arXiv:0704.0597v1  [hep-ex]  4 Apr 2007
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN–PH-EP/2006-037
22 November 2006
Investigation of
Colour Reconnection in WW Events
with the DELPHI detector at LEP-2
DELPHI Collaboration
Abstract
In the reaction e+e− → WW → (q1q̄2)(q3q̄4) the usual hadronization models
treat the colour singlets q1q̄2 and q3q̄4 coming from two W bosons indepen-
dently. However, since the final state partons may coexist in space and time,
cross-talk between the two evolving hadronic systems may be possible during
fragmentation through soft gluon exchange. This effect is known as Colour
Reconnection. In this article the results of the investigation of Colour Recon-
nection effects in fully hadronic decays of W pairs in DELPHI at LEP are
presented. Two complementary analyses were performed, studying the particle
flow between jets and W mass estimators, with negligible correlation between
them, and the results were combined and compared to models. In the frame-
work of the SK-I model, the value for its κ parameter most compatible with
the data was found to be:
κSK−I = 2.2
corresponding to the probability of reconnection Preco to be in the range
0.31 < Preco < 0.68 at 68% confidence level with its best value at 0.52.
(Accepted by Eur. Phys. J. C)
http://arxiv.org/abs/0704.0597v1
J.Abdallah26, P.Abreu23, W.Adam55, P.Adzic12, T.Albrecht18, R.Alemany-Fernandez9, T.Allmendinger18, P.P.Allport24,
U.Amaldi30, N.Amapane48, S.Amato52, E.Anashkin37, A.Andreazza29, S.Andringa23, N.Anjos23, P.Antilogus26,
W-D.Apel18, Y.Arnoud15, S.Ask27, B.Asman47, J.E.Augustin26, A.Augustinus9, P.Baillon9, A.Ballestrero49,
P.Bambade21, R.Barbier28, D.Bardin17, G.J.Barker57, A.Baroncelli40, M.Battaglia9, M.Baubillier26, K-H.Becks58,
M.Begalli7, A.Behrmann58, E.Ben-Haim21, N.Benekos33, A.Benvenuti5, C.Berat15, M.Berggren26, L.Berntzon47,
D.Bertrand2, M.Besancon41, N.Besson41, D.Bloch10, M.Blom32, M.Bluj56, M.Bonesini30, M.Boonekamp41,
P.S.L.Booth†24, G.Borisov22, O.Botner53, B.Bouquet21, T.J.V.Bowcock24, I.Boyko17, M.Bracko44, R.Brenner53,
E.Brodet36, P.Bruckman19, J.M.Brunet8, B.Buschbeck55, P.Buschmann58, M.Calvi30, T.Camporesi9, V.Canale39,
F.Carena9, N.Castro23, F.Cavallo5, M.Chapkin43, Ph.Charpentier9, P.Checchia37, R.Chierici9, P.Chliapnikov43,
J.Chudoba9, S.U.Chung9, K.Cieslik19, P.Collins9, R.Contri14, G.Cosme21, F.Cossutti50, M.J.Costa54, D.Crennell38,
J.Cuevas35, J.D’Hondt2, J.Dalmau47, T.da Silva52, W.Da Silva26, G.Della Ricca50, A.De Angelis51, W.De Boer18,
C.De Clercq2, B.De Lotto51 , N.De Maria48, A.De Min37, L.de Paula52, L.Di Ciaccio39, A.Di Simone40, K.Doroba56,
J.Drees58,9, G.Eigen4, T.Ekelof53, M.Ellert53, M.Elsing9, M.C.Espirito Santo23, G.Fanourakis12, D.Fassouliotis12,3,
M.Feindt18, J.Fernandez42 , A.Ferrer54, F.Ferro14, U.Flagmeyer58, H.Foeth9, E.Fokitis33, F.Fulda-Quenzer21, J.Fuster54,
M.Gandelman52, C.Garcia54, Ph.Gavillet9, E.Gazis33, R.Gokieli9,56, B.Golob44,46, G.Gomez-Ceballos42, P.Goncalves23,
E.Graziani40, G.Grosdidier21, K.Grzelak56, J.Guy38, C.Haag18, A.Hallgren53, K.Hamacher58, K.Hamilton36, S.Haug34,
F.Hauler18, V.Hedberg27, M.Hennecke18, H.Herr†9, J.Hoffman56, S-O.Holmgren47, P.J.Holt9, M.A.Houlden24,
J.N.Jackson24, G.Jarlskog27, P.Jarry41, D.Jeans36, E.K.Johansson47, P.D.Johansson47, P.Jonsson28, C.Joram9,
L.Jungermann18, F.Kapusta26, S.Katsanevas28 , E.Katsoufis33, G.Kernel44, B.P.Kersevan44,46, U.Kerzel18, B.T.King24,
N.J.Kjaer9, P.Kluit32, P.Kokkinias12, C.Kourkoumelis3, O.Kouznetsov17, Z.Krumstein17, M.Kucharczyk19, J.Lamsa1,
G.Leder55, F.Ledroit15, L.Leinonen47, R.Leitner31, J.Lemonne2, V.Lepeltier21, T.Lesiak19, W.Liebig58, D.Liko55,
A.Lipniacka47, J.H.Lopes52, J.M.Lopez35, D.Loukas12, P.Lutz41, L.Lyons36, J.MacNaughton55 , A.Malek58, S.Maltezos33,
F.Mandl55, J.Marco42, R.Marco42, B.Marechal52, M.Margoni37, J-C.Marin9, C.Mariotti9, A.Markou12,
C.Martinez-Rivero42, J.Masik13, N.Mastroyiannopoulos12, F.Matorras42, C.Matteuzzi30, F.Mazzucato37 ,
M.Mazzucato37, R.Mc Nulty24, C.Meroni29, E.Migliore48, W.Mitaroff55, U.Mjoernmark27, T.Moa47, M.Moch18,
K.Moenig9,11, R.Monge14, J.Montenegro32 , D.Moraes52, S.Moreno23, P.Morettini14, U.Mueller58, K.Muenich58,
M.Mulders32, L.Mundim7, W.Murray38, B.Muryn20, G.Myatt36, T.Myklebust34, M.Nassiakou12, F.Navarria5,
K.Nawrocki56, R.Nicolaidou41, M.Nikolenko17,10, A.Oblakowska-Mucha20, V.Obraztsov43, A.Olshevski17, A.Onofre23,
R.Orava16, K.Osterberg16, A.Ouraou41, A.Oyanguren54, M.Paganoni30, S.Paiano5, J.P.Palacios24, H.Palka19,
Th.D.Papadopoulou33, L.Pape9, C.Parkes25, F.Parodi14, U.Parzefall9, A.Passeri40, O.Passon58, L.Peralta23,
V.Perepelitsa54, A.Perrotta5, A.Petrolini14, J.Piedra42, L.Pieri40, F.Pierre41, M.Pimenta23, E.Piotto9, T.Podobnik44,46,
V.Poireau9, M.E.Pol6, G.Polok19, V.Pozdniakov17, N.Pukhaeva17 , A.Pullia30, J.Rames13, A.Read34, P.Rebecchi9,
J.Rehn18, D.Reid32, R.Reinhardt58, P.Renton36, F.Richard21, J.Ridky13, M.Rivero42, D.Rodriguez42, A.Romero48,
P.Ronchese37, P.Roudeau21, T.Rovelli5, V.Ruhlmann-Kleider41, D.Ryabtchikov43 , A.Sadovsky17, L.Salmi16, J.Salt54,
C.Sander18, A.Savoy-Navarro26, U.Schwickerath9, R.Sekulin38, M.Siebel58, A.Sisakian17, G.Smadja28, O.Smirnova27,
A.Sokolov43, A.Sopczak22, R.Sosnowski56, T.Spassov9, M.Stanitzki18, A.Stocchi21, J.Strauss55, B.Stugu4,
M.Szczekowski56, M.Szeptycka56 , T.Szumlak20, T.Tabarelli30, A.C.Taffard24, F.Tegenfeldt53 , J.Timmermans32,
L.Tkatchev17 , M.Tobin24, S.Todorovova13, B.Tome23, A.Tonazzo30, P.Tortosa54, P.Travnicek13, D.Treille9, G.Tristram8,
M.Trochimczuk56, C.Troncon29, M-L.Turluer41, I.A.Tyapkin17, P.Tyapkin17, S.Tzamarias12, V.Uvarov43, G.Valenti5,
P.Van Dam32, J.Van Eldik9, N.van Remortel16, I.Van Vulpen9, G.Vegni29, F.Veloso23, W.Venus38, P.Verdier28,
V.Verzi39, D.Vilanova41, L.Vitale50, V.Vrba13, H.Wahlen58, A.J.Washbrook24, C.Weiser18, D.Wicke9, J.Wickens2,
G.Wilkinson36, M.Winter10, M.Witek19, O.Yushchenko43 , A.Zalewska19, P.Zalewski56, D.Zavrtanik45, V.Zhuravlov17,
N.I.Zimin17, A.Zintchenko17 , M.Zupan12
1Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA
2IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium
3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece
4Department of Physics, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway
5Dipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy
6Centro Brasileiro de Pesquisas F́ısicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil
7Inst. de F́ısica, Univ. Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil
8Collège de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France
9CERN, CH-1211 Geneva 23, Switzerland
10Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, FR-67037 Strasbourg Cedex, France
11Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany
12Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece
13FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic
14Dipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy
15Institut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, FR-38026 Grenoble Cedex, France
16Helsinki Institute of Physics and Department of Physical Sciences, P.O. Box 64, FIN-00014 University of Helsinki,
Finland
17Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation
18Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany
19Institute of Nuclear Physics PAN,Ul. Radzikowskiego 152, PL-31142 Krakow, Poland
20Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland
21Université de Paris-Sud, Lab. de l’Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, FR-91405 Orsay Cedex, France
22School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK
23LIP, IST, FCUL - Av. Elias Garcia, 14-1o, PT-1000 Lisboa Codex, Portugal
24Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK
25Dept. of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ
26LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France
27Department of Physics, University of Lund, Sölvegatan 14, SE-223 63 Lund, Sweden
28Université Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France
29Dipartimento di Fisica, Università di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy
30Dipartimento di Fisica, Univ. di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 3, IT-20126 Milan, Italy
31IPNP of MFF, Charles Univ., Areal MFF, V Holesovickach 2, CZ-180 00, Praha 8, Czech Republic
32NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands
33National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece
34Physics Department, University of Oslo, Blindern, NO-0316 Oslo, Norway
35Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spain
36Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
37Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy
38Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK
39Dipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy
40Dipartimento di Fisica, Università di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy
41DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette Cedex, France
42Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain
43Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation
44J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
45Laboratory for Astroparticle Physics, University of Nova Gorica, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia
46Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
47Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden
48Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy
49INFN,Sezione di Torino and Dipartimento di Fisica Teorica, Università di Torino, Via Giuria 1, IT-10125 Turin, Italy
50Dipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy
51Istituto di Fisica, Università di Udine and INFN, IT-33100 Udine, Italy
52Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundão BR-21945-970 Rio de Janeiro, Brazil
53Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden
54IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain
55Institut für Hochenergiephysik, Österr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria
56Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland
57Now at University of Warwick, Coventry CV4 7AL, UK
58Fachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany
† deceased
1 Introduction
The space-time development of a hadronic system is still poorly understood, and
models are necessary to transform a partonic system, governed by perturbative QCD, to
final state hadrons observed in the detectors.
WW events produced in e+e− collisions at LEP-2 constitute a unique laboratory to
study and test the evolution of such hadronic systems, because of the clean environment
and the well-defined initial energy in the process. Of particular interest is the possibility
to study separately one single evolving hadronic system (one of the W bosons decaying
semi-leptonically, the other decaying hadronically), and compare it with two hadronic
systems evolving at the same time (both W bosons decaying hadronically).
