- Email: [email protected]
Colour reconnection effects in WW production at LEP
ELSEVIER
Proceedings of ICHEP 2002, pp. 394–399 S. Bentvelsen, P. de Jong, J. Koch and E. Laenen (Editors)
1
31st INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS AMSTERDAM
Colour Reconnection Effects in WW Production at LEP E. Bouhova-Thackera a
Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
Preliminary results from the search for colour reconnection effects by the four LEP experiments and a first combination of their measurements of the inclusive particle flow distributions in four-jet events are presented. Data are compared with predictions of various models with and without colour reconnection. The extreme scenario of the SKI model, where almost all events are reconnected, is ruled out and a limit on the model parameter, controlling the fraction of reconnected events, is set.
1. W W decays at LEP2 The LEP2 collider at CERN, Geneva ran for five years above the W + W − threshold. During this time each of the four experiments, ALEPH, DELPHI, L3 and OPAL, collected ∼10000 W W pairs in the energy range 161 - 209 GeV. About 46% of the W W pairs decay via the fully hadronic channel (qqqq), 44% via the semi-leptonic (νqq) and 10% via the fully leptonic (νν) channels. The separation of the W decay vertices at LEP2 energies is ∼0.1 fm, which is small compared to the QCD hadronisation scale, ∼1 fm, and there is no reason to assume that the pair hadronise independently. The FSI leading to colour exchange between the decay products of the two W bosons is known as colour reconnection (or rearrangement). Colour reconnection (CR) may affect the multiplicities and the particle kinematics and can lead to an apparent shift in the W mass measured in the fully hadronic channel. Colour reconnection effects in the perturbative phase are expected to be small [1]. On the other hand, significant interference is expected in the hadronisation process, which can be estimated only in the context of specific models. 2. Models of Colour Reconnection The colour reconnection models studied by the LEP experiments are those implemented in the JETSET/PYTHIA, ARIADNE and HERWIG Monte Carlo programs. The Sj¨ostrand-Khoze c 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(02)02215-6
(SK) models [1] are based on the Lund string fragmentation picture. In these models colour reconnection occurs for overlapping or crossing strings stretched between two qq systems. The models cannot be tuned to Z 0 data. In the SKI scenario, the strings have a significant transverse extension, comparable to hadronic dimensions, and the probability of reconnection depends on the volume of overlap, V , i.e. P reco = 1 − exp(−kI V ), where kI is a free parameter. In the SKII scenario, the strings have negligible thickness and a unit reconnection probability upon their first crossing. In SKII reconnection is only allowed to occur at the first string crossing which reduces the total string length of the system. The Generalised Area Law (GAL) model [2], implemented in JETSET, is also based on the Lund string fragmentation model. The reconnection probability for this model is given by P reco = R0 (1 − exp(−b∆A)), where ∆A is the area difference between the two configurations, with and without CR (in energy-momentum coordinates), b is a phenomenological parameter of the order 0.6 GeV−2 and R0 is a tunable parameter of the order 1/NC2 = 0.11. The ARIADNE Monte Carlo program utilises the dipole cascade model [3]. Colour reconnection is implemented at the end of the parton shower if it leads to a reduction in the string length and is suppressed by a factor of 1/NC2 [4]. Multiple reconnections per event are permitted. They may occur within a single qq system (AR1 model). In the AR2 model, applicable to qqqq events, recon-
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Colour reconnection effects in WW production at LEP
