An additional lower cut at 0.2 is also introduced.
Bin-averaged systematic uncertainties due to different sources for the six event shape variables at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
Event Sample | Source | T | ρ _{H} | B _{T} | B _{W} | C | ${y}_{23}^{\text{J}}$ |
---|---|---|---|---|---|---|---|
All events | Detector | 5.6% | 5.9% | 4.8% | 6.6% | 5.5% | 6.0% |
Frag. Model | 0.6% | 1.3% | 1.5% | 1.4% | 1.6% | 0.5% | |
Background | 2.2% | 2.3% | 2.6% | 2.4% | 2.4% | 2.3% | |
Total | 6.2% | 6.8% | 6.1% | 7.6% | 6.4% | 6.7% | |
Non-b events | Detector | 5.9% | 7.4% | 5.5% | 7.3% | 6.9% | 7.4% |
Frag. Model | 0.9% | 1.4% | 1.1% | 1.1% | 1.3% | 0.4% | |
Background | 2.6% | 2.7% | 3.7% | 3.0% | 3.2% | 3.1% | |
Wrong Flavour | 1.8% | 2.1% | 2.0% | 3.0% | 2.3% | 2.8% | |
Total | 7.1% | 8.6% | 7.2% | 9.0% | 8.9% | 8.5% | |
b events | Detector | 5.3% | 8.1% | 5.7% | 7.1% | 10.2% | 5.7% |
Frag. Model | 0.3% | 0.6% | 1.5% | 1.5% | 1.2% | 0.3% | |
Background | 5.9% | 5.6% | 4.5% | 5.3% | 5.2% | 5.0% | |
Wrong Flavour | 2.3% | 3.0% | 8.9% | 9.6% | 7.6% | 5.8% | |
Total | 8.3% | 10.1% | 11.3% | 12.4% | 14.2% | 8.2% |
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
Differential distribution and first and second moments for event thrust at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
Thrust (T) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}T}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}T}$ (Non-b) | Thrust (T) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}T}$ (b) |
---|---|---|---|---|
0.500–0.600 | 0.00 ± 0.00 ± 0.00 | 0.00 ± 0.00 ± 0.00 | 0.500–0.600 | 0.00 ± 0.00 ± 0.00 |
0.600–0.650 | 0.01 ± 0.01 ± 0.02 | 0.01 ± 0.01 ± 0.04 | 0.600–0.650 | 0.00 ± 0.00 ± 0.00 |
0.650–0.700 | 0.13 ± 0.06 ± 0.06 | 0.26 ± 0.12 ± 0.11 | 0.650–0.700 | 0.04 ± 0.04 ± 0.03 |
0.700–0.750 | 0.19 ± 0.06 ± 0.04 | 0.42 ± 0.13 ± 0.15 | 0.700–0.750 | 0.63 ± 0.31 ± 0.36 |
0.750–0.800 | 0.56 ± 0.08 ± 0.11 | 0.67 ± 0.15 ± 0.15 | 0.750–0.800 | 0.62 ± 0.43 ± 0.37 |
0.800–0.825 | 0.80 ± 0.10 ± 0.11 | 0.88 ± 0.18 ± 0.18 | 0.800–0.850 | 1.14 ± 0.45 ± 0.59 |
0.825–0.850 | 1.05 ± 0.10 ± 0.08 | 1.23 ± 0.20 ± 0.18 | 0.850–0.900 | 2.95 ± 0.70 ± 0.44 |
0.850–0.875 | 1.62 ± 0.11 ± 0.17 | 1.76 ± 0.19 ± 0.26 | 0.900–0.925 | 3.43 ± 0.91 ± 1.09 |
0.875–0.900 | 1.72 ± 0.10 ± 0.21 | 1.60 ± 0.17 ± 0.32 | 0.925–0.950 | 5.02 ± 1.05 ± 0.45 |
0.900–0.925 | 3.03 ± 0.12 ± 0.23 | 3.24 ± 0.22 ± 0.19 | 0.950–0.975 | 8.97 ± 1.43 ± 0.97 |
0.925–0.950 | 4.72 ± 0.14 ± 0.23 | 5.09 ± 0.27 ± 0.38 | 0.975–1.000 | 11.83 ± 1.94 ± 0.70 |