Interconnection effects between the products of the hadronic decays of the two W
bosons (in the same event) are expected since the lifetime of the W bosons (τW ≃ ~/ΓW ≃
0.1 fm/c) is an order of magnitude smaller than the typical hadronization times. These
effects can happen at two levels:
• in the evolution of the parton shower, between partons from different hadronic sys-
tems by exchanging coloured gluons [1] (this effect is called Colour Reconnection
(CR) for historical reasons);
• between the final state hadrons, due to quantum-mechanical interference, mainly
due to Bose-Einstein Correlations (BEC) between identical bosons (e.g. pions with
the same charge).
A detailed study by DELPHI of this second effect was recently published [2].
The first effect, the possible presence of colour flow between the two W hadronization
systems, is the topic studied in this paper. This effect is worthy of study in its own right
and for the possible effects induced on the W mass measurement in fully hadronic events
(see for instance [3] for an introduction and [4] for an experimental review).
The effects at the perturbative level are expected to be small [3], whereas they may
be large at the hadronization level (many soft gluons sharing the space-time) for which
models have to be used to compare with the data.
The most tested model is the Sjöstrand-Khoze “Type 1” CR model SK-I [5]. This
model of CR is based on the Lund string fragmentation phenomenology. The strings are
considered as colour flux tubes with some volume, and reconnection occurs when these
tubes overlap. The probability of reconnection in an event is parameterised by the value
κ, set globally by the user, according to the space-time volume overlap of the two strings,
Voverlap :
Preco(κ) = 1− e−κVoverlap . (1)
The parameter κ was introduced in the SK-I model to allow a variation of the percentage
of reconnected events and facilitate studies of sensitivity to the effect. In this model
only one string reconnection per event was allowed. The authors of the model propose
the value of κ = 0.66 to give similar amounts of reconnection as other models of Colour
Reconnection. By comparing the data with the model predictions evaluated at several
κ values, it is possible to determine the value of κ most consistent with the data and
extract the corresponding reconnection probability. Another model was proposed by the
same authors, considering the colour flux tubes as infinitely thin, which allows for Colour
Reconnection in the case the tubes cross each other and provided the total string length
is reduced (SK-II′). This last model was not tested.
Two further models are tested here, these are the models implemented in HERWIG [6]
and ARIADNE [7] Monte Carlo programs. In HERWIG the partons are reconnected, with a
reconnection probability of 1/9, if the reconnection results in a smaller total cluster mass.
In ARIADNE, which implements an adapted version of the Gustafson-Häkkinen model [8],
the model used [9] allows for reconnections between partons originating in the same W
boson, or from different W bosons if they have an energy smaller than the width of the
W boson (this model will be referred as ‘AR-2’).
Colour Reconnection has been previously investigated in DELPHI by comparing in-
clusive distributions of charged particles, such as the charged-particle multiplicity dis-
tribution or the production of identified (heavy) particles, in fully hadronic WW events
and the distributions in semi-leptonic WW events. The investigations did not show any
effect as they were limited by statistical and systematic errors and excluded only the
most extreme models of CR (see [10]).
This article presents the results of the investigations of Colour Reconnection effects in
hadronically decaying W pairs using two techniques. The first, proposed by L3 in [11],
looks at the particle flow between the jets in a 4-jet WW event. The second, proposed
by DELPHI in [12], takes into account the different sensitivity to Colour Reconnection of
several W mass estimators. The first technique is more independent of the model and it
can provide comparisons based on data. The second technique is more dependent on the
model tested, but has a much larger sensitivity to the models SK-I and HERWIG. Since
the particle flow and W mass estimator methods were found to be largely uncorrelated a
combination of the results of these two methods is provided.
The paper is organised as follows. In the next section, the LEP operation and the
components of the DELPHI detector relevant to the analyses are briefly described. In
section 3 data and simulation samples are explained. Then both of the analysis methods
discussed above are described and their results presented in sections 4 and 5. The com-
bination of the results is given in section 6 and conclusions are drawn in the seventh and
final section.
2 LEP Operation and Detector Description
At LEP-2, the second phase of the e+e− collider at CERN, the accelerator was operated
at centre-of-mass energies above the threshold for double W boson production from 1996
to 2000. In this period, the DELPHI experiment collected about 12000 WW events
corresponding to a total integrated luminosity of 661 pb−1. About 46% of the WW
events are WW → q1q̄2q3q̄4 events (fully hadronic), and 44% are WW → q1q̄2ℓν̄, where
ℓ is a lepton (semi-leptonic).
The detailed description of the DELPHI detector and its performance is provided
in [13,14]. A brief summary of the main characteristics of the detector important for the
analyses follows.
The tracking system of DELPHI consisted of a Time Projection Chamber (TPC), the
main tracking device of DELPHI, and was complemented by a Vertex Detector (VD)
closest to the beam pipe, the Inner and the Outer Detectors in the barrel region, and two
Forward Chambers in the end caps. It was embedded in a 1.2 T magnetic field, aligned
parallel to the beam axis.
The electromagnetic calorimeter consisted of the High density Projection Chamber
(HPC) in the barrel region, the Forward Electromagnetic Calorimeter (FEMC) and the
Small angle Tile Calorimeter (STIC) in the forward regions, complemented by detectors to
tag the passage of electron-positron pairs from photons converted in the regions between
the FEMC and the HPC. The total depths of the calorimeters corresponded to about 18
radiation lengths. The hadronic calorimeter was composed of instrumented iron with a
total depth along the shortest trajectory for a neutral particle of 6 interaction lengths,
and covered 98% of the total solid angle. Embedded in the hadronic calorimeter were
two planes of muon drift chambers to tag the passage of muons. The whole detector was
surrounded by a further double plane of staggered muon drift chambers.
For LEP-2, the DELPHI detector was upgraded as described in the following.
Changes were made to some of the subdetectors, the trigger system [15], the run
control and the algorithms used in the offline reconstruction of tracks, which improved
the performance compared to the earlier LEP-1 period.
The major changes were the extensions of the Vertex Detector (VD) and the Inner
Detector (ID), and the inclusion of the Very Forward Tracker (VFT) [16], which increased
the coverage of the silicon tracker to polar angles with respect to the z-axis1 of 11◦ <
θ < 169◦. To further improve the track reconstruction efficiency in the forward regions
of DELPHI, the tracking algorithms and the alignment and calibration procedures were
optimised for LEP-2.
Changes were also made to the electronics of the trigger and timing system which
improved the stability of the running during data taking. The trigger conditions were
optimised for LEP-2 running, to give high efficiency for 2- and 4-fermion processes in the
Standard Model and also to give sensitivity to events which may have been signatures
of new physics. In addition, improvements were made to the operation of the detector
during the LEP operating states, to prepare the detector for data taking at the very start
of stable collisions of the e+e− beams, and to respond to adverse background from LEP
when it arose. These changes led to an overall improvement in the efficiency for collecting
the delivered luminosity from about 85% in 1995, before the start of LEP-2, to about
95% at the end in 2000.
During the operation of the DELPHI detector in 2000 one of the 12 sectors of the
central tracking chamber, the TPC, failed. After 1st September it was not possible to
detect the tracks left by charged particles inside the broken sector. The data affected
corresponds to around 1/4 of the data collected in 2000. Nevertheless, the redundancy of
the tracking system of DELPHI meant that tracks passing through the sector could still
be reconstructed from signals in any of the other tracking detectors. As a result, the track
reconstruction efficiency was only slightly reduced in the region covered by the broken
sector, but the track parameter resolutions were degraded compared with the data taken
prior to the failure of this sector.
3 Data and Simulation Samples
The analyses presented here use the data collected by DELPHI in the years 1997 to
2000, at centre-of-mass energies
s between 183 and 209 GeV. The data collected in the
year 2000 with the TPC working in full, with centre-of-mass energies from 200 to 208
GeV and a integrated luminosity weighted average centre-of-mass energy of 206 GeV, were
analysed together. Data acquired with the TPC with a broken sector, corresponding to a
integrated luminosity weighted average centre-of-mass energy of 207 GeV, were analysed
separately and included in the results presented here.
The total integrated luminosity of the data sample is 660.8 pb−1, and the integrated
luminosity weighted average centre-of-mass energy of the data is 197.1 GeV.
To compare with the expected results from processes in the Standard Model including
or not including CR, Monte Carlo (MC) simulation was used to generate events and
1The DELPHI coordinate system is a right-handed system with the z-axis collinear with the incoming electron beam,
and the x axis pointing to the centre of the LEP accelerator.
simulate the response of the DELPHI detector. These events were reconstructed and
analysed with the same programs as used for the real data.
The 4-fermion final states were generated with the code described in [17], based on
WPHACT [18], for the WW signal (charged currents) and for the ZZ background (neutral
currents), after which the events were fragmented with PYTHIA [19] tuned to DELPHI
data [20]. The same WW events generated at 189, 200 and 206 GeV were also fragmented
with PYTHIA implementing the SK-I model, with 100% reconnection probability. The
systematic effects of fragmentation were studied using the above WW samples and WW
samples generated with WPHACT and fragmented with either ARIADNE [7] or HERWIG [6] at
183, 189, 200 and 206 GeV. For systematic studies of Bose-Einstein Correlations (BEC),
WW samples generated with WPHACT and fragmented with PYTHIA implementing the BE32
model [21] of BEC, were used at all energies, except at 207 GeV. The integrated luminosity
of the simulated samples was at least 10 times that of the data of the corresponding year,
and the majority corresponded to 100 times that of the data.
To test the consistency of the SK-I model and measure the κ parameter, large WW
samples were generated in an early stage of this work with EXCALIBUR [22] at 200 and
206 GeV, keeping only the fully hadronic decays. These samples were then fragmented
with PYTHIA. It was verified for smaller subsets that the results using these large samples
and the samples generated later with WPHACT are compatible.
The qq̄(γ) background events were generated at all energies with KK2f [23] and frag-
mented with PYTHIA. For systematic studies, similar KK2f samples fragmented with
ARIADNE [7] were used at 183, 189, 200 and 206 GeV.
These samples will be referred to as “DELPHI samples”.
At 189 GeV, to compare with the other LEP experiments and with different CR mod-
els, 6 samples generated with KORALW [24] for the 4-fermion final states were also used.
These samples 2 will be referred to as “Cetraro samples”. The events in the different sam-
ples have the final state quarks generated with the same kinematics, and differ only in the
parton shower evolution and fragmentation. Three samples were fragmented respectively
with PYTHIA, ARIADNE and HERWIG (using the tuning of the ALEPH collaboration), with
no CR implementation. Three other samples were fragmented in the same manner but
now implementing several CR models: the SK-I model with 100% reconnection proba-
bility, the AR-2 model, and the HERWIG implementation of CR with 1/9 of reconnected
events, respectively.
4 The Particle Flow Method
The first of the two analyses presented in this paper is based on the so-called “particle
flow method”. The particle flow algorithm is based on the selection of special event
topologies, in order to obtain well defined regions between any two jets originating from
the same W (called the Inside-W region) or from different Ws (called the Between-W
region). It is expected that Colour Reconnection decreases (increases) particle production
in the Inside-W (Between-W) region. Hence, by studying the particle production in the
inter-jet regions it is possible to measure the effects of Colour Reconnection. However,
this method requires a selection of events with a suitable topology (see below) which has
a low efficiency (<∼25%).
2produced by ALEPH after the LEP-W Physics Workshop in Cetraro, Italy, October 2001
4.1 Event and Particle Selection
Events with both Ws decaying into q1q̄2 are characterised by high multiplicity, large
visible energy, and the tendency of the particles to be grouped in 4 jets. The background
is dominated by qq̄(γ) events.
Charged particles were required to have momentum p larger than 100 MeV/c and below
1.5 times the beam energy, a relative error on the momentum measurement ∆p/p < 1,
and polar angle θ with respect to the beam axis between 20◦ and 160◦. To remove tracks
from secondary interactions, the distance of closest approach of the extrapolated track
to the interaction point was required to be less than 4 cm in the plane perpendicular to
the beam axis and less than 4/sin θ cm along the beam axis, and the reconstructed track
length was required to be larger than 30 cm.