nections are only allowed for gluons with energies less than 2 GeV. The AR3 model, which imposes no such restriction, is disfavoured on both theoretical and experimental grounds [5]. An alternative to string fragmentation is the cluster model implemented in HERWIG. After showering the gluons are split non-perturbatively into qq pairs and colour singlet clusters are formed, which then decay into a small number of hadrons. Colour reconnection would change the cluster formation if the cluster size can be reduced [6]. The multiplicity of the decayed cluster depends on the cluster mass, leading to an increase in the multiplicity predicted by the HERWIG CR model with respect to the non-reconnected scenario. In string-based models, on the other hand, colour reconnection tends to minimise the string length, which is correlated with the string energy, and leads to a decrease in multiplicity. The SKI model predicts a W mass shift of up to 250 MeV depending on the reconnection probability. Unless otherwise specified, results are quoted for the extreme case of maximal reconnection probability (referred to as SKI 100%). From theoretical considerations the fraction of reconnected events is expected to be in the range of 30 to 60%. All other models under study predict a much smaller shift, typically of the order of a few tens of MeV. 3. Multiplicity studies - an ALEPH update The effects of colour reconnection on W W charged track multiplicity was among the first signatures probed by the LEP experiments. ALEPH has submitted updated results [7], which include all data in the range 189 - 207 GeV. In the absence of colour reconnection the difference between the charged track multiplicity in fully hadronic (4q) and twice the multiplicity in semi-leptonic (2q) events in data should be consistent with zero. The latest ALEPH result, as well as some earlier results [8] from the other three experiments, are shown in Table 1. The first uncertainty is statistical, the second systematic. The results do not show any evidence for colour reconnection effects. ALEPH also compare the observed data multiplicity to model predictions (see Table 2). In or-
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Table 1 Difference in the charged particle multiplicity in fully hadronic and twice the multiplicity in semileptonic events. √ Experiment s (GeV) 4q − 2(2q) ALEPH∗ 189-207 0.31 ± 0.23 ± 0.10 DELPHI 183-189 −0.26 ± 0.60 ± 0.38 L3 183-189 −0.29 ± 0.26 ± 0.30 OPAL 183-202 0.07 ± 0.39 ± 0.37 ∗ Not corrected for event selection and pT cut of 200 MeV.
Table 2 The double difference ∆cr for some Monte Carlo models without and with colour reconnection. MC Model ∆cr significance JETSET 0.14 ± 0.23 ± 0.1 0.6σ HERWIG 0.14 ± 0.23 ± 0.1 0.6σ ARIADNE 0.10 ± 0.23 ± 0.1 0.4σ SKI 100% 0.35 ± 0.23 ± 0.1 1.4σ SKII 0.20 ± 0.23 ± 0.1 0.8σ 0.24 ± 0.23 ± 0.1 1.0σ SKII HERWIG CR −0.15 ± 0.23 ± 0.1 −0.6σ AR2 0.36 ± 0.23 ± 0.1 1.4σ GAL 0.12 ± 0.23 ± 0.1 0.5σ
der to account for any selection biases, the double difference ∆cr = [4q−2(2q)]data −[4q−2(2q)]MC is constructed. All models are compatible with the data, due to the large uncertainty in the measurements. The largest deviation between data and Monte Carlo is observed in the SKI 100% and AR2 models. The charge particle multiplicities in fully hadronic events as a function of the rescaled mo2p for data and Monte Carlo are mentum Xp = √ s shown in Figure 1. The largest colour reconnection effects are expected in the soft momentum region (p < 1 GeV). No significant effects are observed and the uncertainty on the data points in that region does not allow a distinction between the different models to be made. The bottom plot shows a comparison of different models to JETSET, which has the best fit to data in the full momentum range. HERWIG pro-
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gles between the two jets of a W decay (regions A and B in Figure 2) are in the range 100-140◦ and the angles between jets from different W bosons are < 100◦ . This results in a rather low efficiency (∼14%), but in most events (∼90%) the correct assignment of the two reconstructed jets to a W is made. The W mass analysis selection uses the standard analysis of an experiment for measuring the W mass, which has higher efficiency (40-80%). Each experiment’s analysis [11] varies slightly in the exact method of resolving the ambiguities in constructing the four planes.
1.15 1.1 1.05 1 0.95 0.9 0.85 0.8
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Figure 1. ξ distributions for fully hadronic W W decays for data and different MC models with √ and without colour reconnection, ξ = − ln(2p/ s).
Figure 2. Schematic drawing of the topological selection. The four jets do not lie in a single plane. A and B define the regions between the jets from the same W boson.
vides a relatively better description of data for low momentum tracks, but does not give a very good fit for higher momenta. The string fragmentation models, both with and without colour reconnection, do not describe data in the soft region very well. The same conclusions follow from semi-leptonic events and from studies at the Z 0 peak [9].