0.950–0.975 | 9.24 ± 0.19 ± 0.22 | 8.95 ± 0.37 ± 0.24 | ||
0.975–1.000 | 16.04 ± 0.25 ± 1.09 | 14.54 ± 0.56 ± 1.11 | ||
First Moment | 0.943 ± 0.010 ± 0.004 | 0.935 ± 0.020 ± 0.003 | 0.927 ± 0.072 ± 0.010 | |
Second Moment | 0.893 ± 0.010 ± 0.007 | 0.879 ± 0.021 ± 0.006 | 0.865 ± 0.072 ± 0.016 |
Differential distribution and first and second moments for scaled heavy jet mass at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
ρ _{H} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{\rho}_{H}}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{\rho}_{H}}$ (Non-b) | ρ _{H} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{\rho}_{H}}$ (b) |
---|---|---|---|---|
0.000–0.015 | 20.31 ± 0.33 ± 1.68 | 18.24 ± 0.74 ± 1.76 | 0.000–0.015 | 15.10 ± 2.49 ± 1.16 |
0.015–0.030 | 15.93 ± 0.34 ± 0.61 | 15.60 ± 0.69 ± 0.73 | 0.015–0.030 | 15.32 ± 2.71 ± 0.95 |
0.030–0.045 | 8.72 ± 0.26 ± 0.19 | 8.58 ± 0.47 ± 0.44 | 0.030–0.045 | 7.77 ± 1.93 ± 1.72 |
0.045–0.060 | 5.12 ± 0.21 ± 0.41 | 5.18 ± 0.38 ± 0.56 | 0.045–0.060 | 4.95 ± 1.46 ± 1.11 |
0.060–0.075 | 3.59 ± 0.18 ± 0.42 | 3.74 ± 0.33 ± 0.66 | 0.060–0.075 | 4.39 ± 1.39 ± 0.45 |
0.075–0.090 | 2.76 ± 0.17 ± 0.14 | 3.05 ± 0.31 ± 0.14 | 0.075–0.090 | 4.34 ± 1.57 ± 0.51 |
0.090–0.105 | 2.22 ± 0.16 ± 0.27 | 2.37 ± 0.28 ± 0.42 | 0.090–0.120 | 3.46 ± 0.91 ± 0.53 |
0.105–0.120 | 1.89 ± 0.16 ± 0.25 | 1.96 ± 0.28 ± 0.32 | 0.120–0.150 | 1.69 ± 0.60 ± 0.97 |
0.120–0.150 | 1.11 ± 0.10 ± 0.12 | 1.22 ± 0.18 ± 0.16 | 0.150–0.180 | 0.95 ± 0.69 ± 0.45 |
0.150–0.180 | 0.75 ± 0.10 ± 0.06 | 0.96 ± 0.18 ± 0.16 | 0.180–0.210 | 0.49 ± 0.40 ± 0.49 |
0.180–0.210 | 0.51 ± 0.09 ± 0.11 | 0.63 ± 0.17 ± 0.17 | 0.210–0.240 | 0.21 ± 0.26 ± 0.21 |
0.210–0.240 | 0.27 ± 0.08 ± 0.06 | 0.39 ± 0.14 ± 0.13 | 0.240–0.270 | 0.32 ± 0.23 ± 0.17 |
0.240–0.270 | 0.23 ± 0.07 ± 0.04 | 0.41 ± 0.15 ± 0.11 | 0.270–0.300 | 0.26 ± 0.15 ± 0.10 |
0.270–0.300 | 0.17 ± 0.06 ± 0.05 | 0.37 ± 0.16 ± 0.14 | ||
First Moment | 0.046 ± 0.001 ± 0.003 | 0.053 ± 0.002 ± 0.003 | 0.057 ± 0.005 ± 0.006 | |
Second Moment | 0.005 ± 0.001 ± 0.001 | 0.006 ± 0.001 ± 0.001 | 0.006 ± 0.001 ± 0.001 |
Differential distribution and first and second moments for total jet broadening at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
B _{T} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{T}}}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{T}}}$ (Non-b) | B _{T} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{T}}}$ (b) |
---|---|---|---|---|
0.000–0.020 | 0.75 ± 0.06 ± 0.30 | 0.68 ± 0.11 ± 0.37 | 0.000–0.020 | 0.20 ± 0.20 ± 0.29 |
0.020–0.040 | 8.61 ± 0.21 ± 0.61 | 8.17 ± 0.50 ± 0.71 | 0.020–0.040 | 4.80 ± 1.30 ± 0.68 |
