Search for Colour Reconnection Effects in e+e- ->W+W- ->hadrons through Particle-Flow Studies at LEP

A search for colour reconnection effects in hadronic decays of W pairs is performed with the L3 detector at centre-of-mass energies between 189 and 209 GeV. The analysis is based on the study of the particle flow between jets associated to the same W boson and between two different W bosons in qqqq events. The ratio of particle yields in the different interjet regions is found to be sensitive to colour reconnection effects implemented in some hadronisation models. The data are compared to different models with and without such effects. An extreme scenario of colour reconnection is ruled out.


Introduction
According to the string model of hadronisation, the particles produced in the process e + e − → W + W − → hadrons originate, in the absence of colour reconnection, from the fragmentation of two colour singlet strings each of which is stretched between the two quarks from a W boson. In this case the hadrons are uniquely associated to a particular W and there is a direct correspondence between the jets formed by these hadrons and the primary quarks from the W boson decays. Energy-momentum is separately conserved for each of the W systems. However, it has been suggested that interactions may occur between the decay products of the two W bosons [1,2,3,4]. The main justification for this "cross-talk" is the relatively short distance separating the decay vertices of the W bosons produced in e + e − annihilation (≈ 0.1 fm) compared to the typical hadronic scale (1 fm), which implies a large space-time overlap of the two hadronising systems.
The main consequence of these interactions, called Colour Reconnection (CR) effects, is a modification of the distribution in phase space of hadrons. CR effects are thought to be suppressed in the hard perturbative phase, but may be more important in the soft gluon emission regime [2]. While hard gluons, with energy greater than the W width, are radiated independently from different colour singlets, soft gluons could in principle be affected by the colour strings of both decaying W's. Such CR would affect the number of soft particles in specific phase space regions, especially outside the jet cores.
The study of CR is interesting not only for probing QCD dynamics but also for determining a possible bias in the W mass measurement in the four-quark channel. CR could affect the invariant masses of jet pairs originating from W decays. Therefore the precision with which the W mass may be determined using the four-quark channel depends strongly on the understanding of CR effects. Events where only one W decays hadronically are unaffected by CR.
Previous LEP studies of CR, performed at centre-of-mass energy √ s ≤ 183 GeV, were based on charged particle multiplicity and momentum distributions [5]. The analysis presented in this paper uses the method suggested in Reference 6 based on energy and particle flow to probe the string topology of four-quark events to search for particular effects of particle depletion and enhancement. The results are based on 627 pb −1 of data collected with the L3 detector [7] at √ s=189−209 GeV. Comparisons with various models are made at detector level and the compatibility with the existence of CR effects in various models is investigated.

Colour Reconnection Models
Several phenomenological models have been proposed [2,3,8,9,10,11] to describe CR effects in e + e − → W + W − → hadrons events. The analysis presented in this paper is performed with some of those CR models, which are implemented in the PYTHIA [12], ARIADNE [13] and HERWIG [14] Monte Carlo (MC) programs. We investigate two models by Sjöstrand and Khoze [2] implemented in PYTHIA. They are based on rearrangement of the string configuration during the fragmentation process. They follow the space-time evolution of the strings and allow local reconnections if the strings overlap or cross, depending on the string definition (elongated bags or vortex lines).
In the type I model (SKI) the strings are associated with colour flux tubes having a significant transverse extension. The reconnection occurs when these tubes overlap and only one reconnection is allowed, the one with the largest overlap volume. The reconnection probability depends on this volume of overlap and is controlled by one free parameter, k I , which can be varied in the model to generate event samples with different fractions of reconnected events. The relation with the event reconnection probability (P reco ) is given by the following formula: where f is a function of the overlap volume of the two strings, which depends on W-pair kinematics varying with √ s. The default value of k I is 0.6 [2], which corresponds to a reconnection probability of about 30% at √ s=189 GeV. This analysis is performed with three different values of k I : 0.6, 3 and 1000, corresponding to reconnection probabilities at √ s=189 GeV of about 30%, 66% and nearly 100%, respectively.
In the type II model (SKII) the strings have no lateral extent and the reconnection occurs, with unit probability, when they cross. The fraction of reconnected events in this model is of the order of 30% at √ s=189 GeV.
The CR model implemented in ARIADNE is based on reconnection of coloured dipoles before the string fragmentation takes place [9]. In the AR2 scheme, which is investigated here, reconnections are allowed if they reduce the string length. While reconnections within a W are allowed at all scales, those between W's are only allowed after the parton showers have evolved down to gluon energies less than 2 GeV. At √ s =189 GeV they affect about 55% of the events.
The CR scheme implemented in HERWIG is, as for the string fragmentation, a local phenomenon since the cluster fragmentation process follows the space-time development. In this model [10] the clusters are rearranged if their space-time extension is reduced. This rearrangement occurs with a probability equal to 1/N 2 colour , with default value N colour = 3, giving about 23% of reconnected events.
All probabilities discussed above are derived as fraction of events where at least one reconnection occurs either within the same W or between two W's.