The next step is to project all particles onto the planes (Figure 3) and add together the distributions in the four planes to form the particle flow, ensuring that each particle enters the distribution only once. As the angles between the jets vary from event to event, a normalised particle flow (Figure 4) is constructed by rescaling the angles to the angle between the two jets defining the corresponding plane, φr = φ/φj j+1 .
4. The particle flow method Fully hadronic W W events are reconstructed as four-jet events with two jet pairings with invariant mass close to the nominal W mass. The particle flow method [10] aims to study the effects of colour reconnection on the distribution of particles in the regions between jets from the same W and between jets from different W bosons. Two types of selection are used by the experiments. The topological one selects events where the an-
pi
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Jet 4 Jet 1
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Figure 3. Projection of particles onto the four planes defined by pairs of reconstructed jets.
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Colour reconnection effects in WW production at LEP
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Figure 5. The ratio R for data and the SKI model with and without colour reconnection.
Figure 4. Normalised particle flow distribution.
In order to compare the distributions in the regions between jets from the same W to the distributions in the regions between jets from different A+B is formed. Colour W bosons, the ratio R = C+D reconnection leads to an increase in the particle flow in the region between jets from different W bosons as can be seen from Figure 5 for the case of the SKI model. To extract quantitative information, the particle flow is integrated in the most sensitive region before taking the ratio. The observable Rn is then defined as 0.8 dnA dnB 0.2 ( dφr + dφr )dφr . Rn (0.2 − 0.8) = 0.8 dn dnD C 0.2 ( dφr + dφr )dφr The values for the statistical sensitivity, defined as |Rn (model noCR)−Rn (model CR)|/(σRn )stat , where (σRn )stat is the statistical error on the full data sample of each experiment, are shown in Table 3. The Rn observable is sensitive to the predictions of the SKI model but the reconnected and non-reconnected HERWIG and ARIADNE models are only 1σ apart and therefore it would not be possible to distinguish between them using this method. The values are calculated using Monte Carlo samples, generated specifically for
the purposes of LEP combination with ALEPH tuning at the Z 0 peak. The experiments measure Rn at several centreof-mass energies which are combined by determining the energy dependence from non-reconnected JETSET samples and extrapolating all measurements to a single centre-of-mass energy, where a statistically weighted average is taken.
Table 3 Statistical sensitivity of Rn using the full data samples (189 - 208 GeV). Experiment ALEPH DELPHI L3 OPAL
SKI 5.9 3.2 5.0 6.3
HERWIG CR 1.0 0.1 0.0 1.2
AR2 0.9 0.1 0.2 0.4
The values of Rn for data for the four experiments are given in Table 4, where the first uncertainty is statistical, the second systematic and the third is from the extrapolation process. Due to the differences in the analysis methods and the types of events, which are selected, these values cannot be compared directly.
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Table 4 Statistically weighted average values of Rn in data estimated at 189 GeV. Experiment Rn ALEPH 1.095 ± 0.014 ± 0.006 ± 0.006 DELPHI 0.900 ± 0.031 ± 0.015 ± 0.012 L3 0.844 ± 0.022 ± 0.021 ± 0.002 OPAL 1.257 ± 0.025 ± 0.020 ± 0.003
ALEPH DELPHI L3 OPAL LEP 0.969±0.015
5. LEP combination procedure and results The combination of the Rn results [12] is performed with the help of common samples of events, processed by each experiment. For each Rdata n model m, the ratio r = Rm,noCR is formed, where n
Rndata
Rnm,noCR
and are the values of Rn for data and for the common sample without CR of that model. The r values of the four experiments for the model are then combined with weights, given 2 2 + σsyst ), by wm = (Rnm,CR − Rnm,noCR )2 /(σstat where Rnm,CR is the Rn value for the common sample with CR, σstat and σsyst are the total statistical and systematic uncertainties. Figure 6 shows the r measurements of each experiment and the combined LEP result obtained with JETSET SKI 100%. The solid line is the prediction of JETSET without colour reconnection (at 2σ of the total error) and the dashed line is the combined LEP result for the prediction of SKI 100%, which is 5.2σ away from data. The reconnection probability in the SKI model is governed by an arbitrary, free parameter, kI . By comparing data with the model predictions for different values of kI , it is possible to determine the value which is most consistent with data. The LEP combination procedure is repeated several times for each value of kI and the data preferred reconnection probability is found to be 0.49 (kI = 1.18). The 68%CL lower and upper limits on P reco are 0.25 and 0.65, respectively. The upper limit corresponds to a 90 MeV shift in the measured mass of the W in fully hadronic events. The r values obtained with the HERWIG models (Figure 7) with and without colour reconnection differ from the measured data value by 2.6σ and 3.3σ, respectively. The AR2 model is
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Figure 6. Combined particle flow results, testing the SKI model of colour reconnection with maximal fraction of reconnected events.