0.040–0.060 | 10.10 ± 0.22 ± 0.41 | 9.15 ± 0.48 ± 0.51 | 0.040–0.060 | 8.03 ± 1.84 ± 1.08 |
0.060–0.080 | 7.50 ± 0.19 ± 0.16 | 6.73 ± 0.37 ± 0.18 | 0.060–0.080 | 7.47 ± 1.53 ± 0.64 |
0.080–0.100 | 5.58 ± 0.16 ± 0.18 | 6.03 ± 0.33 ± 0.37 | 0.080–0.100 | 5.85 ± 1.27 ± 0.70 |
0.100–0.120 | 4.17 ± 0.15 ± 0.18 | 4.18 ± 0.27 ± 0.39 | 0.100–0.120 | 4.83 ± 1.26 ± 0.91 |
0.120–0.140 | 3.22 ± 0.13 ± 0.22 | 3.37 ± 0.24 ± 0.46 | 0.120–0.140 | 4.15 ± 1.12 ± 0.54 |
0.140–0.160 | 2.43 ± 0.12 ± 0.19 | 2.43 ± 0.23 ± 0.17 | 0.140–0.160 | 3.62 ± 1.05 ± 1.20 |
0.160–0.180 | 2.01 ± 0.12 ± 0.16 | 2.27 ± 0.22 ± 0.16 | 0.160–0.200 | 2.27 ± 0.67 ± 0.47 |
0.180–0.200 | 1.54 ± 0.12 ± 0.19 | 1.46 ± 0.22 ± 0.22 | 0.200–0.240 | 1.28 ± 0.63 ± 0.49 |
0.200–0.240 | 1.24 ± 0.10 ± 0.12 | 1.52 ± 0.19 ± 0.22 | 0.240–0.280 | 1.58 ± 0.72 ± 0.40 |
0.240–0.280 | 0.53 ± 0.10 ± 0.15 | 0.63 ± 0.18 ± 0.17 | 0.280–0.320 | 0.30 ± 0.21 ± 0.21 |
0.280–0.320 | 0.16 ± 0.07 ± 0.07 | 0.50 ± 0.14 ± 0.18 | 0.320–0.360 | 0.10 ± 0.10 ± 0.07 |
0.320–0.360 | 0.11 ± 0.05 ± 0.06 | 0.12 ± 0.07 ± 0.13 | ||
0.360–0.400 | 0.01 ± 0.01 ± 0.01 | 0.01 ± 0.01 ± 0.01 | ||
First Moment | 0.093 ± 0.001 ± 0.004 | 0.100 ± 0.002 ± 0.004 | 0.114 ± 0.007 ± 0.008 | |
Second Moment | 0.013 ± 0.001 ± 0.001 | 0.015 ± 0.001 ± 0.001 | 0.018 ± 0.002 ± 0.003 |
Differential distribution and first and second moments for wide jet broadening at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
B _{W} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{W}}}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{W}}}$ (Non-b) | B _{W} | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{B}_{\text{W}}}$ (b) |
---|---|---|---|---|
0.000–0.015 | 2.57 ± 0.12 ± 0.55 | 2.39 ± 0.27 ± 0.78 | 0.000–0.015 | 1.02 ± 0.51 ± 0.73 |
0.015–0.030 | 14.86 ± 0.32 ± 0.92 | 13.29 ± 0.72 ± 0.76 | 0.015–0.030 | 12.33 ± 2.56 ± 1.19 |
0.030–0.045 | 12.25 ± 0.27 ± 0.80 | 11.28 ± 0.59 ± 1.07 | 0.030–0.045 | 8.81 ± 1.91 ± 1.18 |
0.045–0.060 | 8.61 ± 0.24 ± 0.27 | 8.74 ± 0.49 ± 0.43 | 0.045–0.060 | 9.78 ± 2.00 ± 1.45 |
0.060–0.075 | 6.49 ± 0.21 ± 0.25 | 6.87 ± 0.42 ± 0.49 | 0.060–0.075 | 6.70 ± 1.72 ± 0.95 |
0.075–0.090 | 5.06 ± 0.20 ± 0.27 | 5.19 ± 0.36 ± 0.19 | 0.075–0.090 | 4.46 ± 1.30 ± 0.63 |
0.090–0.105 | 3.53 ± 0.17 ± 0.40 | 3.53 ± 0.31 ± 0.63 | 0.090–0.105 | 2.68 ± 0.98 ± 1.33 |
0.105–0.120 | 3.03 ± 0.17 ± 0.19 | 3.36 ± 0.31 ± 0.25 | 0.105–0.120 | 7.14 ± 1.87 ± 2.32 |
0.120–0.135 | 2.24 ± 0.16 ± 0.36 | 2.45 ± 0.29 ± 0.31 | 0.120–0.150 | 2.19 ± 0.74 ± 0.67 |
0.135–0.150 | 2.10 ± 0.16 ± 0.26 | 2.16 ± 0.30 ± 0.38 | 0.150–0.180 | 1.50 ± 0.64 ± 0.77 |