Clusters in the electromagnetic or hadronic calorimeters with energy larger than 0.5
GeV and polar angle in the interval 10◦ < θ < 170◦, not associated to charged particles,
were considered as neutral particles.
The events were pre-selected by requiring at least 12 charged particles, with a sum
of the modulus of the momentum transverse to the beam axis, of charged and neutral
particles, above 20% of the centre-of-mass energy. These cuts reduced the contributions
from gamma-gamma processes and beam-gas interactions to a negligible amount. The
momentum distribution of the charged particles for the pre-selected events is shown in
Figure 1 and compared to the expected distribution from the simulation. A good agree-
ment between data and simulation is observed.
DELPHI 189 GeV
WW WPHACT
WW semileptonic
p (GeV/c)
0 5 10 15 20 25 30 35 40 45 50
DELPHI 189 GeV
WW WPHACT
WW semileptonic
p (GeV/c)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Figure 1: Momentum distribution for charged particles (range 0-50 GeV/c (a) and
0-5 GeV/c (b)). Points represent the data and the histograms represent the contributions
from simulation for the different processes (signal (white) and background contributions).
About half of the e+e−→qq̄(γ) events at high-energy are associated with an energetic
photon emitted by one of the beam electrons or positrons (radiative return events), thus
reducing the energy available in the hadronic system to the Z mass. To remove these
radiative return events, the effective centre-of-mass energy
s′, computed as described
in [25], was required to be above 110 GeV. It was verified that this cut does not affect the
signal from W pairs, but reduces significantly the contribution from the qq̄(γ) process.
In the WW fully hadronic decays four well separated energetic jets are expected which
balance the momentum of the event and have a total energy near to the centre-of-mass
energy. The charged and neutral particles in the event were thus clustered using the
DURHAM algorithm [26], for a separation value of ycut = 0.005, and the events were
kept if there were 4 and only 4 jets and a multiplicity (charged plus neutral) in each
jet larger than 3. The combination of these two cuts removed most of the semi-leptonic
WW decays and the 2-jet and 3-jet events of the qq̄(γ) background. The charged-particle
multiplicity distribution for the selected events at 189 GeV is given in Figure 2, with data
points compared to the histogram from simulation of signal and background processes.
0 10 20 30 40 50 60 70 80 90
DELPHI 189 GeV
WW WPHACT
WW semileptonic
Figure 2: Uncorrected charged-particle multiplicity distribution at a centre-of-mass en-
ergy of 189 GeV. Points represent the data and the histograms represent the contribution
from simulation for the different processes.
For the study of the charged-particle flow between jets, the initial quark configuration
should be well reconstructed with a good quark-jet association. At 183 GeV and above,
the produced W bosons are significantly boosted. This produces smaller angles in the
laboratory frame of reference between the jets into which the W decays, when compared
to these angles at threshold (back-to-back). Hence, this property tends to reduce the
ambiguity in the definition of the Between-W and Inside-W regions. The selection criteria
were designed in order to minimize the situation of one jet from one W boson appearing
in the Inside-W region of the other W boson.
The selection criteria are based on the event topology, with cuts in 4 of the 6 jet-jet
angles. The smallest and the second smallest jet-jet angle should be below 100◦ and not
adjacent (not have a common jet). Two other jet-jet angles should be between 100◦ and
140◦ and not adjacent (large angles).
In the case that there are two different combinations of jets satisfying the above criteria
for the large angles, the combination with the highest sum of large angles is chosen. This
selection increases the probability to have a correct pairing of jets to the same W boson.
s L Eff. Pur. Nsel MC tot. WW 4j qq̄(γ) ZZ W lep. εPAIR
183 52.7 22% 74% 127 114.2 84.4 22.3 0.7 7.0 69%
189 157.6 21% 75% 340 341.4 255.9 56.8 2.4 26.4 75%
192 25.9 21% 75% 61 56.1 41.9 9.4 0.4 4.4 77%
196 77.3 19% 74% 176 159.2 117.6 26.2 1.3 14.0 79%
200 83.4 18% 72% 173 165.0 119.5 27.8 1.3 16.4 82%
202 40.6 17% 72% 82 75.7 54.6 12.5 0.7 8.0 82%
206 163.9 15% 70% 282 274.7 193.1 47.8 2.7 31.1 79%
207 59.4 15% 70% 102 99.7 70.1 17.6 1.0 11.1 80%
Table 1: Centre-of-mass energy (
s in GeV), integrated luminosity (L in pb−1), efficiency
and purity of the data samples, number of selected events, number of expected events
from 4-jet WW and background processes (total and separated by process), and efficiency
of correct pairing of jets to the same W boson.
The integrated luminosity, the efficiency to select 4-jet WW events and the purity of
the selected data samples, estimated using simulation, and the number of selected events
are summarised for each centre-of-mass energy in Table 1. The numbers of expected
events are also given separately for the signal and the background processes, and were
estimated using simulation. The efficiency to select the correct pairing of jets to the
same W boson, estimated with simulation as the fraction of WW events for which the
selected jets 1 and 2 (see later) correspond indeed to the same W boson, is given in the
last column of the Table.
The efficiency of the event selection criteria decreases with increasing centre-of-mass
energy. This is primarily due to the ‘large’ angles being reduced as a result of the
increased boost (becoming lower than the cut value of 100◦) and ‘small’ angles being
increased due to the larger phase-space available (becoming higher than the cut value of
100◦). Much for the same reason, the efficiency to assign two jets to the same W boson in
the selected events increases slightly with increasing centre-of-mass energy, in opposition
to what would happen at threshold with the W boson decaying into two back-to-back
jets, that would never be selected to come from the same W boson by the requirement
that their interjet angle should be between 100◦ and 140◦.
In the following analysis the jets and planar regions are labeled as shown in Figure 3:
the planar region corresponding to the smallest jet-jet angle is region B in the plane
made by jets 2 and 3; the second smallest jet-jet angle corresponds to the planar region D
between jets 1 and 4 in the plane made by these two jets; the planar region corresponding
to the greatest of the large jet-jet angles in this combination is region A and spans
the angle between jets 1 and 2 in the plane made by these jets; and finally region C
corresponds to the planar region spanned by the second large angle, between jets 3 and
4 in the plane made by these two jets. In general, the planar regions are not in the same
plane, as the decay planes of the W bosons do not coincide, and the large angles in this
combination are not necessarily the largest jet-jet angles in the event.
The distribution of the reconstructed masses of the jet pairings (1,2) and (3,4), after
applying a 4C kinematic fit requiring energy and momentum conservation, is shown in
Figure 4 (two entries per event). In the figure, data at 189 GeV (points) are compared
to the expected distribution from the 4-jet WW signal without CR, plus background
processes, estimated using the simulation (histograms). The contribution from the 4-jet
Inside-W region
Inside-W region
Between-W region
Between-W region
jet 2
jet 1
jet 3
jet 4
Figure 3: Schematic drawing of the angular selection.
WW signal simulation is split between the case in which the two pairs of jets making the
large angles actually come from their parent W bosons and the case in which the jets of
a pair come from different W bosons (mismatch).
4.2 Particle Flow Distribution
The particle flow analysis uses the number of particles in the Inside-W and the
Between-W regions. An angular ordering of the jets is performed as in Figure 3. The
two large jet-jet angles in the event are used to define the Inside-W regions, and the two
smallest angles span the Between-W regions, the regions between the different Ws.
In general, the two W bosons will not decay in the same plane, and this must be
accounted for when comparing the particle production in the Inside-W and Between-W
regions. So, for each region (A, B, C and D) the particle momenta of all charged particles
are projected onto the plane spanned by the jets of that region: jets 1 and 2 for region
A; jets 2 and 3 for region B; jets 3 and 4 for region C; jets 4 and 1 for region D. Then,
for each particle the rescaled angle Φrescaled is determined as a ratio of two angles:
Φrescaled = Φi/Φr , (2)
when the particle momentum is projected onto the plane of the region r. The angle Φi is
then the angle between the projected particle momentum and the first mentioned jet in
the definition of the regions given above. The angle Φr is the full opening angle between
the jets. Hence Φrescaled varies between 0 and 1 for the particles whose momenta are
projected between the pair of jets defining the plane.
However, due to the aplanarity of the event about 9% of the particles in the data and in
the 4-jet WW simulation have projected angles outside all four regions. These particles
were discarded from further analysis. In the case where a particle could be projected
onto more than one region, with 0 < Φrescaled < 1, the solution with the lower momentum
transverse to the region was used. This happened for about 13% of the particles in data,
after background subtraction, and in the 4-jet WW simulation.
This leads to the normalised particle flow distribution shown in Figure 5 at 189 GeV,
where the rescaled angle of region A is plotted from 0 to 1, region B from 1 to 2, region
0 20 40 60 80 100 120
DELPHI 189 GeV
WW WPHACT
WW wrong pairing
WW semileptonic
Mass (GeV/c
Figure 4: Reconstructed dijet masses (after a 4C kinematic fit) for the selected pairs at
189 GeV (2 entries per event)(see text).
C from 2 to 3 and region D from 3 to 4. The statistical error on the bin contents (the
average multiplicity per bin of Φrescaled divided by the bin width) was estimated using
the Jackknife method [27], to correctly account for correlations between different bins.
In this distribution the regions between the jets coming from the same W bosons (A and
C), and from different W bosons (B and D), have the same scale and thus can be easily
compared.
After subtracting bin-by-bin the expected background from the observed distributions,
we define the Inside-W (Between-W) particle flow as the bin-by-bin sum of regions A and
C (B and D). These distributions are compared by performing the bin-by-bin ratio of
the Inside-W particle flow to the Between-W particle flow. This ratio of distributions is
shown for 189 GeV and 206 GeV in Figure 6. The data points are compared to several
fully simulated WW MC samples with and without CR.
A good agreement was found between the predictions using the WPHACT WW MC sam-
ples and the predictions based on the KORALW WW MC samples, both for the scenario
without CR and for the scenario with CR (SK-I model with 100% probability of recon-
nection). For both sets of predictions the regions of greatest difference between the two
scenarios span the rescaled variable Φrescaled from 0.2 to 0.8.
4.3 Particle Flow Ratio
After summing the particle flow distributions for regions A and C, and regions B and
D, the resulting distributions are integrated from 0.2 to 0.8. The ratio R of the Inside-W
to the Between-W particle flow is then defined as (with Φ being the rescaled variable
Φrescaled):
0 0.5 1 1.5 2 2.5 3 3.5 4
A B C D
DELPHI 189 GeV
WPH. SK-I 100%
WW WPHACT
WW semilept.
Φrescaled
Figure 5: Normalised charged-particle flow at 189 GeV. The lines correspond to the sum
of the simulated 4-jet WW signal with the background contributions (estimated from
DELPHI MC samples), normalised to the total number of expected events (Nevents). The
dashed histogram corresponds to the sum with the simulated 4-jet WW signal generated
by WPHACT with 100% SK-I.
0 0.2 0.4 0.6 0.8 1
Φrescaled
DELPHI 189 GeV
KW. SK-I 100%WPH. SK-I 100%
WW KORALWWW WPHACT
0 0.2 0.4 0.6 0.8 1
Φrescaled
DELPHI 206 GeV
WPH. SK-I 100%
WW WPHACT
Figure 6: The ratio of the particle flow distributions (A+C)/(B+D) at 189 GeV (a) and at
206 GeV (b). The data (dots) are compared to WW MC samples generated with WPHACT
(DELPHI samples) and KORALW (Cetraro samples), both without CR and implementing
the SK-Imodel with 100% probability of reconnection. The lines corresponding to WPHACT
are hardly distinguishable from the lines corresponding to KORALW in the same condition
of implementation of CR.
s (GeV) RData Rno CR RSK-I:100%
183 0.889 ± 0.084 0.928 ± 0.005 -
189 1.025 ± 0.063 0.966 ± 0.006 0.864 ± 0.005
192 1.008 ± 0.150 0.970 ± 0.006 -
196 1.041 ± 0.093 0.995 ± 0.006 -
200 0.922 ± 0.084 1.022 ± 0.007 0.889 ± 0.006
202 0.952 ± 0.126 1.015 ± 0.008 -
206 1.116 ± 0.088 1.012 ± 0.008 0.889 ± 0.006
207 1.039 ± 0.135 1.019 ± 0.008 -
Table 2: Values of the ratio R for each energy (errors are statistical only), and expected
values with errors due to limited statistics of the simulation, all from DELPHI WPHACT
WW samples.