2.1σ away from data, while the non-reconnected ARIADNE model is 2.9σ away (Figure 8). The dashed lines in the plots are the combined LEP predictions of the CR models. The observed deviations of the r values from all non-reconnected models may indicate a possible systematic effect in the description of particle flow for four-jet events. Table 5 shows the deviation of data Rn from the predictions of some other models of colour reconnection, estimated using the experiment’s own Monte Carlo samples. Table 5 Deviation of data Rn from the predictions of the SKII and GAL models of colour reconnection. Experiment SKII SKII GAL∗ ALEPH -2.01σ -2.32σ -1.65σ L3 -0.16σ − − OPAL -1.05σ -1.18σ − ∗ R0 = 0.004, from a global fit to Z 0 data
6. Conclusions The study of W W multiplicity and momentum distributions does not allow a distinction between the various models of colour reconnection
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Colour reconnection effects in WW production at LEP
DELPHI
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Figure 7. Combined particle flow results, testing the HERWIG model of colour reconnection.
Figure 8. Combined particle flow results, testing the AR2 model of colour reconnection.
to be made. Apart from some earlier successes in the exclusion of more extreme CR models, not discussed here, the measurements are limited by statistics and large systematic uncertainties. The particle flow distribution studies show that the observable Rn is sensitive to colour reconnection in the SKI model. The combined LEP data disfavour by more than 5σ the extreme version of the model with maximal reconnection probability, however the no colour reconnection scenario is not ruled out. The combined data favours the model where about half of the events at 189 GeV are reconnected. The values obtained with HERWIG and ARIADNE models differ from the measured data value by more than 2σ. The differences between the results from the reconnected and nonreconnected scenarios for these models are small and do not allow the particle flow method to distinguish between them.
306 (1988) 746; B. Andersson et al., Z. Phyz. C43 (1989) 625. L. L¨ onnblad, Z.Phys. C70 (1996) 107. OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J.. C 11 (1999) 217. G. Marchesini et al., hep-ph/9607393; G. Corcella et al., CERN-TH/2000-284. ALEPH Collaboration, ALEPH 2002-015, CONF 2002-004, ICHEP02 ABS343. taken from M. Pearson’s talk at Lake Louise Winter Institute, Workshop on Fundamental Interactions, 17-23 February 2002, proceedings to be published by World Scientific. ALEPH Collaboration, CERN-PPE-96-186, Phys. Rept. 294 (1998) 1. D. Duchesneau, preprint LAPP-EXP 200002. ALEPH Collaboration, ALEPH 2002020, CONF 2002-009, ICHEP02 ABS341; DELPHI Collaboration, DELPHI 2002047, CONF 581, ICHEP02 ABS226; L3 Collaboration, L3 Note 2748, ICHEP02 ABS460; OPAL Collaboration, OPAL PN506, ICHEP02 ABS390. The LEP Collaborations and the LEP W Working Group, LEPEWWG/FSI/2002-01, ICHEP02 ABS385.
4. 5. 6. 7. 8.
9. 10. 11.
REFERENCES 1. T. Sj¨ ostrand, V.A. Khoze, Z. Phys. C62 (1994) 281. 2. J. Rathsman, Phys. Lett. B 452 (1999) 364. 3. G. Gustafson, Phys. Lett. B 175 (1986) 453; G. Gustafson, U. Pettersson, Nucl. Phys. B
12.