0.150–0.180 | 1.31 ± 0.11 ± 0.21 | 1.49 ± 0.19 ± 0.24 | 0.180–0.210 | 1.68 ± 0.67 ± 0.55 |
0.180–0.210 | 0.94 ± 0.11 ± 0.07 | 1.10 ± 0.19 ± 0.17 | 0.210–0.240 | 0.59 ± 0.49 ± 0.25 |
0.210–0.240 | 0.37 ± 0.10 ± 0.10 | 0.53 ± 0.17 ± 0.22 | 0.240–0.270 | 0.79 ± 0.39 ± 0.36 |
0.240–0.270 | 0.27 ± 0.07 ± 0.04 | 0.42 ± 0.14 ± 0.13 | 0.270–0.300 | 0.13 ± 0.13 ± 0.10 |
0.270–0.300 | 0.07 ± 0.03 ± 0.03 | 0.16 ± 0.06 ± 0.04 | ||
First Moment | 0.068 ± 0.001 ± 0.003 | 0.073 ± 0.002 ± 0.003 | 0.083 ± 0.005 ± 0.006 | |
Second Moment | 0.007 ± 0.001 ± 0.001 | 0.009 ± 0.001 ± 0.001 | 0.010 ± 0.001 ± 0.001 |
Differential distribution and first and second moments for C-parameter at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
C-parameter | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}C}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}C}$ (Non-b) | C-parameter | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}C}$ (b) |
---|---|---|---|---|
0.000–0.050 | 1.98 ± 0.07 ± 0.21 | 1.66 ± 0.13 ± 0.29 | 0.000–0.050 | 1.68 ± 0.48 ± 0.37 |
0.050–0.100 | 4.80 ± 0.10 ± 0.29 | 4.45 ± 0.22 ± 0.23 | 0.050–0.100 | 2.82 ± 0.68 ± 0.40 |
0.100–0.150 | 3.10 ± 0.08 ± 0.13 | 2.84 ± 0.16 ± 0.22 | 0.100–0.150 | 3.21 ± 0.64 ± 0.29 |
0.150–0.200 | 1.95 ± 0.06 ± 0.07 | 1.92 ± 0.12 ± 0.18 | 0.150–0.200 | 2.18 ± 0.52 ± 0.48 |
0.200–0.250 | 1.64 ± 0.06 ± 0.06 | 1.66 ± 0.11 ± 0.08 | 0.200–0.250 | 1.45 ± 0.42 ± 0.43 |
0.250–0.300 | 1.23 ± 0.05 ± 0.05 | 1.34 ± 0.10 ± 0.14 | 0.250–0.300 | 1.49 ± 0.41 ± 0.32 |
0.300–0.350 | 0.97 ± 0.05 ± 0.04 | 0.96 ± 0.08 ± 0.11 | 0.300–0.350 | 1.12 ± 0.33 ± 0.19 |
0.350–0.400 | 0.85 ± 0.05 ± 0.09 | 0.95 ± 0.09 ± 0.09 | 0.350–0.400 | 1.04 ± 0.36 ± 0.40 |
0.400–0.450 | 0.64 ± 0.04 ± 0.04 | 0.74 ± 0.08 ± 0.07 | 0.400–0.500 | 0.72 ± 0.23 ± 0.16 |
0.450–0.500 | 0.59 ± 0.04 ± 0.05 | 0.53 ± 0.07 ± 0.07 | 0.500–0.600 | 0.80 ± 0.26 ± 0.18 |
0.500–0.600 | 0.48 ± 0.03 ± 0.05 | 0.53 ± 0.06 ± 0.07 | 0.600–0.700 | 0.34 ± 0.19 ± 0.14 |
0.600–0.700 | 0.41 ± 0.04 ± 0.03 | 0.47 ± 0.07 ± 0.09 | 0.700–0.850 | 0.44 ± 0.16 ± 0.14 |
0.700–0.850 | 0.15 ± 0.03 ± 0.03 | 0.31 ± 0.07 ± 0.05 | ||
0.850–1.000 | 0.01 ± 0.01 ± 0.01 | 0.01 ± 0.01 ± 0.01 | ||
First Moment | 0.222 ± 0.004 ± 0.014 | 0.248 ± 0.007 ± 0.011 | 0.271 ± 0.019 ± 0.028 | |
Second Moment | 0.084 ± 0.003 ± 0.010 | 0.104 ± 0.006 ± 0.008 | 0.117 ± 0.015 ± 0.026 |
Differential distribution and first and second moments for 3-jet resolution parameter (${y}_{23}^{\text{J}}$) in Jade algorithm at $\u3008\sqrt{s}\u3009$ = 197 GeV for all, non-b and b events.