MC Sample χ2/DF α,A β,B γ
no CR 7.31/5 1.001± 0.003 (3.20± 0.36)× 10−3 (−1.35± 0.40)× 10−4
SK-I 100% 1.46/1 0.880± 0.003 (1.68± 0.44)× 10−3 -
Table 3: Results of the fit to the evolution of R with (
s(GeV)− 197.5).
∫ 0.8
dnch/dΦ(A+ C)dΦ
∫ 0.8
dnch/dΦ(B +D)dΦ
. (3)
To take into account possible statistical correlations between particles in the Inside-W
and Between-W regions, the statistical error on this ratio R was again estimated through
the Jackknife method [27].
The values forR obtained for the different centre-of-mass energies are shown in Table 2,
and compared to the expectations from the DELPHI WPHACT WW samples without CR
and implementing the SK-I model with 100% reconnection probability. These values for
data and MC are plotted as function of the centre-of-mass energy in Figure 7.
The changes in the value of R for the MC samples are mainly due to the dif-
ferent values of the boost of the W systems. In order to quantify this effect
a linear function R(
s− 197.5) = A + B · (
s− 197.5) was fitted to the MC points
with CR (with
s in GeV), while for the points without CR the quadratic func-
tion R(
s− 197.5) = α+ β · (
s− 197.5) + γ · (
s− 197.5)2 was assumed (with
GeV), giving reasonable χ2/d.o.f. values. The fits yielded the results shown in Table 3.
The MC without CR shows a stronger dependence on
s. The function fitted to this
sample was used to rescale the measured values of R for the data collected at different
energies to the energy of 189 GeV, the centre-of-mass energy at which the combination
of the results of the LEP experiments was proposed in [4]. All the rescaled values were
combined with a statistical error-weighted average. The average of the R ratios rescaled
to 189 GeV was found to be
〈R〉 = 0.979± 0.032(stat). (4)
180 185 190 195 200 205 210
WW no CR Fit to no CR
WW SK-I 100% Fit to SK-I 100%Fit to SK-I 100%
Combined Ratio
√s (GeV)
DELPHI
Figure 7: The ratio R as function of
s for data and MC (DELPHI WPHACTWW samples),
and fits to the MC with and without CR, and the combined ratio after rescaling all values
s = 189 GeV (see text). The value of the combined ratio at 189 GeV is shown at
a displaced energy (upwards by 1 GeV) for better visibility, as well as all the values
for the MC ‘WW no CR’ points and the corresponding fitted curve which are shown at
centre-of-mass energies shifted downwards by 0.5 GeV. All errors for the MC values are
smaller than the size of the markers.
Performing the same weighted average when using for the rescaling the fit to the MC
with CR, one obtains:
〈RCR rescale〉 = 0.987± 0.032(stat). (5)
Repeating the procedure, but now without rescaling the R ratios, the result is:
〈Rno rescale〉 = 0.999± 0.033(stat). (6)
4.4 Study of the Systematic Errors in the Particle Flow
The following effects were studied as sources of systematic uncertainties in this anal-
ysis.
4.4.1 Fragmentation and Detector response
A direct comparison between the particle flow ratios measured in fully hadronic data
and MC samples, R4qData and R4qMC, respectively, is hampered by the uncertainties as-
sociated with the modelling of the WW fragmentation and the detector response. These
systematic uncertainties were estimated using mixed semi-leptonic events. In this tech-
nique, two hadronically decaying W bosons from semi-leptonic events were mixed together
to emulate a fully hadronic WW decay.
Mixing Technique
Semi-leptonic WW decays were selected from the data collected by DELPHI at centre-
of-mass energies between 189 and 206 GeV, by requiring two hadronic jets, a well isolated
identified muon or electron or, in case of a tau candidate, a well isolated particle, all
associated with missing momentum (corresponding to the neutrino) pointing away from
the beam pipe. A neural network selection, developed in [28], was used to select the
events. The same procedure was applied to the WPHACT samples fragmented with PYTHIA
and HERWIG at centre-of-mass energies of 189, 200 and 206 GeV and with ARIADNE at 189
and 206 GeV. The background to this selection was found to be of negligible importance
in this analysis. Samples of mixed semi-leptonic events were built separately at each
centre-of-mass energy for data and Monte Carlo semi-leptonic samples, following the
mixing procedure developed in [2].
In each semi-leptonic event, the lepton (or tau-decay jet) was stripped off and the
remaining particles constituted the hadronically decaying W boson. Two hadronically
decaying W bosons were then mixed together to emulate a fully hadronic WW decay.
The hadronic parts of W bosons were mixed in such a way as to have the parent W
bosons back-to-back in the emulated fully hadronic WW decay. To increase the statistics
of emulated events, and profiting from the cylindrical symmetry of the detector along
the z axis, the hadronic parts of W bosons were rotated around the z axis, but were not
moved from barrel to forward regions or vice-versa, as detailed in the following.
When mixing the hadronic parts of different W events it was required that the two Ws
had reconstructed polar angles back-to-back or equal within 10 degrees. In the latter case,
when both Ws are on the same side of the detector, the z component of the momentum
is sign flipped for all the particles in one of the Ws.
The particles of one W event were then rotated around the beam axis, in order to have
the two Ws also back-to-back in the transverse plane. Each semi-leptonic event was used
in the mixing procedure between 4 and 9 times, to minimize the statistical error on the
particle flow ratio R measured in the mixed semi-leptonic data sample.
The mixed events were then subjected to the same event selection and particle flow
analysis used for the fully hadronic events. The particle flow ratios Rmixed SLData and
Rmixed SLMC were measured in the mixed semi-leptonic data and MC samples, respectively,
and are plotted as function of the centre-of-mass energy in Figure 8.
The values of Rmixed SL measured in MC show a dependence on
s. This effect is
quantified by performing linear fits to the points measured with PYTHIA, ARIADNE and
HERWIG, respectively. The differences between the measured slopes were found to be small.
The function fitted to the PYTHIA points was used to rescale the values of R measured in
data at different energies to 189 GeV. The rescaled values were then combined using as
weights the scaled statistical errors. The weighted average R at 189 GeV for the mixed
semi-leptonic events built from data was found to be
〈Rmixed SLData〉 = 1.052± 0.027(stat). (7)
For each MC sample, the ratio Rmixed SLData/Rmixed SLMC was used to calibrate the
particle flow ratio measured in the corresponding fully hadronic sample, R4qMC, to
compare it to the ratio measured in the data, 〈R4qData〉. The correction factor
Rmixed SLData/Rmixed SLMC was computed from the values of R rescaled to 189 GeV, calcu-
lated from the fits to the mixed semi-leptonic samples built from the data and the MC.
185 190 195 200 205 210
Data Mixed SL
PYTHIA
Fit to PYTHIA
ARIADNE
Fit to ARIADNE
HERWIG
Fit to HERWIG
√s (GeV)
DELPHI
Figure 8: The ratio Rmixed SL as function of
s for data and MC, and fits to the MC (see
text). The ARIADNE points at 189 GeV and at 206 GeV have their centre-of-mass energy
shifted and the error bars on data are tilted for readability.
MC sample PYTHIA ARIADNE HERWIG
Rmixed SLData/Rmixed SLMC 1.053 1.044 0.997
RCalibrated4qMC 1.018 1.011 1.004
Table 4: Ratio of data to MC fitted values of R in mixed semi-leptonic samples, used
to calibrate the R4qMC values for different models (upper line), and calibrated values of
R4qMC. All values were computed at
s = 189 GeV.
The values for Rmixed SLMC are presented in Table 4, for the different models, along with
the calibrated values of R4q for the same models.
The calibration factors differ from unity by less than 6%, and the largest difference of
the calibrated R4qMC values when changing the fragmentation model, 0.014, was consid-
ered as an estimate of the systematic error due to simulation of the fragmentation and of
the detector response, and was added in quadrature to the systematic error. The error
in the calibrated R4qMC values due to the statistical error on 〈Rmixed SLData〉 value used
for the calibration, 0.026, was also added in quadrature to the systematic error.
4.4.2 Bose-Einstein Correlations
Bose-Einstein correlations (BEC) between identical pions and kaons are known to
exist and were established and studied in Z hadronic decays in [29]. They are expected
to exist with a similar behaviour in the W hadronic decays, and this is studied in [2].
They are implemented in the MC simulation samples with BEC via the BE32 model
of LUBOEI [21], which was tuned to describe the DELPHI data in [2]. However, the
situation for the WW (ZZ) fully hadronic decays is not so clear, i.e. whether there are
correlations only between pions and kaons coming from the same W(Z) boson or also
between pions and kaons from different W(Z) bosons. The analyses of Bose-Einstein
correlations between identical particles coming from the decay of different W bosons do
not show a significant effect [30] for three of the LEP experiments, whereas for DELPHI,
an effect was found at the level of 2.4 standard deviations [2]. Thus, a comparison was
made between the WPHACT samples without CR and with BEC only between the identical
pions coming from the same W boson (BEC only inside), to the samples without CR
and with BEC allowed for all the particles stemming from both W bosons, implemented
with the BE32 variant of the LUBOEI model (BEC all). The R values were obtained
at each centre-of-mass energy, after which a linear fit was performed for each model to
obtain a best prediction at 189 GeV. The fit values were found to be in agreement to the
estimate at 189 GeV alone, and for simplicity this estimate was used. The measurement
of BEC from DELPHI of 2.4 standard deviations above zero (corresponding to BEC only
inside), was used to interpolate the range of 4.1 standard deviations of separation between
BEC only inside and BEC all. To include the error on the measured BEC effect, one
standard deviation was added to the effect before the interpolation. The difference in the
estimated values of R at
s = 189 GeV, between the model with BEC only inside and
the model with partial BEC all (at the interpolated point of 3.4/4.1), -0.013, was added
in quadrature to the systematic error.
4.4.3 qq̄(γ) Background Shape
The fragmentation effects, in the shape of the qq̄(γ) background, were estimated by
comparing the values of R obtained when the subtracted qq̄(γ) sample was fragmented
with ARIADNE instead of PYTHIA at the centre-of-mass energy of 189 GeV, and the differ-
ence, 0.003, was added in quadrature to the systematic error.
4.4.4 qq̄(γ) and ZZ Background Contribution
At the centre-of-mass energy of 189 GeV, the qq̄(γ) cross-section in the 4-jet region
is poorly known, due to the difficulty in isolating the qq̄(γ) → 4-jet signal from other
4-jet processes such as WW and ZZ. The study performed in [31] has shown that the
maximal difference in the estimated qq̄(γ) background rate is 10% coming from changing
from PYTHIA to HERWIG as the hadronization model, with the ARIADNE model giving
intermediate results. Conservatively, at each centre-of-mass energy a variation of 10%
on the qq̄(γ) cross-section was assumed, and the largest shift in R, 0.011, was added in
quadrature to the systematic error.
The other background process considered is the Z pair production. The Standard
Model predicted cross-sections are in agreement with the data at an error level of 10% [32].
The cross-section was thus varied by ±10% at each energy and the effect in R was found
to be negligible.
4.4.5 Evolution of R with Energy
The R ratios were rescaled to
s = 189 GeV using the fit to the MC without CR,
however the correct behaviour might be given by the MC with CR. Hence, the difference of
0.009 between the R values obtained using the two rescaling methods, using MC without
CR 〈R〉 and with CR 〈RCR rescale〉, was added in quadrature to the systematic error.