Proceedings of ICHEP 2002, pp. 394–399 S. Bentvelsen, P. de Jong, J. Koch and E. Laenen (Editors)
1
31st INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS AMSTERDAM
Colour Reconnection Effects in WW Production at LEP E. Bouhova-Thackera a
Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
Preliminary results from the search for colour reconnection effects by the four LEP experiments and a first combination of their measurements of the inclusive particle flow distributions in four-jet events are presented. Data are compared with predictions of various models with and without colour reconnection. The extreme scenario of the SKI model, where almost all events are reconnected, is ruled out and a limit on the model parameter, controlling the fraction of reconnected events, is set.
1. W W decays at LEP2 The LEP2 collider at CERN, Geneva ran for five years above the W + W − threshold. During this time each of the four experiments, ALEPH, DELPHI, L3 and OPAL, collected ∼10000 W W pairs in the energy range 161 - 209 GeV. About 46% of the W W pairs decay via the fully hadronic channel (qqqq), 44% via the semi-leptonic (νqq) and 10% via the fully leptonic (νν) channels. The separation of the W decay vertices at LEP2 energies is ∼0.1 fm, which is small compared to the QCD hadronisation scale, ∼1 fm, and there is no reason to assume that the pair hadronise independently. The FSI leading to colour exchange between the decay products of the two W bosons is known as colour reconnection (or rearrangement). Colour reconnection (CR) may affect the multiplicities and the particle kinematics and can lead to an apparent shift in the W mass measured in the fully hadronic channel. Colour reconnection effects in the perturbative phase are expected to be small [1]. On the other hand, significant interference is expected in the hadronisation process, which can be estimated only in the context of specific models. 2. Models of Colour Reconnection The colour reconnection models studied by the LEP experiments are those implemented in the JETSET/PYTHIA, ARIADNE and HERWIG Monte Carlo programs. The Sj¨ostrand-Khoze c 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0920-5632(02)02215-6
(SK) models [1] are based on the Lund string fragmentation picture. In these models colour reconnection occurs for overlapping or crossing strings stretched between two qq systems. The models cannot be tuned to Z 0 data. In the SKI scenario, the strings have a significant transverse extension, comparable to hadronic dimensions, and the probability of reconnection depends on the volume of overlap, V , i.e. P reco = 1 − exp(−kI V ), where kI is a free parameter. In the SKII scenario, the strings have negligible thickness and a unit reconnection probability upon their first crossing. In SKII reconnection is only allowed to occur at the first string crossing which reduces the total string length of the system. The Generalised Area Law (GAL) model [2], implemented in JETSET, is also based on the Lund string fragmentation model. The reconnection probability for this model is given by P reco = R0 (1 − exp(−b∆A)), where ∆A is the area difference between the two configurations, with and without CR (in energy-momentum coordinates), b is a phenomenological parameter of the order 0.6 GeV−2 and R0 is a tunable parameter of the order 1/NC2 = 0.11. The ARIADNE Monte Carlo program utilises the dipole cascade model [3]. Colour reconnection is implemented at the end of the parton shower if it leads to a reduction in the string length and is suppressed by a factor of 1/NC2 [4]. Multiple reconnections per event are permitted. They may occur within a single qq system (AR1 model). In the AR2 model, applicable to qqqq events, recon-
2
Colour reconnection effects in WW production at LEP
nections are only allowed for gluons with energies less than 2 GeV. The AR3 model, which imposes no such restriction, is disfavoured on both theoretical and experimental grounds [5]. An alternative to string fragmentation is the cluster model implemented in HERWIG. After showering the gluons are split non-perturbatively into qq pairs and colour singlet clusters are formed, which then decay into a small number of hadrons. Colour reconnection would change the cluster formation if the cluster size can be reduced [6]. The multiplicity of the decayed cluster depends on the cluster mass, leading to an increase in the multiplicity predicted by the HERWIG CR model with respect to the