Event Selection
The energy measured in the electromagnetic and hadronic calorimeters and in the tracking chamber is used to select e + e − → W + W − → hadrons events. The total visible energy (E vis ) and the energy imbalance parallel (E ) and perpendicular (E ⊥ ) to the beam direction are measured. The number of clusters, defined as objects obtained from a non-linear combination of charged tracks with a transverse momentum greater than 100 MeV and calorimetric clusters with a minimum energy of 100 MeV, is denoted by N cluster . The selection criteria are: In addition the events must have 4 jets reconstructed with the Durham algorithm [15] with y cut = 0.01. To reduce the contamination from semileptonic W decays, events with energetic µ or e are rejected. Events with hard initial state radiation (ISR) are rejected as described in Reference 16. Additional criteria select events with nearly perfect quark-jet association, necessary for the study of particle and energy flow between jets. The two largest interjet angles are required to be between 100 • and 140 • and not adjacent. The two other interjet angles must be less than 100 • . This selection guarantees similar sharing of energy between the four primary partons with the two strings evolving back-to-back and similar interjet regions between the two W's. The above cuts are optimized by studying MC W + W − events at √ s=189 GeV using the KORALW [17] MC generator interfaced with the PYTHIA fragmentation model without CR.
Relaxing the angular criteria increases the efficiency but gives lower probability to have correct W-jet pairing due to the more complicated event topology. The number of selected events, the number of expected events, the selection efficiency and the percentage of correct pairing are given in Table 1. After applying all the cuts the full sample contains 666 events with an average efficiency of 12% and a purity of about 85% for e + e − → W + W − → hadrons. The average probability to have the correct pairing between the W bosons and their associated jets is estimated to be 91%.
The background is composed of qq(γ) events and Z-pair production events, in similar amounts. Background from semileptonic W pair decays is found to be negligible (less than 0.3%). The qq(γ) process is modeled with the KK2F MC program [18], interfaced with JET-SET [19] routines to describe the QCD processes, and the background from Z-pair production is simulated with PYTHIA. For CR studies W-pair events are simulated with PYTHIA. All MC samples are passed through a realistic detector simulation [20] which takes into account time dependent detector effects and inefficiencies.