4.5 Results of the Particle Flow Analysis
The final result for the average of the ratios R rescaled to 189 GeV is
MC Sample R
PYTHIA no CR 1.037± 0.004
PYTHIA SK-I 100% 0.917± 0.003
ARIADNE no CR 1.053± 0.004
ARIADNE AR2 1.021± 0.004
HERWIG no CR 1.059± 0.004
HERWIG 1/9 CR 1.040± 0.003
Table 5: R ratios for the Cetraro samples at 189 GeV, calibrated with the mixed semi-lep-
tonic events.
〈R〉 = 0.979± 0.032(stat)± 0.035(syst). (8)
In order to facilitate comparisons between the four LEP experiments, this value can
be normalised by the one determined from simulation samples produced with the full
detector simulation and analysed with the same method. The LEP experiments agreed
to use for this purpose the Cetraro PYTHIA samples. These events were generated with the
ALEPH fragmentation tuning but have been reconstructed with the DELPHI detector
simulation and analysed with this analysis. The values of the R ratios obtained from the
Cetraro samples at 189 GeV, calibrated using the mixed semi-leptonic events from these
samples, are given in Table 5.
The value of 〈R〉 measured from data is between the expected R ratios from PYTHIA
without CR and with the SK-I model with 100% fraction of reconnection. The error
of this measurement is larger than the difference between the values of R from ARIADNE
samples without and with CR, and than the difference between values of R from the
HERWIG samples without CR and with 1/9 of reconnected events.
The following normalised ratios are obtained for the sample without CR and imple-
menting the SK-I model with 100% CR probability, respectively:
rdatano CR =
〈R〉data
Rno CR
= 0.944± 0.031(stat)± 0.034(syst), (9)
rdataCR =
〈R〉data
= 1.067± 0.035(stat)± 0.039(syst). (10)
In the above expressions, the statistical errors in the MC predicted values were propagated
and added quadratically to the systematic errors on the ratios.
It is also possible to define the following quantity, taking the predictions for RCR and
Rno CR at
s = 189 GeV from the PYTHIA samples in Table 5,
〈Rdata〉 −Rno CR
RCR − Rno CR
= 0.49± 0.27(stat)± 0.29(syst) , (11)
from which it can be concluded that the measured 〈Rdata〉 is compatible with intermediate
probability of CR, and differs from the CR in the SK-I model at 100% at the level of
1.3 standard deviations. The ability to distinguish between these two models can be
computed from the inverse of the sum in quadrature of the statistical and systematic
errors; it amounts to be 2.5 standard deviations. In Figure 9 the result of δr is compared
to the predicted values, in the scope of the SK-I model, as a funtion of the fraction of
reconnected events.
Fraction of reconnected events %
DELPHI
0 20 40 60 80 100
Figure 9: Comparison of the measurement of the δr observable to the predictions from
the SK-I model as a function of the fraction of reconnected events.
The result for the value of 〈R〉 can also be used to test for consistency with the SK-I
model as a function of κ and a log-likelihood curve was obtained. This also facilitates
combination with the result obtained in the analysis in the following section, and for this
reason the value of 〈R〉 is rescaled with PYTHIA without CR to a centre-of-mass energy
of 200 GeV: the value obtained at 200 GeV is 〈R〉(200 GeV) = 1.024 ± 0.050. The
values obtained for the predicted ratios RN at 200 GeV and the log-likelihood curve, as
a function of κ, are shown in Figure 10. The value of κ most compatible with the data
within one standard deviation is
κSK-I = 4.13
+20.97
−3.46 . (12)
5 Different MW Estimators as Observables
It has been shown [12] that the MW measurement inferred from hadronically decaying
W+W− events at LEP-2, by the method of direct reconstruction, is influenced by CR
effects, most visible when changing the value of κ in the SK-I model. For the MW(4q)
estimator within DELPHI this is shown in [33]. Other published MW estimators in LEP
experiments are equally sensitive to κ [34].
To probe this sensitivity to CR effects, alternative estimators for the MW measure-
ment were designed which have different sensitivity to κ. In the following, the standard
estimator and two alternative estimators, studied in this paper, are presented. The stan-
dard estimator corresponds to that previously used in the measurement of the W mass
by DELPHI [33]. Note that in the final DELPHI W mass analysis [35] results are given
0. 0.
Fraction of reconnected events %
DELPHI
DELPHI
Fraction of reconnected events %
DELPHI
DELPHI
0 20 40 60 80 100
0 20 40 60 80 100
Figure 10: a) Estimated ratio RN at 200 GeV plotted as a function of different κ values
(top scale), or as function of the corresponding reconnection probabilities (bottom scale),
compared to 〈R〉 measured from data after rescaling to 200 GeV (horizontal lines marked
with R for the value and with 1σ(2σ) for the 〈R〉 value added/subtracted by one(two)
standard deviations); the last three marks on the x axis, close to 100% of reconnection
probability, correspond respectively to the values κ = 100, 300, 800; b) corresponding
log-likelihood curve for the comparison of the estimated values (RN ) with the data (〈R〉).
for the standard and hybrid cone estimators, with the hybrid cone estimator used to
provide the primary result. The data samples, efficiencies and purities for the analysis
corresponding to the standard estimator are provided in [33, 35].
• The standard MW estimator :
This estimator is described in [33] and was optimised to obtain the smallest sta-
tistical uncertainty for the W mass measurement. It results in an event-by-event
likelihood Li(MW) for the parameter MW.
• The momentum cut MW estimator :
For this alternative MW estimator the event selection was performed in exactly
the same way as for the standard MW estimator. The particle-jet association was
also taken from this analysis. However, when reconstructing the event for the MW
extraction a tighter track selection was applied. The momentum and energy of the
jets were calculated only from those tracks having a momentum higher than a certain
pcut value. An event-by-event likelihood L
i (MW) was then calculated.
• The hybrid cone MW estimator :
In this second alternative MW estimator the reconstruction of the event is the same
as for the standard analysis, except when calculating the jet momenta used for the
MW extraction.
coneR
(cone) (std)
Figure 11: Illustration of the iterative cone algorithm within a predefined jet as explained
in the text.
An iterative procedure was used within each jet (defined by the clustering algorithm
used in the standard analysis) to find a stable direction of a cone excluding some
particles in the calculation of the jet momentum, illustrated in Figure 11. Starting
with the direction of the original jet ~p
std , the jet direction was recalculated (direction
(1) on the Figure) only from those particles which have an opening angle smaller
than Rcone with this original jet. This process was iterated by constructing a second
cone (of the same opening angle) around this new jet direction and the jet direction
was recalculated again. The iteration was continued until a stable jet direction ~p jetcone
was found. The jet momenta obtained, ~p jetcone, were rescaled to compensate for the
lost energy of particles outside the stable cone,
~p jetcone → ~p jetcone ·
Ejetcone
. (13)
The energies of the jets were taken to be the same as those obtained with the
standard clustering algorithm (E jetcone → E jet). This was done to increase the
correlation of this estimator with the standard one. The rescaling was not done
for the pcut estimator as it will be used in a cross-check observable with different
systematic properties. Again the result is an event-by-event likelihood LRconei (MW).
Each of these previously defined MW likelihoods had to be calibrated. The slope of
the linear calibration curve for the MW estimators is tuned to be unity, therefore only
a bias correction induced by the reconstruction method has to be applied. This bias
is estimated with the nominal WPHACT Monte Carlo events and the dependence on the
value of κ is estimated with the EXCALIBUR simulation. It was verified for smaller subsets
that the results using these large EXCALIBUR samples and the samples generated with
WPHACT are compatible. Neglecting the possible existence of Colour Reconnection (CR) in
the Monte Carlo simulation results in event likelihoods Li(MW|event without CR), while
Li(MW|event with CR) are the event likelihoods obtained when assuming the hypothesis
that events do reconnect (100% CR in the scope of the SK-I model). To construct the
event likelihoods for intermediate CR (values of κ larger than 0) the following weighting
formula is used :
Li(MW|κ) = [1−Pi(κ)]·Li(MW|event without CR)+Pi(κ)·Li(MW|event with CR) (14)
where Pi(κ) is defined in Equation 1. The combined likelihood is produced for
the event sample; the calibrated values for MW(κ) were obtained for different val-
ues of κ using the maximum likelihood principle. In Figure 12 the difference
dMW(κ) = MW(κ)−MW(κ = 0) or the influence of κ on the bias of the MW estimator is
presented as function of κ.
The uncertainty on this difference is estimated with the Jackknife method [27] to
take the correlation between MW(κ) and MW(κ = 0) into account. It was observed from
simulations that the estimators dependency on κ, for κ below about 5, was not signifi-
cantly different in the centre-of-mass range between 189 and 207 GeV. Therefore in the
determination of κ the dependency at 200 GeV was taken as default for all centre-of-
mass energies. This value of centre-of-mass energy is close to the integrated luminosity
weighted centre-of-mass energy of the complete data sample, which is 197.1 GeV.
When neglecting the information content of low momentum particles or when using
the hybrid cone algorithm, the influence of Colour Reconnection on the MW estimator is
decreased. The dependence ∂MW
of the estimator to κ is decreased when increasing the
value of pcut or when working with smaller cone opening angles Rcone.
5.1 The Measurement of κ
The observed difference ∆MW(std, i) = MW
std − MWi in the event sample, where i
is a certain alternative analysis, provides a measurement of κ. When both estimators
std and MW
i are calibrated in the same hypothesis of κ, the expectation values of
∆MW(std, i) will be invariant under a change of pcut or Rcone.
When neglecting part of the information content of the events in these alternative MW
analyses, by increasing pcut or decreasing Rcone, the statistical uncertainty on the value of
1 10 10
Standard MW analysis    DELPHI
pcut = 1 GeV/c
pcut = 2 GeV/c
pcut = 3 GeV/c
Cone R=1.00 rad
Cone R=0.75 rad
Cone R=0.50 rad
Cone R=0.25 rad
SK-I Model parameter κ
κ = 0.66
Figure 12: The difference dMW(κ) = MW(κ)−MW(κ = 0) is presented as a function of
κ, for different MW estimators. The curve for the standard MW estimator is the curve
at the top. The curves obtained with the hybrid cone analysis for different values of the
cone opening angle, starting from the top with 1.00 rad down to 0.75 rad, 0.50 rad and
0.25 rad are indicated with dotted lines. The curves obtained with the momentum cut
analysis for different values of pcut, starting from the top with 1 GeV/c, down to 2 GeV/c
and 3 GeV/c are dashed. The vertical line indicates the value of κ preferred by the SK-I
authors [5] and commonly used to estimate systematic uncertainties on measurements
using e+e− → W+W− → q1q̄2q3q̄4 events.
the MW estimator is increased. Therefore a balance must be found between the statistical
precision on ∆MW(std, i) and the dependence of this difference to κ in order to obtain
the largest sensitivity for a κ measurement. This optimum was found using the Monte
Carlo simulated events and assuming that the data follow the κ = 0 hypothesis, resulting
in the smallest expected uncertainty on the estimation of κ.
For the pcut analysis an optimal sensitivity was found when using the difference
∆MW(std, pcut) with pcut equal to 2 GeV/c or 3 GeV/c. Even more information about
κ could be extracted from the data, when using the difference ∆MW(std,Rcone), which
was found to have an optimal sensitivity around Rcone = 0.5 rad. No significant im-
provement in the sensitivity was found when combining the information from these two
observables. Therefore the best measure of κ using this method is extracted from the
∆MW(std,Rcone = 0.5 rad) observable. Nevertheless, the ∆MW(std, pcut = 2GeV/c) ob-
servable was studied as a cross-check.