non-reconnected scenario. In string-based models, on the other hand, colour reconnection tends to minimise the string length, which is correlated with the string energy, and leads to a decrease in multiplicity. The SKI model predicts a W mass shift of up to 250 MeV depending on the reconnection probability. Unless otherwise specified, results are quoted for the extreme case of maximal reconnection probability (referred to as SKI 100%). From theoretical considerations the fraction of reconnected events is expected to be in the range of 30 to 60%. All other models under study predict a much smaller shift, typically of the order of a few tens of MeV. 3. Multiplicity studies - an ALEPH update The effects of colour reconnection on W W charged track multiplicity was among the first signatures probed by the LEP experiments. ALEPH has submitted updated results [7], which include all data in the range 189 - 207 GeV. In the absence of colour reconnection the difference between the charged track multiplicity in fully hadronic (4q) and twice the multiplicity in semi-leptonic (2q) events in data should be consistent with zero. The latest ALEPH result, as well as some earlier results [8] from the other three experiments, are shown in Table 1. The first uncertainty is statistical, the second systematic. The results do not show any evidence for colour reconnection effects. ALEPH also compare the observed data multiplicity to model predictions (see Table 2). In or-
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Table 1 Difference in the charged particle multiplicity in fully hadronic and twice the multiplicity in semileptonic events. √ Experiment s (GeV) 4q − 2(2q) ALEPH∗ 189-207 0.31 ± 0.23 ± 0.10 DELPHI 183-189 −0.26 ± 0.60 ± 0.38 L3 183-189 −0.29 ± 0.26 ± 0.30 OPAL 183-202 0.07 ± 0.39 ± 0.37 ∗ Not corrected for event selection and pT cut of 200 MeV.
Table 2 The double difference ∆cr for some Monte Carlo models without and with colour reconnection. MC Model ∆cr significance JETSET 0.14 ± 0.23 ± 0.1 0.6σ HERWIG 0.14 ± 0.23 ± 0.1 0.6σ ARIADNE 0.10 ± 0.23 ± 0.1 0.4σ SKI 100% 0.35 ± 0.23 ± 0.1 1.4σ SKII 0.20 ± 0.23 ± 0.1 0.8σ 0.24 ± 0.23 ± 0.1 1.0σ SKII HERWIG CR −0.15 ± 0.23 ± 0.1 −0.6σ AR2 0.36 ± 0.23 ± 0.1 1.4σ GAL 0.12 ± 0.23 ± 0.1 0.5σ
der to account for any selection biases, the double difference ∆cr = [4q−2(2q)]data −[4q−2(2q)]MC is constructed. All models are compatible with the data, due to the large uncertainty in the measurements. The largest deviation between data and Monte Carlo is observed in the SKI 100% and AR2 models. The charge particle multiplicities in fully hadronic events as a function of the rescaled mo2p for data and Monte Carlo are mentum Xp = √ s shown in Figure 1. The largest colour reconnection effects are expected in the soft momentum region (p < 1 GeV). No significant effects are observed and the uncertainty on the data points in that region does not allow a distinction between the different models to be made. The bottom plot shows a comparison of different models to JETSET, which has the best fit to data in the full momentum range. HERWIG pro-
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gles between the two jets of a W decay (regions A and B in Figure 2) are in the range 100-140◦ and the angles between jets from different W bosons are < 100◦ . This results in a rather low efficiency (∼14%), but in most events (∼90%) the correct assignment of the two reconstructed jets to a W is made. The W mass analysis selection uses the standard analysis of an experiment for measuring the W mass, which has higher efficiency (40-80%). Each experiment’s analysis [11] varies slightly in the exact method of resolving the ambiguities in constructing the four planes.
1.15 1.1 1.05 1 0.95 0.9 0.85 0.8
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Figure 1. ξ distributions for fully hadronic W W decays for data and different MC models with √ and without colour reconnection, ξ = − ln(2p/ s).
Figure 2. Schematic drawing of the topological selection. The four jets do not lie in a single plane. A and B define the regions between the jets from the same W boson.
vides a relatively better description of data for low momentum tracks, but does not give a very good fit for higher momenta. The string fragmentation models, both with and without colour reconnection, do not describe data in the soft region very well. The same conclusions follow from semi-leptonic events and from studies at the Z 0 peak [9].