Particle-and Energy-Flow Distributions
The algorithm to build the particle-and energy-flow distributions [6] (Figure 1) starts by defining the plane spanned by the most energetic jet (jet 1) and the closest jet making an angle with jet 1 greater than 100 • which is most likely associated to the same W (jet 2). For each event, the momentum vector direction of each particle is then projected on to this plane. The particle and energy flows are measured as a function of the angle, φ, between jet 1 and the projected momentum vector for the particles located between jets 1 and 2. In order to take into account the fact that the W-pair events are not planar a new plane is defined for each remaining pair of adjacent jets. In this four-plane configuration the angle φ is defined as increasing from jet 1 toward jet 2, then to the closest jet from the other W (jet 3) toward the remaining jet (jet 4) and back to jet 1. The angle φ j,i of a particle i having a projected momentum vector located between jets j and j + 1 is calculated in the plane spanned by these two jets. A particle i making an angle φ i with respect to jet 1 adds an entry equal to 1 in the particle-flow distribution and adds an entry equal to its energy, normalised to the total event energy, in the energy-flow distribution for the corresponding φ bin.
The distributions are calculated using, for the particle definition, the clusters defined in the previous section. Figure 2 shows the particle-and energy-flow distributions obtained for the data and the MC predictions at detector level by using only the first plane for projecting all the particles. The data and MC distributions agree over the full angular range in both cases.
In order to compare the interjet regions the angles in the planes are rescaled by the angle between the two closest jets. For a particle i located between jets j and j + 1 the rescaled angle is where φ j,i is the angle between jet j and particle i and ψ j,j+1 is the angle between jets j and j + 1. With this definition the four jets have fixed rescaled angle values equal to 0, 1, 2 and 3. Figure 3a shows the rescaled particle-flow distribution normalised to the number of events after a bin-by-bin background subtraction for the data and MC predictions without CR and for the SKI model with k I =1000, later referred to as SKI 100%. As expected, the latter shows some depletion in the number of particles in the intra-W regions spanned by the two W bosons (regions A and B) and some particle enhancement in the two inter-W regions (regions C and D) when compared to the model without CR (no-CR).
To improve the sensitivity to CR effects the particle flows in regions A and B are averaged as are the particle flows in regions C and D. The results are shown in Figures 3b and 3c where the angle is redefined to be in the range [0,1]. MC studies at particle level with particles having a momentum greater than 100 MeV show that the CR effects are consistent with the detector level results and have similar magnitudes. The ratio of the particle flow between the quarks from the same W to that between quarks from different W's is found to be a sensitive observable to cross-talk effects as predicted by the SKI model. These ratios, computed from the particle-and energy-flow distributions at detector level, are shown in Figure 4 for the data, the PYTHIA prediction without CR, the SKI model with k I =3 and SKI 100%.
The differences between the models with and without CR are larger in the middle of the interjet regions. Therefore, in order to quantify the CR effects the ratio R is computed in an interval, 0.2 < φ resc < 0.8, optimized with respect to the sensitivity to SKI 100%. The corresponding variables for particle and energy flow are defined as follows: where, in a region i, The measured values of R N and R E obtained at each centre-of-mass energy are summarised in Table 2 An estimate of the sensitivity to the SKI 100% model, shows that R N is 2.6 times more sensitive than R E . Accordingly, the following results and discussion are only based on R N . Figure 5 shows the measured R N as a function of √ s together with PYTHIA no-CR and SKI model predictions. The energy dependence originating from the different pairing purities and jet configurations is in agreement with the model predictions. For the PYTHIA SKI predictions, the ratio decreases with the reconnection probability over the whole energy range with similar magnitude. The data indicate little or no CR.

Semileptonic Decays
To verify the quality of the MC simulation of the W → qq fragmentation process and the possible biases which may arise when determining the particle yields between reconstructed jets in the detector, the particle-and energy-flow distributions are investigated in e + e − → W + W − → qqlν where l = e, µ. For this analysis events are selected with high multiplicity, large missing momentum and a high energy electron or muon. The missing momentum is considered as a fictitious particle in order to apply the Durham jet algorithm to select 4-jet events with y cut =0.01. The same angular criteria on the four interjet angles as applied in the fully hadronic channel are used here. The purity obtained after selection is about 96% and the efficiency is about 12%. The number of selected semileptonic events is 315 with an expectation of 314.5 events. Particleand energy-flow distributions are built in a similar way as in the fully hadronic channel with the additional requirement that the charged lepton should be in jet 3 or 4. Figure 6a shows the corresponding particle-flow distribution projected on to the plane of jets 1 and 2 for the data and the KORALW MC prediction. There is good agreement between data and MC over the whole distribution. Figure 6b shows the rescaled particle-flow distribution where the structure of the two different W's is clearly visible. The region between jet 1 and jet 2 corresponds to the hadronically decaying W (W 1 ) and the region between jet 3 and jet 4 corresponds to the W decaying semileptonically (W 2 ). The activity in the W 2 region is mainly due to low energy fragments from the hadronic decay of the first W. A comparison of data and MC for the particle flow obtained by summing the regions W 1 and W 2 is shown in Figure 7a. The ratio between the data and the MC distributions is shown in Figure 7b. This ratio is consistent with unity over the whole range. This result gives additional confidence in the correctness of the modelling of the fragmentation process of quark pairs according to the fragmentation parameters used in KORALW and PYTHIA as well as the particle flow definition and reconstruction.
In the absence of CR effects, the activity found in regions A+B of a fully hadronic event should be equivalent to twice the particle activity in the regions W 1 +W 2 of the distribution for a semileptonic event. Figure 7c shows the ratio of the particle flow in four-quark events divided by twice the particle flow in semileptonic events for the data and the predictions from no-CR PYTHIA MC and the SKI 100% model. The CR model shows the expected deficit in the hadronic channel compared to the semileptonic one. The data are consistent with the no-CR scheme but the large statistical uncertainty prevents a quantitative statement based on this model-independent comparison.