5.2 Study of the Systematic Errors in the ∆MW Method
The estimation of systematic uncertainties on the observables ∆MW(std, i) follows
similar methods to those used within the MW analysis. Here the double difference is a
measure of the systematic uncertainty between Monte Carlo simulation (‘MC’) and real
data (‘DA’):
∆syst(MC,DA) =
std(MC)−MWstd(DA)]− [MWi(MC)−MWi(DA)]
∣ (15)
where i is one of the alternative MW estimators. The systematic error components are
described below and summarised in Table 6.
5.2.1 Jet Reconstruction systematics with MLBZs
A novel technique was proposed in [36] to study systematic uncertainties on jet recon-
struction and fragmentation in W physics measurements with high statistical precision
through the use of Mixed Lorentz Boosted Z events (MLBZs). The technique is similar to
the one described in section 4.4.1. The main advantage of this method was that Monte
Carlo simulated jet properties in W+W− events could be directly compared with the
corresponding ones from real data using the large Z statistics.
The main extension of the method beyond that described in [36] consisted in an
improved mixing and boosting procedure of the Z events into MLBZs, demonstrated
in Figure 13.
The 4-momenta of the four primary quarks in WPHACT generated W+W− → q1q̄2q3q̄4
events were used as event templates. The Z events from data or simulation were chosen
such that their thrust axis directions were close in polar angle to one of the primary quarks
of the W+W− event template. Each template W was then boosted to its rest frame. The
particles in the final state of a selected Z event were rotated so that the thrust axis matches
the rest frame direction of the primary quarks in the W+W− template. After rescaling the
kinematics of the Z events to match the W boson mass in the generated W+W− template,
the two Z events were boosted to the lab frame of the W+W− template. All particles
having an absolute polar angle with the beam direction smaller than 11◦ were removed
from the event. The same generated WPHACT events were used for the construction of both
the data MLBZs and Monte Carlo MLBZs in order to increase the correlation between
both emulated samples to about 31%. This correlation was taken into account when
boost
lab frame WW
"re−boost" rotate
rest frame WW
lab frame  MLBZ
boost
Figure 13: Illustration of the mixing and boosting procedure within the MLBZ method
(see text for details).
quoting the statistical uncertainty on the systematic shift on the observables between
data and Monte Carlo MLBZs.
It was verified that when introducing a significant mass shift of 300 MeV/c2 on MW
by using the cone rejection algorithm, it was reproduced within 15% by applying the
MLBZ technique. Because the expected systematic uncertainties on the ∆MW(std, i)
observables of interest are one order of magnitude smaller than 300 MeV/c2, this method
is clearly justified.
The double difference of Equation 15 was determined with the MLBZ method using
Z events selected in the data sets collected during the 1998 calibration runs and Z events
from the corresponding Monte Carlo samples. The following results were obtained for
the ∆MW(std,Rcone = 0.5 rad) observable:
∆syst(ARIADNE ,DA) = −1.9 ± 3.9(stat)MeV/c2
∆syst(PYTHIA ,DA) = −5.7 ± 3.9(stat)MeV/c2
∆syst(HERWIG ,DA) = −10.6 ± 3.9(stat)MeV/c2
where the statistical uncertainty takes into account the correlation between the Monte
Carlo and the data MLBZ events, together with the correlation between the two MW
estimators. This indicates that most of the fragmentation, detector and Between-W
Bose-Einstein Correlation systematics are small. The study was not performed for the
∆MW(std, pcut) observable.
Other systematic sources on the reconstructed jets are not considered as the MW
estimators used in the difference ∆MW(std, i) have a large correlation.
5.2.2 Additional Fragmentation systematic study
The fragmentation of the primary partons is modelled in the Monte Carlo simulation
used for the calibration of the MW
i observables.
The expected values on the MW estimators from simulation (in the κ = 0 hypothe-
sis) are changed when using different fragmentation models [33], resulting in systematic
uncertainties on the measured MW
i observables and hence possibly also on our esti-
mated κ. In Figure 14 the systematic shift δMW in the different MW
i observables is
shown when using HERWIG or ARIADNE rather than PYTHIA as the fragmentation model
in the no Colour Reconnection hypothesis. When inferring κ from the data difference,
∆MW(std, i), the PYTHIA model is used to calibrate each MW
i observable. This data
difference for MW
pcut=2GeV/c, ∆MW(std, pcut = 2GeV/c), changes
3 by (27 ± 12) MeV/c2
or (8 ± 12) MeV/c2 when replacing PYTHIA by respectively HERWIG or ARIADNE. Simi-
larly, the observable ∆MW(std,Rcone = 0.5 rad) changes by (-4 ± 10) MeV/c2 or (-6 ±
10) MeV/c2 when replacing PYTHIA by respectively HERWIG or ARIADNE. The largest
shift of the observable when changing fragmentation models (or the uncertainty on this
shift if larger) is taken as systematic uncertainty on the value of the observable. Hence,
systematic errors of 27 MeV/c2 for the ∆MW(std, pcut = 2GeV/c) observable and 10
MeV/c2 for the ∆MW(std,Rcone = 0.5 rad) observable were assumed as the contribution
from fragmentation uncertainties. The MLBZ studies (see above) are compatible with
these results, hence no additional systematic due to fragmentation was quoted for the
∆MW(std,Rcone = 0.5 rad) observable.
3This change, ∆MW(std, pcut = 2GeV/c)
PYTHIA
− ∆MW(std, pcut = 2GeV/c)
HERWIG
, is given by
δMW(std ≡ pcut = 0.2GeV/c)
PYTHIA−HERWIG
− δMW(pcut = 2GeV/c)
PYTHIA−HERWIG, and similar expressions for the
ARIADNE and Rcone cases (for Rcone, std ≡ Rcone = π).
0 0.5 1 1.5 2 2.5 3 3.5 4
PYTHIA-ARIADNE         DELPHI
PYTHIA-HERWIG
pcut / GeV/c
0 0.2 0.4 0.6 0.8 1 1.2
PYTHIA-ARIADNE         DELPHI
PYTHIA-HERWIG
Rcone / rad
Figure 14: Systematic shifts δMW, on MW observables, when applying different fragmen-
tation models as a function of the pcut or Rcone values used in the construction of the
MW observable. These Monte Carlo estimates were obtained at a centre-of-mass energy
of 189 GeV. The uncertainties are determined with the Jackknife method.
5.2.3 Energy Dependence
The biases of the different MW estimators have a different dependence on the centre-
of-mass energy, hence the calibration of ∆MW(i, j) will be energy dependent. The energy
dependence of each individual MW estimator was parameterised with a second order poly-
nomial. Since WPHACT event samples were used at a range of centre-of-mass energies
the uncertainty on the parameters describing these curves are small. Therefore a small
systematic uncertainty of 3 MeV/c2 was quoted on the ∆MW(i, j) observables due to the
calibration.
5.2.4 Background
The same event selection criteria were applied for all the MW estimators, hence the
same background contamination is present in all analyses. The influence of the qq̄(γ)
background events on the individual MW estimators is small [33] and was taken into
account when constructing the centre-of-mass energy dependent calibration curves of
the individual MW estimators. The residual systematic uncertainty on both ∆MW(i, j)
observables is 3 MeV/c2.
5.2.5 Bose-Einstein Correlations
As for the particle flow method, the systematic uncertainties due to possible Bose-
Einstein Correlations are estimated via Monte Carlo simulations. The relevant values
for the systematic uncertainties on the observables are the differences between the ob-
servables obtained from the Monte Carlo events with Bose-Einstein Correlations inside
individual W’s (BEI) and those with, in addition, Bose-Einstein Correlations between
identical particles from different W’s (BEA). The values were estimated to be (6.4 ±
9.3) MeV/c2 for the ∆MW(std, pcut = 2GeV/c) observable, and (7.2 ± 8.2) MeV/c2 for
the ∆MW(std,Rcone = 0.5 rad) observable. As the uncertainties in the estimated contri-
butions were larger than the contributions themselves, these uncertainties were added in
quadrature to the systematic errors on the relevant observables.
5.2.6 Cross-check in the Semi-leptonic Channel
Colour Reconnection between the decay products originating from different W boson
decays can only occur in the W+W− → q1q̄2q3q̄4 channel. The semi-leptonic W+W−
decay channel (i.e, qq̄′ℓνℓ) is by definition free of those effects. Therefore the determi-
nation of Colour Reconnection sensitive observables, like ∆MW(std,Rcone = 0.5 rad), in
this decay channel could indicate the possible presence of residual systematic effects. A
study of the ∆MW(std,Rcone = 0.5 rad) observable was performed in the semi-leptonic
decay channel. The semi-leptonic MW analysis in [33] was used and the cone algorithm
was implemented in a similar way as for the fully hadronic decay channel. The same
data sets have been used as presented throughout this paper and the following result was
obtained:
∆MW(std,Rcone) = MW
std − MWRcone = (8 ± 56(stat))MeV/c2 (17)
where the statistical uncertainty was computed taking into account the correlation be-
tween both measurements. Although the statistical significance of this cross-check is
small, a good agreement was found for both MW estimators.
5.3 Results from the MW Estimators Analyses
The observable ∆MW(std,Rcone) with Rcone equal to 0.5 rad (defined above), was
found to be the most sensitive to the SK-I Colour Reconnection model, and the
∆MW(std, pcut = 2GeV/c) observable was measured as a cross-check. The analyses were
calibrated with PYTHIA κ = 0 WPHACT generated simulation events. The values measured
from the combined DELPHI data at centre-of-mass energies ranging between 183 and
208 GeV are:
∆MW(std,Rcone) = MW
std − MWRcone = (59 ± 35(stat) ± 14(syst))MeV/c2
∆MW(std, pcut) = MW
std − MWpcut = (143 ± 61(stat) ± 29(syst))MeV/c2
where the first uncertainty numbers represent the statistical components and the sec-
ond the combined systematic ones. The full breakdown of the uncertainties on both
observables can be found in Table 6.
Uncertainty contribution (MeV/c2)
Source ∆MW(std,Rcone = 0.5 rad) ∆MW(std, pcut = 2GeV/c)
Fragmentation 11 27
Calibration 3 3
Background 3 3
BEI-BEA 8 9
Total systematic 14 29
Statistical Error 35 61
Total 38 67
Table 6: Breakdown of the total uncertainty on both relevant observables.
From these values estimates were made for the κ parameter by comparing them with
the Monte Carlo expected values in different hypothesis of κ, shown in Figure 15 for the
observable ∆MW(std,Rcone = 0.5 rad).
The Gaussian uncertainty on the measured observables was used to construct a log-
likelihood function L(κ) = −2 log L(κ) for κ. The log-likelihood function obtained is
shown in Figure 16 for the first and in Figure 17 for the second observable.
The result shown in Figure 16 is the primary result of this analysis, because of the
larger sensitivity of the ∆MW(std,Rcone = 0.5 rad) observable to the value of κ (see sec-
tion 5.1). The value of κ most compatible with the data within one standard deviation
of the measurement is
κSK-I = 1.75
+2.60
−1.30 . (19)
The result on κ extracted from the cross-check ∆MW(std, pcut = 2GeV/c) observable
is found not to differ significantly from the quoted result obtained with the more opti-
mal ∆MW(std,Rcone = 0.5 rad) observable. The significance can be determined by the
difference between both MW estimators :
pcut − MWRcone = (−84 ± 59(stat))MeV/c2 . (20)
Taking into account that the expectation of this difference depends on κ, we find a sta-
tistical deviation of about 1 to 1.5σ between the measurements. No improved sensitivity
is obtained by combining the information of both observables.
200 DELPHI
at 188.6 GeV
at 199.5 GeV
at 206.5 GeV
SK-I Model parameter κ
κ = 0.66
Figure 15: The dependence of the observable ∆MW(std,Rcone = 0.5 rad) from simulation
events on the value of the SK-I model parameter κ. The dependence is given at three
centre-of-mass energies.