The next step is to project all particles onto the planes (Figure 3) and add together the distributions in the four planes to form the particle flow, ensuring that each particle enters the distribution only once. As the angles between the jets vary from event to event, a normalised particle flow (Figure 4) is constructed by rescaling the angles to the angle between the two jets defining the corresponding plane, φr = φ/φj j+1 .
4. The particle flow method Fully hadronic W W events are reconstructed as four-jet events with two jet pairings with invariant mass close to the nominal W mass. The particle flow method [10] aims to study the effects of colour reconnection on the distribution of particles in the regions between jets from the same W and between jets from different W bosons. Two types of selection are used by the experiments. The topological one selects events where the an-
pi
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Jet 4 Jet 1
Jet 3
φ
Jet 2
Figure 3. Projection of particles onto the four planes defined by pairs of reconstructed jets.
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Figure 5. The ratio R for data and the SKI model with and without colour reconnection.
Figure 4. Normalised particle flow distribution.
In order to compare the distributions in the regions between jets from the same W to the distributions in the regions between jets from different A+B is formed. Colour W bosons, the ratio R = C+D reconnection leads to an increase in the particle flow in the region between jets from different W bosons as can be seen from Figure 5 for the case of the SKI model. To extract quantitative information, the particle flow is integrated in the most sensitive region before taking the ratio. The observable Rn is then defined as 0.8 dnA dnB 0.2 ( dφr + dφr )dφr . Rn (0.2 − 0.8) = 0.8 dn dnD C 0.2 ( dφr + dφr )dφr The values for the statistical sensitivity, defined as |Rn (model noCR)−Rn (model CR)|/(σRn )stat , where (σRn )stat is the statistical error on the full data sample of each experiment, are shown in Table 3. The Rn observable is sensitive to the predictions of the SKI model but the reconnected and non-reconnected HERWIG and ARIADNE models are only 1σ apart and therefore it would not be possible to distinguish between them using this method. The values are calculated using Monte Carlo samples, generated specifically for
the purposes of LEP combination with ALEPH tuning at the Z 0 peak. The experiments measure Rn at several centreof-mass energies which are combined by determining the energy dependence from non-reconnected JETSET samples and extrapolating all measurements to a single centre-of-mass energy, where a statistically weighted average is taken.
Table 3 Statistical sensitivity of Rn using the full data samples (189 - 208 GeV). Experiment ALEPH DELPHI L3 OPAL
SKI 5.9 3.2 5.0 6.3
HERWIG CR 1.0 0.1 0.0 1.2
AR2 0.9 0.1 0.2 0.4
The values of Rn for data for the four experiments are given in Table 4, where the first uncertainty is statistical, the second systematic and the third is from the extrapolation process. Due to the differences in the analysis methods and the types of events, which are selected, these values cannot be compared directly.
398
5
E. Bouhova-Thacker
No CR
SK-I 100%
Table 4 Statistically weighted average values of Rn in data estimated at 189 GeV. Experiment Rn ALEPH 1.095 ± 0.014 ± 0.006 ± 0.006 DELPHI 0.900 ± 0.031 ± 0.015 ± 0.012 L3 0.844 ± 0.022 ± 0.021 ± 0.002 OPAL 1.257 ± 0.025 ± 0.020 ± 0.003
ALEPH DELPHI L3 OPAL LEP 0.969±0.015
5. LEP combination procedure and results The combination of the Rn results [12] is performed with the help of common samples of events, processed by each experiment. For each Rdata n model m, the ratio r = Rm,noCR is formed, where n
Rndata
Rnm,noCR
and are the values of Rn for data and for the common sample without CR of that model. The r values of the four experiments for the model are then combined with weights, given 2 2 + σsyst ), by wm = (Rnm,CR − Rnm,noCR )2 /(σstat where Rnm,CR is the Rn value for the common sample with CR, σstat and σsyst are the total statistical and systematic uncertainties. Figure 6 shows the r measurements of each experiment and the combined LEP result obtained with JETSET SKI 100%. The solid line is the prediction of JETSET without colour reconnection (at 2σ of the total error) and the dashed line is the combined LEP result for the prediction of SKI 100%, which is 5.2σ away from data. The reconnection probability in the SKI model is governed by an arbitrary, free parameter, kI . By comparing data with the model predictions for different values of kI , it is possible to determine the value which is most consistent with data. The LEP combination procedure is repeated several times for each value of kI and the data preferred reconnection probability is found to be 0.49 (kI = 1.18). The 68%CL lower and upper limits on P reco are 0.25 and 0.65, respectively. The upper limit corresponds to a 90 MeV shift in the measured mass of the W in fully hadronic events. The r values obtained with the HERWIG models (Figure 7) with and without colour reconnection differ from the measured data value by 2.6σ and 3.3σ, respectively. The AR2 model is
0.8
1
1.2
1.4
r at 189 GeV
Figure 6. Combined particle flow results, testing the SKI model of colour reconnection with maximal fraction of reconnected events.