${y}_{23}^{\text{J}}$ | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{y}_{23}^{\text{J}}}$ (All) | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{y}_{23}^{\text{J}}}$ (Non-b) | ${y}_{23}^{\text{J}}$ | $\frac{1}{\sigma}\cdot \frac{\text{d}\sigma}{\text{d}{y}_{23}^{\text{J}}}$ (b) |
---|---|---|---|---|
0.000–0.012 | 37.89 ± 0.62 ± 3.70 | 33.51 ± 1.30 ± 3.25 | 0.000–0.012 | 29.89 ± 4.75 ± 4.44 |
0.012–0.024 | 12.82 ± 0.31 ± 0.75 | 13.47 ± 0.65 ± 0.81 | 0.012–0.024 | 11.72 ± 2.48 ± 0.96 |
0.024–0.036 | 7.04 ± 0.24 ± 0.56 | 7.34 ± 0.47 ± 0.58 | 0.024–0.036 | 6.41 ± 1.68 ± 1.03 |
0.036–0.048 | 4.93 ± 0.20 ± 0.47 | 5.18 ± 0.40 ± 0.54 | 0.036–0.048 | 6.03 ± 1.62 ± 1.66 |
0.048–0.060 | 3.63 ± 0.18 ± 0.49 | 3.82 ± 0.35 ± 0.74 | 0.048–0.060 | 4.07 ± 1.24 ± 1.15 |
0.060–0.072 | 2.73 ± 0.16 ± 0.35 | 3.21 ± 0.32 ± 0.37 | 0.060–0.072 | 4.19 ± 1.33 ± 0.95 |
0.072–0.084 | 2.12 ± 0.15 ± 0.26 | 2.20 ± 0.28 ± 0.32 | 0.072–0.084 | 1.54 ± 0.71 ± 0.55 |
0.084–0.096 | 2.01 ± 0.15 ± 0.24 | 2.29 ± 0.27 ± 0.34 | 0.084–0.096 | 1.91 ± 1.04 ± 0.57 |
0.096–0.108 | 1.66 ± 0.14 ± 0.20 | 1.97 ± 0.27 ± 0.24 | 0.096–0.120 | 2.22 ± 0.74 ± 0.62 |
0.108–0.120 | 1.14 ± 0.13 ± 0.31 | 1.14 ± 0.23 ± 0.30 | 0.120–0.144 | 1.67 ± 0.68 ± 0.80 |
0.120–0.144 | 1.26 ± 0.10 ± 0.11 | 1.39 ± 0.18 ± 0.13 | 0.144–0.168 | 1.74 ± 0.74 ± 0.75 |
0.144–0.168 | 0.69 ± 0.09 ± 0.11 | 0.82 ± 0.17 ± 0.15 | 0.168–0.204 | 0.89 ± 0.45 ± 0.50 |
0.168–0.204 | 0.47 ± 0.08 ± 0.08 | 0.72 ± 0.14 ± 0.18 | 0.204–0.252 | 0.55 ± 0.31 ± 0.22 |
0.204–0.252 | 0.31 ± 0.06 ± 0.06 | 0.41 ± 0.12 ± 0.10 | 0.252–0.300 | 0.35 ± 0.19 ± 0.15 |
0.252–0.300 | 0.21 ± 0.05 ± 0.04 | 0.24 ± 0.08 ± 0.08 | ||
First Moment | 0.044 ± 0.001 ± 0.003 | 0.048 ± 0.002 ± 0.003 | 0.060 ± 0.006 ± 0.008 | |
Second Moment | 0.005 ± 0.001 ± 0.001 | 0.006 ± 0.001 ± 0.001 | 0.008 ± 0.001 ± 0.002 |
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, C-parameter and the 3-jet JADE resolution parameter for all hadronic events, b-events and non-b 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 non-b events are also shown together with predictions from parton shower models. For the b-events in the two-jet region, the model predictions seem to overestimate the data, in particular for the thrust (Figure 4a), wide jet broadening (Figure 7a) and C-parameter (Figure 8a) distributions.
Comparison of different parton shower models with the data at $\u3008\sqrt{s}\u3009$ = 197 GeV for all events, non-b events and b events for the six event-shape variables.
Event Sample | Model | T | ρ _{H} | B _{T} | B _{W} | C | ${y}_{23}^{\text{J}}$ | |
---|---|---|---|---|---|---|---|---|
All events | JETSET | χ^{2}/d.o.f. | 7.7/12 | 6.9/14 | 10.2/15 | 7.4/15 | 10.4/14 | 9.7/15 |
C.L. | 0.74 | 0.91 | 0.75 | 0.92 | 0.66 | 0.79 | ||
HERWIG | χ^{2}/d.o.f. | 9.0/12 | 8.5/14 | 10.1/15 | 9.9/15 | 14.9/14 | 9.7/15 | |
C.L. | 0.62 | 0.81 | 0.75 | 0.77 | 0.32 | 0.78 | ||
ARIADNE | χ^{2}/d.o.f. | 6.9/12 | 7.6/14 | 6.4/15 | 9.0/15 | 12.5/14 | 9.7/15 | |
C.L. | 0.80 | 0.87 | 0.95 | 0.83 | 0.48 | 0.78 | ||
Non-b events | JETSET | χ^{2}/d.o.f. | 15.1/12 | 12.3/14 | 20.1/15 | 17.5/15 | 16.8/14 | 12.6/15 |
C.L. | 0.18 | 0.50 | 0.13 | 0.23 | 0.21 | 0.56 | ||
HERWIG | χ^{2}/d.o.f. | 15.1/12 | 12.3/14 | 20.1/15 | 20.5/15 | 17.0/14 | 12.3/15 | |
C.L. | 0.18 | 0.50 | 0.13 | 0.11 | 0.20 | 0.58 | ||
ARIADNE | χ^{2}/d.o.f. | 13.4/12 | 12.9/14 | 16.1/15 | 19.7/15 | 14.8/14 | 10.3/15 | |
C.L. | 0.27 | 0.46 | 0.31 | 0.14 | 0.32 | 0.74 | ||
b events | JETSET | χ^{2}/d.o.f. | 11.1/9 | 11.6/13 | 12.8/13 | 11.8/14 | 12.5/12 | 12.1/14 |