1 10 10
Likelihood of indirect measurement of κ SK-I
DELPHI measured : std - R=0.50 (stat+syst)
DELPHI measured : std - R=0.50 (stat)
SK-I Model parameter κ
Figure 16: The log-likelihood function −2 log L(κ) obtained from the DELPHI data mea-
surement of ∆MW(std,Rcone = 0.5 rad). The bottom curve (full line) gives the final result
including the statistical uncertainty on ∆MW(std,Rcone = 0.5 rad) and the investigated
systematic uncertainty contributions. The top curve (dashed) is centred on the same min-
imum and reflects the log-likelihood function obtained when only statistical uncertainties
are taken into account.
1 10 10
Likelihood of indirect measurement of κ SK-I
DELPHI measured : std - pcut=2 (stat+syst)
DELPHI measured : std - pcut=2 (stat)
SK-I Model parameter κ
Figure 17: The log-likelihood function −2 log L(κ) obtained from the DELPHI data mea-
surement of ∆MW(std, pcut = 2GeV/c). The bottom curve (full line) gives the final result
including the statistical uncertainty on ∆MW(std, pcut = 2GeV/c) and the investigated
systematic uncertainty contributions. The top curve (dashed) is centred on the same min-
imum and reflects the log-likelihood function obtained when only statistical uncertainties
are taken into account.
In this paper the SK-I model for Colour Reconnection implemented in PYTHIA was
studied because it parameterizes the effect as function of the model parameter κ. Other
phenomenological models implemented in the ARIADNE [7,8] and HERWIG [6] Monte Carlo
fragmentation schemes exist and are equally plausible. Unfortunately their effect in
W+W− → q1q̄2q3q̄4 events cannot be scaled with a model parameter, analogous to κ
in SK-I, without affecting the fragmentation model parameters. Despite this non-
factorization property, the consistency of these models with the data can still be ex-
amined. The Monte Carlo predictions of the observables in the hypothesis with Colour
Reconnection (calibrated in the hypothesis of no Colour Reconnection) give the following
values:
ARIADNE → MWstd − MWRcone = (7.2 ± 4.1) MeV/c2
ARIADNE → MWstd − MWpcut = (9.4 ± 7.0) MeV/c2
HERWIG → MWstd − MWRcone = (19.7 ± 4.0) MeV/c2
HERWIG → MWstd − MWpcut = (22.8 ± 6.9) MeV/c2 .
The small effects on the observables with the HERWIG implementation of Colour Reconnec-
tion compared to those predicted by SK-I are due to the fact that the fraction of events
that reconnect is smaller in HERWIG (1/9) compared to SK-I (& 25% at
s = 200 GeV).
After applying this scale factor between both models, their predicted effect on the W
mass and on the ∆MW(i, j) observables becomes compatible. The ARIADNE implementa-
tion of Colour Reconnection has a much smaller influence on the observables compared
to those predicted with the SK-I and HERWIG Monte Carlo.
5.4 Correlation with Direct MW Measurement
When using a data observable to estimate systematic uncertainties on some measur-
and inferred from the same data sample, the correlation between the estimator used to
measure the systematic bias and the estimator of the absolute value of the measurand
should be taken into account. Therefore the correlation between the Colour Reconnection
sensitive observables ∆MW(std,Rcone = 0.5 rad) and ∆MW(std, pcut = 2GeV/c) and the
absolute MW(std) estimator was calculated. The correlation was determined from the
Monte Carlo events and with κ = 0 or no Colour Reconnection. The values obtained
were found to be stable as a function of κ within the statistical precision. The correlation
between ∆MW(std,Rcone = 0.5 rad) and MW(std) was found to be 11%, while for the one
between ∆MW(std, pcut = 2GeV/c) and MW(std) a value of 8% was obtained. Also the
correlation between the different MW estimators was estimated and found to be stable
with the value of κ. A value of 83% was obtained for the correlation between MW(std)
and MW
Rcone=0.5 rad, while 66% was obtained between MW(std) and MW
pcut=2GeV/c.
6 Combination of the Results in the Scope of the
SK-I Model
The log-likelihood curve from the particle flow method was combined with the curve
from the ∆MW method and the result is shown in Figure 18. The correlations between the
analyses were neglected because the overlap between the samples is small and the nature
of the analyses is very different. The total errors were used (statistical and systematic
added in quadrature) in the combination.
1 10 10
Log-Likelihood of measurement    of κ SK-I
from ∆MW
from particle flow
∆MW+part.flow combined
SK-I Model parameter κ
DELPHI
Figure 18: The log-likelihood function −2 log L(κ) obtained from the combined DELPHI
measurement via ∆MW(std,Rcone = 0.5 rad) and the particle flow. The full line gives
the final result including the statistical and systematic uncertainties. The log-likelihood
functions are combined in the hypothesis of no correlation between the statistical and
systematic uncertainties of both measurements.
The best value for κ from the minimum of the curve, with its error given by the width
of the curve at the value −2 log L = (−2 log L)min + 1, is:
κSK-I = 2.2
−1.3 . (22)
7 Conclusions
Colour Reconnection (CR) effects in the fully hadronic decays of W pairs, produced
in the DELPHI experiment at LEP, were investigated using the methods of the particle
flow and the MW estimators, notably the ∆MW(std,Rcone = 0.5 rad) observable.
The average of the ratios R of the integrals between 0.2 and 0.8 of the particle distri-
bution in Inside-W regions to the Between-W regions was found to be
〈R〉 = 0.979± 0.032(stat)± 0.035(syst) . (23)
The values used in this average were obtained after rescaling the value at each energy to
the value at a centre-of-mass energy of 189 GeV using a fit to the MC without CR.
The effects of CR on the values of the reconstructed mass of the W boson, as imple-
mented in different Monte Carlo models, were studied with different estimators. From
the estimator of the W mass with the strongest sensitivity to the SK-I model of CR, the
∆MW(std,Rcone = 0.5 rad) method, the difference in data was found to be
∆MW(std,Rcone) = MW
std −MWRcone=0.5 rad = ( 59± 35(stat)± 14(syst) )MeV/c2 . (24)
From the combination of the results from particle flow and MW estimators, corre-
sponding to the curve in full line shown in Figure 18, the best value and total error for
the κ parameter in the SK-I model was extracted to be:
κSK-I = 2.2
−1.3 (25)
which corresponds to a probability of reconnection of Preco = 52% and lies in the range
31% < Preco < 68% at 68% confidence level.
The two analysis methods used in this paper are complementary: the method of parti-
cle flow provides a model-independent measurement but has significantly less sensitivity
towards the SK-I model of CR than the method of ∆MW estimators.
The obtained value of κ in equation (25) can be compared with similar values obtained
by other LEP experiments, and it was found to be compatible with, but higher than, the
values obtained with the particle flow by L3 [37] and OPAL [38]. It is also compatible
with, but higher than, the values obtained with the method of different MW estimators
by OPAL [39] and ALEPH [40].
Acknowledgements
We thank the ALEPH Collaboration for the production of the simulated “Cetraro
Samples”.
We are greatly indebted to our technical collaborators, to the members of the CERN-
SL Division for the excellent performance of the LEP collider, and to the funding agencies
for their support in building and operating the DELPHI detector.
We acknowledge in particular the support of
Austrian Federal Ministry of Education, Science and Culture, GZ 616.364/2-III/2a/98,
FNRS–FWO, Flanders Institute to encourage scientific and technological research in the
industry (IWT) and Belgian Federal Office for Scientific, Technical and Cultural affairs
(OSTC), Belgium,
FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil,
Czech Ministry of Industry and Trade, GA CR 202/99/1362,
Commission of the European Communities (DG XII),
Direction des Sciences de la Matière, CEA, France,
Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Germany,
General Secretariat for Research and Technology, Greece,
National Science Foundation (NWO) and Foundation for Research on Matter (FOM),
The Netherlands,
Norwegian Research Council,
State Committee for Scientific Research, Poland, SPUB-M/CERN/PO3/DZ296/2000,
SPUB-M/CERN/PO3/DZ297/2000, 2P03B 104 19 and 2P03B 69 23(2002-2004)
FCT - Fundação para a Ciência e Tecnologia, Portugal,
Vedecka grantova agentura MS SR, Slovakia, Nr. 95/5195/134,
Ministry of Science and Technology of the Republic of Slovenia,
CICYT, Spain, AEN99-0950 and AEN99-0761,
The Swedish Research Council,
Particle Physics and Astronomy Research Council, UK,
Department of Energy, USA, DE-FG02-01ER41155,
EEC RTN contract HPRN-CT-00292-2002.
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  In the reaction e+e- -> WW -> (q_1 qbar_2)(q_3 qbar_4) the usual
hadronization models treat the colour singlets q_1 qbar_2 and q_3 qbar_4 coming
from two W bosons independently. However, since the final state partons may
coexist in space and time, cross-talk between the two evolving hadronic systems
may be possible during fragmentation through soft gluon exchange. This effect
is known as Colour Reconnection. In this article the results of the
investigation of Colour Reconnection effects in fully hadronic decays of W
pairs in DELPHI at LEP are presented. Two complementary analyses were
performed, studying the particle flow between jets and W mass estimators, with
negligible correlation between them, and the results were combined and compared
to models. In the framework of the SK-I model, the value for its kappa
parameter most compatible with the data was found to be: kappa_{SK-I} =
2.2^{+2.5}_{-1.3} corresponding to the probability of reconnection P_{reco} to
be in the range 0.31 < P_{reco} < 0.68 at 68% confidence level with its best
value at 0.52.

Introduction
The space-time development of a hadronic system is still poorly understood, and
models are necessary to transform a partonic system, governed by perturbative QCD, to
final state hadrons observed in the detectors.
WW events produced in e+e− collisions at LEP-2 constitute a unique laboratory to
study and test the evolution of such hadronic systems, because of the clean environment
and the well-defined initial energy in the process. Of particular interest is the possibility
to study separately one single evolving hadronic system (one of the W bosons decaying
semi-leptonically, the other decaying hadronically), and compare it with two hadronic
systems evolving at the same time (both W bosons decaying hadronically).
Interconnection effects between the products of the hadronic decays of the two W
bosons (in the same event) are expected since the lifetime of the W bosons (τW ≃ ~/ΓW ≃
0.1 fm/c) is an order of magnitude smaller than the typical hadronization times. These
effects can happen at two levels:
• in the evolution of the parton shower, between partons from different hadronic sys-
tems by exchanging coloured gluons [1] (this effect is called Colour Reconnection
(CR) for historical reasons);
• between the final state hadrons, due to quantum-mechanical interference, mainly
due to Bose-Einstein Correlations (BEC) between identical bosons (e.g. pions with
the same charge).
A detailed study by DELPHI of this second effect was recently published [2].
The first effect, the possible presence of colour flow between the two W hadronization
systems, is the topic studied in this paper. This effect is worthy of study in its own right
and for the possible effects induced on the W mass measurement in fully hadronic events
(see for instance [3] for an introduction and [4] for an experimental review).
The effects at the perturbative level are expected to be small [3], whereas they may
be large at the hadronization level (many soft gluons sharing the space-time) for which
models have to be used to compare with the data.
The most tested model is the Sjöstrand-Khoze “Type 1” CR model SK-I [5]. This
model of CR is based on the Lund string fragmentation phenomenology. The strings are
considered as colour flux tubes with some volume, and reconnection occurs when these
tubes overlap. The probability of reconnection in an event is parameterised by the value
κ, set globally by the user, according to the space-time volume overlap of the two strings,
Voverlap :
Preco(κ) = 1− e−κVoverlap . (1)
The parameter κ was introduced in the SK-I model to allow a variation of the percentage
of reconnected events and facilitate studies of sensitivity to the effect. In this model
only one string reconnection per event was allowed. The authors of the model propose
the value of κ = 0.66 to give similar amounts of reconnection as other models of Colour
Reconnection. By comparing the data with the model predictions evaluated at several
κ values, it is possible to determine the value of κ most consistent with the data and
extract the corresponding reconnection probability. Another model was proposed by the
same authors, considering the colour flux tubes as infinitely thin, which allows for Colour
Reconnection in the case the tubes cross each other and provided the total string length
is reduced (SK-II′). This last model was not tested.