Systematic Uncertainties
Several sources of systematic uncertainties are investigated. The first important test is whether the result depends on the definition of the particles. The analysis is repeated using calorimetric clusters only. Half the difference between the two analyses is assigned as the uncertainty due to this effect. This is found to be the dominant systematic uncertainty.
The second source of systematic uncertainty is the limited knowledge of quark fragmentation modelling. The systematic effect in the qq(γ) background is estimated by comparing results using the JETSET and HERWIG MC programs. The corresponding uncertainty is assigned to be half the difference between the two models.
The systematic uncertainty from quark fragmentation modelling in W-pair events is estimated by comparing results using PYTHIA, HERWIG and ARIADNE MC samples without CR. The uncertainty is assigned as the RMS between the R N values obtained with the three fragmentation models. Such comparisons between different models test also possible effects of different fragmentation schemes which are not taken into account when varying only fragmentation parameters within one particular model.
Another source associated with fragmentation modelling is the effect of Bose-Einstein correlations (BEC) in hadronic W decays. This effect is estimated by repeating the analysis using a MC sample with BEC only between particles originating from the same W. An uncertainty is assigned equal to half the difference with the default MC which includes full BEC simulation (BE32 option) [21] in W pairs. The sensitivity of the R N variable to BEC is found to be small.
The third main source of systematic uncertainty is the background estimation. The qq(γ) background which is subtracted corresponds mainly to QCD four-jet events for which the rate is not well modelled by parton shower programs. PYTHIA underestimates, by about 10%, the four-jet rate in the selected phase space region [22]. A systematic uncertainty is estimated by varying the qq(γ) cross section by ± 5% after correcting the corresponding background by +5%. This correction increases the value of R N by 0.004.
A last and small systematic uncertainty is associated with Z-pair production. It is estimated by varying the corresponding cross section by ± 10%. This variation takes into account all possible uncertainties pertaining to the hadronic channel, from final state interaction effects to the theoretical knowledge of the hadronic cross section.
A summary of the different contributions to the systematic uncertainty is given in Table 3. The ratio obtained by taking into account the systematic uncertainties is then:

Comparison with Models
The R N values predicted by the PYTHIA no-CR, SKI, SKII, ARIADNE no-CR, AR2, HERWIG no-CR and HERWIG CR models are given in Table 4. The data disfavour extreme scenarios of CR. A comparison with ARIADNE and HERWIG shows that the CR schemes implemented in these two models do not modify significantly the interjet particle activity in the hadronic W-pair decay events. Thus it is not possible to constrain either of these models in the present analysis.
The dependence of R N on the reconnection probability is investigated with the SKI model. For this, four MC samples are used: the no-CR sample and those with k I =0.6, 3 and 1000. In the SKI model the fraction of reconnected events is controlled by the k I parameter and the dependence of R N on k I is parametrized as R N (k I ) = p 1 (1 − exp(−p 2 k I )) + p 3 where p i are free parameters. A χ 2 fit to the data is performed. The χ 2 minimum is at k I = 0.08. This value corresponds to about 6% reconnection probability at √ s=189 GeV. Within the large uncertainty the result is also consistent with no CR effect. The upper limits on k I at 68% and 95% confidence level are derived as 1.            Figure 7: a) Particle-flow distributions as a function of the rescaled angle for the semileptonic W decays for data and the KORALW prediction. b) Ratio of data and MC as a function of the rescaled angle. c) Ratio R of the particle flow in hadronic events divided by twice the particle flow in semileptonic events.