C.L. | 0.20 | 0.48 | 0.38 | 0.55 | 0.33 | 0.52 | ||
HERWIG | χ^{2}/d.o.f. | 11.5/9 | 10.6/13 | 14.5/13 | 13.7/14 | 11.0/12 | 11.9/14 | |
C.L. | 0.18 | 0.56 | 0.27 | 0.40 | 0.45 | 0.54 | ||
ARIADNE | χ^{2}/d.o.f. | 10.0/9 | 11.0/13 | 13.6/13 | 13.4/14 | 10.7/12 | 10.1/14 | |
C.L. | 0.27 | 0.53 | 0.32 | 0.42 | 0.47 | 0.68 |
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 non-b 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 b-quark 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. Aguilar-Benitez^{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. Fesefeldt^{1}, E. Fiandrini^{33}, J. H. Field^{20}, F. Filthaut^{31}, P. H. Fisher^{13}, W. Fisher^{37}, G. Forconi^{13}, K. Freudenreich^{49}, C. Furetta^{27}, Yu. Galaktionov^{28,13}, S. N. Ganguli^{9}, P. Garcia-Abia^{25}, M. Gataullin^{32}, S. Gentile^{39}, S. Giagu^{39}, Z. F. Gong^{22}, G. Grenier^{24}, O. Grimm^{49}, M. W. Gruenewald^{16}, V. K. Gupta^{37}, A. Gurtu^{9}, L. J. Gutay^{46}, D. Haas^{5}, D. Hatzifotiadou^{8}, T. Hebbeker^{1}, A. Hervé^{18}, J. Hirschfelder^{35}, H. Hofer^{49}, M. Hohlmann^{26}, G. Holzner^{49}, S. R. Hou^{44}, B. N. Jin^{7}, P. Jindal^{14}, L. W. Jones^{4}, P. de Jong^{2}, I. Josa-Mutuberria^{25}, M. Kaur^{14}, M. N. Kienzle-Focacci^{20}, J. K. Kim^{43}, J. Kirkby^{18}, W. Kittel^{31}, A. Klimentov^{13,28}, A. C. König^{31}, M. Kopal^{46}, V. Koutsenko^{13,28}, M. Kräber^{49}, R. W. Kraemer^{35}, A. Krüger^{48}, A. Kunin^{13}, P. Ladron de Guevara^{25}, I. Laktineh^{24}, G. Landi^{17}, M. Lebeau^{18}, A. Lebedev^{13}, P. Lebrun^{24}, P. 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. Nessi-Tedaldi^{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. Perret-Gallix^{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. Rahal-Callot^{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. Rosier-Lees^{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, D-52056 Aachen, Germany.
^{2}National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands.
^{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}UCD School of 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 Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, F-69622 Villeurbanne, France.
^{25}Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 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 Università 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}Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 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.
Declarations
Authors’ Affiliations
References
- Fritzsch H, Gell-Mann M, Leytwyler H: Phys Lett. 1973, B47: 365-View ArticleADSGoogle Scholar
- Weinberg S: Phys Rev Lett. 1973, 31: 494-10.1103/PhysRevLett.31.494.View ArticleADSGoogle Scholar
- Gross DJ, Wilczek F: Phys Rev Lett. 1973, 30: 1343-10.1103/PhysRevLett.30.1343.View ArticleADSGoogle Scholar
- Gross DJ, Wilczek F: Phys Rev. 1973, D8: 3633-ADSGoogle Scholar
- Politzer HD: Phys Rev Lett. 1973, 30: 1346-10.1103/PhysRevLett.30.1346.View ArticleADSGoogle Scholar
- Ellis RK, Stirling WJ, Webber BR: QCD and Collider Physics. 1996, Cambridge University PressView ArticleGoogle Scholar
- L3 Collaboration, Adeva B, et al: Nucl Inst Meth. 1990, A289: 35-ADSGoogle Scholar
- Chemarin M, Depasse P, Fay J, Felcini M, Fredj L, Ille B, Nessi-Tedaldi F, Susinno GF: Nucl Inst Meth. 1994, A349: 345-View ArticleADSGoogle Scholar
- Brock IC, Engler A, Ferguson T, Filthaut F, Kraemer RW, Merk M, Rippich C, Shi X, Shukla J, Sutton RB, Tsipolitis G, Vogel H, You J, Lecoq P, Bobbink GJ, Buskens J, Cerjak I, Groenstege H, Koffeman E, Linde FL, Raven G, Rewiersma P, Schuijlenberg HWA, de Waard A, Commichau V, Hangarter K, Schmitz P: Nucl Inst Meth. 1996, A381: 236-View ArticleADSGoogle Scholar