2.1σ away from data, while the non-reconnected ARIADNE model is 2.9σ away (Figure 8). The dashed lines in the plots are the combined LEP predictions of the CR models. The observed deviations of the r values from all non-reconnected models may indicate a possible systematic effect in the description of particle flow for four-jet events. Table 5 shows the deviation of data Rn from the predictions of some other models of colour reconnection, estimated using the experiment’s own Monte Carlo samples. Table 5 Deviation of data Rn from the predictions of the SKII and GAL models of colour reconnection. Experiment SKII SKII GAL∗ ALEPH -2.01σ -2.32σ -1.65σ L3 -0.16σ − − OPAL -1.05σ -1.18σ − ∗ R0 = 0.004, from a global fit to Z 0 data
6. Conclusions The study of W W multiplicity and momentum distributions does not allow a distinction between the various models of colour reconnection
6
Colour reconnection effects in WW production at LEP
DELPHI
No CR
ARIADNE-AR2
No CR
HERWIG CR
ALEPH
ALEPH DELPHI
L3
L3
OPAL
OPAL
LEP 0.950±0.015 0.8
1
399
1.2
LEP 0.959±0.014
1.4
0.8
r at 189 GeV
1
1.2
1.4
r at 189 GeV
Figure 7. Combined particle flow results, testing the HERWIG model of colour reconnection.
Figure 8. Combined particle flow results, testing the AR2 model of colour reconnection.
to be made. Apart from some earlier successes in the exclusion of more extreme CR models, not discussed here, the measurements are limited by statistics and large systematic uncertainties. The particle flow distribution studies show that the observable Rn is sensitive to colour reconnection in the SKI model. The combined LEP data disfavour by more than 5σ the extreme version of the model with maximal reconnection probability, however the no colour reconnection scenario is not ruled out. The combined data favours the model where about half of the events at 189 GeV are reconnected. The values obtained with HERWIG and ARIADNE models differ from the measured data value by more than 2σ. The differences between the results from the reconnected and nonreconnected scenarios for these models are small and do not allow the particle flow method to distinguish between them.
306 (1988) 746; B. Andersson et al., Z. Phyz. C43 (1989) 625. L. L¨ onnblad, Z.Phys. C70 (1996) 107. OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J.. C 11 (1999) 217. G. Marchesini et al., hep-ph/9607393; G. Corcella et al., CERN-TH/2000-284. ALEPH Collaboration, ALEPH 2002-015, CONF 2002-004, ICHEP02 ABS343. taken from M. Pearson’s talk at Lake Louise Winter Institute, Workshop on Fundamental Interactions, 17-23 February 2002, proceedings to be published by World Scientific. ALEPH Collaboration, CERN-PPE-96-186, Phys. Rept. 294 (1998) 1. D. Duchesneau, preprint LAPP-EXP 200002. ALEPH Collaboration, ALEPH 2002020, CONF 2002-009, ICHEP02 ABS341; DELPHI Collaboration, DELPHI 2002047, CONF 581, ICHEP02 ABS226; L3 Collaboration, L3 Note 2748, ICHEP02 ABS460; OPAL Collaboration, OPAL PN506, ICHEP02 ABS390. The LEP Collaborations and the LEP W Working Group, LEPEWWG/FSI/2002-01, ICHEP02 ABS385.
4. 5. 6. 7. 8.
9. 10. 11.
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