- Anderhub H, Beissel F, Betev B, Biland A, Böhm A, Bourilkov D, Camps C, Commichau V, Djambazov L, Göttlicher P, Hangarter K, Hofer H, Holzner A, Horisberger U, Kopp A, Leiste R, Lohmann W, Lustermann W, Mnich J, Paus C, Pohl M, Rahal G, Röser U, Sassowsky M, Schäfer C, Schmidt-Kärst AS, Schmitz P, Spickermann T, Straessner A, Suter H, Szczesny H, Viertel G, Vogt H, Von Gunten HP, Waldmeier S, Weber M, Wienemann P: Nucl Inst Meth. 2003, A515: 31-View ArticleADSGoogle Scholar
- L3 Collaboration, Achard P, et al: Physics Reports. 2004, 399: 71-ADSGoogle Scholar
- ALEPH Collaboration, Heister A, et al: European Physics Journal. 2004, C35: 457-View ArticleADSGoogle Scholar
- DELPHI Collaboration, Abdallah J, et al: European Physics Journal. 2004, C37: 1-10.1140/epjc/s2004-02011-4.ADSGoogle Scholar
- OPAL Collaboration, Abbiendi G, et al: European Physics Journal. 2005, C40: 287-View ArticleADSGoogle Scholar
- Dissertori G, Gehrmann-De Ridder A, Gehrmann T, Glover EWN, Heinrich G, Stenzel H: JHEP. 2008, 02: 040-10.1088/1126-6708/2008/02/040.View ArticleADSGoogle Scholar
- OPAL Collaboration, Akers R, et al: Z Physik. 1995, C65: 31-ADSGoogle Scholar
- Brand S, Peyrou Ch, Sosnowski R, Wroblewski A: Phys Lett. 1964, 12: 57-View ArticleADSGoogle Scholar
- Fahri E: Phys Rev Lett. 1977, 39: 1587-10.1103/PhysRevLett.39.1587.View ArticleADSGoogle Scholar
- Chandramohan T, Clavelli L: Nucl Phys. 1981, B184: 365-10.1016/0550-3213(81)90224-8.View ArticleADSGoogle Scholar
- MARK-II Collaboration, Peterson A, et al: Phys Rev. 1998, D37: 1-Google Scholar
- TASSO Collaboration, Barber DP, et al: Z Physik. 1989, C45: 11-Google Scholar
- Catani S, Turnock G, Webber BR: Phys Lett. 1991, B295: 269-ADSGoogle Scholar
- Dokshitzer Yu, Lucenti A, Marchesini G, Salam GP: Journal of High Energy Physics. 1998, 01: 11-10.1088/1126-6708/1998/01/011.View ArticleADSGoogle Scholar
- Parisi G: Phys Lett. 1978, B74: 65-ADSMathSciNetGoogle Scholar
- Donoghue JF, Low FE, Pi SY: Phys Rev. 1979, D20: 2759-ADSGoogle Scholar
- JADE Collaboration, Bartel W, et al: Z Physik. 1986, C33: 23-Google Scholar
- JADE Collaboration, Bethke S, et al: Phys Lett. 1988, B213: 235-ADSGoogle Scholar
- JETSET 7.4 Monte Carlo Program, Sjöstrand T: Comp Phys Comm. 1994, 82: 74-10.1016/0010-4655(94)90132-5.View ArticleGoogle Scholar
- ARIADNE Monte Carlo Program, Lönnblad L: Comp Phys Comm. 1992, 71: 15-10.1016/0010-4655(92)90068-A.View ArticleGoogle Scholar
- HERWIG 5.9 Monte Carlo Program, Marchesini G, Webber BR: Nucl Phys. 1988, B310: 461-Google Scholar
- Knowles IG: Nucl Phys. 1988, B310: 571-10.1016/0550-3213(88)90092-2.View ArticleADSGoogle Scholar
- Marchesini G, Webber BR, Abbie G: Comp Phys Comm. 1992, 67: 465-10.1016/0010-4655(92)90055-4.View ArticleADSGoogle Scholar
- Gribov VN, Lipatov LN: Sov J Nucl Phys. 1972, 15: 438-Google Scholar
- Gribov VN, Lipatov LN: Sov J Nucl Phys. 1972, 15: 675-Google Scholar
- Dokshitzer Yu: Sov J Phys JETP. 1977, 46: 641-ADSGoogle Scholar
- Altarelli G, Parisi G: Nucl Phys. 1977, B126: 298-10.1016/0550-3213(77)90384-4.View ArticleADSGoogle Scholar
- Konishi K, Ukawa A, Veneziano G: Nucl Phys. 1979, B157: 45-10.1016/0550-3213(79)90053-1.View ArticleADSMathSciNetGoogle Scholar
- Odorico R: Nucl Phys. 1980, B172: 157-10.1016/0550-3213(80)90165-0.View ArticleADSGoogle Scholar
- Fox GC, Wolfram S: Nucl Phys. 1980, B168: 285-10.1016/0550-3213(80)90111-X.View ArticleADSGoogle Scholar
- Gottschalk TD: Nucl Phys. 1983, B214: 201-10.1016/0550-3213(83)90658-2.View ArticleADSGoogle Scholar
- Marchesini G, Webber BR: Nucl Phys. 1984, B238: 1-10.1016/0550-3213(84)90463-2.View ArticleADSGoogle Scholar
- Mueller AH: Nucl Phys. 1983, B213: 85-10.1016/0550-3213(83)90176-1.View ArticleADSGoogle Scholar
- Dokshitzer Yu, Khoze VA, Troyan SI, Mueller AH: Rev Mod Phys. 1988, 60: 373-10.1103/RevModPhys.60.373.View ArticleADSGoogle Scholar
- Dokshitzer Yu, Khoze VA, Mueller AH, Troyan SI: Basics of Perturbative QCD, Editions Frontières, Gif-sur-Yvette. 1991Google Scholar
- Kalinowski J, Konishi K, Taylor TR: Nucl Phys. 1981, B181: 221-10.1016/0550-3213(81)90351-5.View ArticleADSGoogle Scholar
- Kalinowski J, Konishi K, Scharbach PN, Taylor TR: Nucl Phys. 1981, B181: 253-10.1016/0550-3213(81)90352-7.View ArticleADSGoogle Scholar
- Gunion JF, Kalinowski J: Phys Rev. 1984, D29: 1545-ADSGoogle Scholar
- Gunion JF, Kalinowski J, Szymanowski L: Phys Rev. 1985, D32: 2303-ADSGoogle Scholar
- Andersson B, Gustafson G, Söderberg B: Z Phys. 1983, C20: 317-ADSGoogle Scholar
- Peterson C, Schlatter D, Schmitt I, Zerwas PM: Phys Rev. 1983, D27: 105-ADSGoogle Scholar
- Fox GC, Wolfram F: Phys Rev Lett. 1978, 41: 1581-10.1103/PhysRevLett.41.1581.View ArticleADSGoogle Scholar
- Fox GC, Wolfram F: Nucl Phys. 1979, B149: 413-10.1016/0550-3213(79)90003-8.View ArticleADSGoogle Scholar
- Fox GC, Wolfram F: Phys Lett. 1979, B82: 134-View ArticleADSGoogle Scholar
- MARK-J Collaboration, Barber DP, et al: Phys Lett. 1979, B89: 139-Google Scholar
- PYTHIA 5.7 Monte Carlo Program, Sjöstrand T: CERN-TH-7112/93, revised August 1995. 1993Google Scholar
- KK2F 4.14 Monte Carlo Program, Jadach S, Ward BFL, Wąs Z: Comp Phys Comm. 2000, 130: 260-10.1016/S0010-4655(00)00048-5.View ArticleGoogle Scholar
- Jadach S, Ward BFL, Wąs Z: Phys Rev. 2001, D63: 113009-ADSGoogle Scholar
- Brun R, Bruyant F, Maire M, McPherson A, Zanarini P: The L3 detector simulation is based on GEANT Version 3.15. "GEANT 3", CERN DD/EE/84-1 (Revised). 1987, SeptemberGoogle Scholar
- The GHEISHA program: (H. Fesefeldt, RWTH Aachen Report PITHA 85/02 (1985)) is used to simulate hadronic interactions.Google Scholar
- PHOJET Monte Carlo Program, Engel R: Z Physik. 1995, C66: 1459-Google Scholar
- Engel R, Ranft J, Roesler S: Phys Rev. 1995, D52: 1459-ADSGoogle Scholar
- KORALZ Monte Carlo Program, Jadach S, Ward BFL, Wąs Z: Comp Phys Comm. 1994, 79: 503-10.1016/0010-4655(94)90190-2.View ArticleGoogle Scholar
- BHAGENE Monte Carlo Program, Field JH: Phys Lett. 1994, B323: 432-Google Scholar
- Field JH, Riemann T: Comp Phys Comm. 1996, 94: 53-10.1016/0010-4655(95)00131-X.View ArticleADSGoogle Scholar
- KoralW Monte Carlo Program, Skrzypek M, Jadach S, Placzek W, Wąs Z: Comp Phys Comm. 1996, 94: 216-10.1016/0010-4655(95)00133-6.View ArticleADSGoogle Scholar
- Skrzypek M, Jadach S, Martinez M, Placzek W, Wąs Z: Phys Lett. 1996, B372: 289-View ArticleADSGoogle Scholar
- Dokshitzer Yu: Contribution to the workshop on Jets at LEP and HERA. 1990Google Scholar
- Brown N, Stirling WJ: Rutherford Preprint RAL-91-049.Google Scholar
- Catani S, Dokshitzer Yu, Olsson M, Turnock G: Phys Lett. 1991, B269: 432-View ArticleADSGoogle Scholar
- Bethke S, Kunszt Z, Soper DE, Stirling WJ, Webber BR: Nucl Phys. 1992, B370: 310-10.1016/0550-3213(92)90289-N.View ArticleADSGoogle Scholar
- L3 Collaboration, Acciarri M, et al: Phys Lett. 1997, B411: 373-ADSGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License(http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.