Two further models are tested here, these are the models implemented in HERWIG [6]
and ARIADNE [7] Monte Carlo programs. In HERWIG the partons are reconnected, with a
reconnection probability of 1/9, if the reconnection results in a smaller total cluster mass.
In ARIADNE, which implements an adapted version of the Gustafson-Häkkinen model [8],
the model used [9] allows for reconnections between partons originating in the same W
boson, or from different W bosons if they have an energy smaller than the width of the
W boson (this model will be referred as ‘AR-2’).
Colour Reconnection has been previously investigated in DELPHI by comparing in-
clusive distributions of charged particles, such as the charged-particle multiplicity dis-
tribution or the production of identified (heavy) particles, in fully hadronic WW events
and the distributions in semi-leptonic WW events. The investigations did not show any
effect as they were limited by statistical and systematic errors and excluded only the
most extreme models of CR (see [10]).
This article presents the results of the investigations of Colour Reconnection effects in
hadronically decaying W pairs using two techniques. The first, proposed by L3 in [11],
looks at the particle flow between the jets in a 4-jet WW event. The second, proposed
by DELPHI in [12], takes into account the different sensitivity to Colour Reconnection of
several W mass estimators. The first technique is more independent of the model and it
can provide comparisons based on data. The second technique is more dependent on the
model tested, but has a much larger sensitivity to the models SK-I and HERWIG. Since
the particle flow and W mass estimator methods were found to be largely uncorrelated a
combination of the results of these two methods is provided.
The paper is organised as follows. In the next section, the LEP operation and the
components of the DELPHI detector relevant to the analyses are briefly described. In
section 3 data and simulation samples are explained. Then both of the analysis methods
discussed above are described and their results presented in sections 4 and 5. The com-
bination of the results is given in section 6 and conclusions are drawn in the seventh and
final section.
2 LEP Operation and Detector Description
At LEP-2, the second phase of the e+e− collider at CERN, the accelerator was operated
at centre-of-mass energies above the threshold for double W boson production from 1996
to 2000. In this period, the DELPHI experiment collected about 12000 WW events
corresponding to a total integrated luminosity of 661 pb−1. About 46% of the WW
events are WW → q1q̄2q3q̄4 events (fully hadronic), and 44% are WW → q1q̄2ℓν̄, where
ℓ is a lepton (semi-leptonic).
The detailed description of the DELPHI detector and its performance is provided
in [13,14]. A brief summary of the main characteristics of the detector important for the
analyses follows.
The tracking system of DELPHI consisted of a Time Projection Chamber (TPC), the
main tracking device of DELPHI, and was complemented by a Vertex Detector (VD)
closest to the beam pipe, the Inner and the Outer Detectors in the barrel region, and two
Forward Chambers in the end caps. It was embedded in a 1.2 T magnetic field, aligned
parallel to the beam axis.
The electromagnetic calorimeter consisted of the High density Projection Chamber
(HPC) in the barrel region, the Forward Electromagnetic Calorimeter (FEMC) and the
Small angle Tile Calorimeter (STIC) in the forward regions, complemented by detectors to
tag the passage of electron-positron pairs from photons converted in the regions between
the FEMC and the HPC. The total depths of the calorimeters corresponded to about 18
radiation lengths. The hadronic calorimeter was composed of instrumented iron with a
total depth along the shortest trajectory for a neutral particle of 6 interaction lengths,
and covered 98% of the total solid angle. Embedded in the hadronic calorimeter were
two planes of muon drift chambers to tag the passage of muons. The whole detector was
surrounded by a further double plane of staggered muon drift chambers.
For LEP-2, the DELPHI detector was upgraded as described in the following.
Changes were made to some of the subdetectors, the trigger system [15], the run
control and the algorithms used in the offline reconstruction of tracks, which improved
the performance compared to the earlier LEP-1 period.
The major changes were the extensions of the Vertex Detector (VD) and the Inner
Detector (ID), and the inclusion of the Very Forward Tracker (VFT) [16], which increased
the coverage of the silicon tracker to polar angles with respect to the z-axis1 of 11◦ <
θ < 169◦. To further improve the track reconstruction efficiency in the forward regions
of DELPHI, the tracking algorithms and the alignment and calibration procedures were
optimised for LEP-2.
Changes were also made to the electronics of the trigger and timing system which
improved the stability of the running during data taking. The trigger conditions were
optimised for LEP-2 running, to give high efficiency for 2- and 4-fermion processes in the
Standard Model and also to give sensitivity to events which may have been signatures
of new physics. In addition, improvements were made to the operation of the detector
during the LEP operating states, to prepare the detector for data taking at the very start
of stable collisions of the e+e− beams, and to respond to adverse background from LEP
when it arose. These changes led to an overall improvement in the efficiency for collecting
the delivered luminosity from about 85% in 1995, before the start of LEP-2, to about
95% at the end in 2000.
During the operation of the DELPHI detector in 2000 one of the 12 sectors of the
central tracking chamber, the TPC, failed. After 1st September it was not possible to
detect the tracks left by charged particles inside the broken sector. The data affected
corresponds to around 1/4 of the data collected in 2000. Nevertheless, the redundancy of
the tracking system of DELPHI meant that tracks passing through the sector could still
be reconstructed from signals in any of the other tracking detectors. As a result, the track
reconstruction efficiency was only slightly reduced in the region covered by the broken
sector, but the track parameter resolutions were degraded compared with the data taken
prior to the failure of this sector.
3 Data and Simulation Samples
The analyses presented here use the data collected by DELPHI in the years 1997 to
2000, at centre-of-mass energies
s between 183 and 209 GeV. The data collected in the
year 2000 with the TPC working in full, with centre-of-mass energies from 200 to 208
GeV and a integrated luminosity weighted average centre-of-mass energy of 206 GeV, were
analysed together. Data acquired with the TPC with a broken sector, corresponding to a
integrated luminosity weighted average centre-of-mass energy of 207 GeV, were analysed
separately and included in the results presented here.
The total integrated luminosity of the data sample is 660.8 pb−1, and the integrated
luminosity weighted average centre-of-mass energy of the data is 197.1 GeV.
To compare with the expected results from processes in the Standard Model including
or not including CR, Monte Carlo (MC) simulation was used to generate events and
1The DELPHI coordinate system is a right-handed system with the z-axis collinear with the incoming electron beam,
and the x axis pointing to the centre of the LEP accelerator.
simulate the response of the DELPHI detector. These events were reconstructed and
analysed with the same programs as used for the real data.
The 4-fermion final states were generated with the code described in [17], based on
WPHACT [18], for the WW signal (charged currents) and for the ZZ background (neutral
currents), after which the events were fragmented with PYTHIA [19] tuned to DELPHI
data [20]. The same WW events generated at 189, 200 and 206 GeV were also fragmented
with PYTHIA implementing the SK-I model, with 100% reconnection probability. The
systematic effects of fragmentation were studied using the above WW samples and WW
samples generated with WPHACT and fragmented with either ARIADNE [7] or HERWIG [6] at
183, 189, 200 and 206 GeV. For systematic studies of Bose-Einstein Correlations (BEC),
WW samples generated with WPHACT and fragmented with PYTHIA implementing the BE32
model [21] of BEC, were used at all energies, except at 207 GeV. The integrated luminosity
of the simulated samples was at least 10 times that of the data of the corresponding year,
and the majority corresponded to 100 times that of the data.
To test the consistency of the SK-I model and measure the κ parameter, large WW
samples were generated in an early stage of this work with EXCALIBUR [22] at 200 and
206 GeV, keeping only the fully hadronic decays. These samples were then fragmented
with PYTHIA. It was verified for smaller subsets that the results using these large samples
and the samples generated later with WPHACT are compatible.
The qq̄(γ) background events were generated at all energies with KK2f [23] and frag-
mented with PYTHIA. For systematic studies, similar KK2f samples fragmented with
ARIADNE [7] were used at 183, 189, 200 and 206 GeV.
These samples will be referred to as “DELPHI samples”.
At 189 GeV, to compare with the other LEP experiments and with different CR mod-
els, 6 samples generated with KORALW [24] for the 4-fermion final states were also used.
These samples 2 will be referred to as “Cetraro samples”. The events in the different sam-
ples have the final state quarks generated with the same kinematics, and differ only in the
parton shower evolution and fragmentation. Three samples were fragmented respectively
with PYTHIA, ARIADNE and HERWIG (using the tuning of the ALEPH collaboration), with
no CR implementation. Three other samples were fragmented in the same manner but
now implementing several CR models: the SK-I model with 100% reconnection proba-
bility, the AR-2 model, and the HERWIG implementation of CR with 1/9 of reconnected
events, respectively.
4 The Particle Flow Method
The first of the two analyses presented in this paper is based on the so-called “particle
flow method”. The particle flow algorithm is based on the selection of special event
topologies, in order to obtain well defined regions between any two jets originating from
the same W (called the Inside-W region) or from different Ws (called the Between-W
region). It is expected that Colour Reconnection decreases (increases) particle production
in the Inside-W (Between-W) region. Hence, by studying the particle production in the
inter-jet regions it is possible to measure the effects of Colour Reconnection. However,
this method requires a selection of events with a suitable topology (see below) which has
a low efficiency (<∼25%).
2produced by ALEPH after the LEP-W Physics Workshop in Cetraro, Italy, October 2001
4.1 Event and Particle Selection
Events with both Ws decaying into q1q̄2 are characterised by high multiplicity, large
visible energy, and the tendency of the particles to be grouped in 4 jets. The background
is dominated by qq̄(γ) events.
Charged particles were required to have momentum p larger than 100 MeV/c and below
1.5 times the beam energy, a relative error on the momentum measurement ∆p/p < 1,
and polar angle θ with respect to the beam axis between 20◦ and 160◦. To remove tracks
from secondary interactions, the distance of closest approach of the extrapolated track
to the interaction point was required to be less than 4 cm in the plane perpendicular to
the beam axis and less than 4/sin θ cm along the beam axis, and the reconstructed track
length was required to be larger than 30 cm.
Clusters in the electromagnetic or hadronic calorimeters with energy larger than 0.5
GeV and polar angle in the interval 10◦ < θ < 170◦, not associated to charged particles,
were considered as neutral particles.
The events were pre-selected by requiring at least 12 charged particles, with a sum
of the modulus of the momentum transverse to the beam axis, of charged and neutral
particles, above 20% of the centre-of-mass energy. These cuts reduced the contributions
from gamma-gamma processes and beam-gas interactions to a negligible amount. The
momentum distribution of the charged particles for the pre-selected events is shown in
Figure 1 and compared to the expected distribution from the simulation. A good agree-
ment between data and simulation is observed.
DELPHI 189 GeV
WW WPHACT
WW semileptonic
p (GeV/c)
0 5 10 15 20 25 30 35 40 45 50
DELPHI 189 GeV
WW WPHACT
WW semileptonic
p (GeV/c)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Figure 1: Momentum distribution for charged particles (range 0-50 GeV/c (a) and
0-5 GeV/c (b)). Points represent the data and the histograms represent the contributions
from simulation for the different processes (signal (white) and background contributions).
About half of the e+e−→qq̄(γ) events at high-energy are associated with an energetic
photon emitted by one of the beam electrons or positrons (radiative return events), thus
reducing the energy available in the hadronic system to the Z mass. To remove these
radiative return events, the effective centre-of-mass energy
s′, computed as described
in [25], was required to be above 110 GeV. It was verified that this cut does not affect the
signal from W pairs, but reduces significantly the contribution from the qq̄(γ) process.
In the WW fully hadronic decays four well separated energetic jets are expected which
balance the momentum of the event and have a total energy near to the centre-of-mass
energy. The charged and neutral particles in the event were thus clustered using the
DURHAM algorithm [26], for a separation value of ycut = 0.005, and the events were
kept if there were 4 and only 4 jets and a multiplicity (charged plus neutral) in each
jet larger than 3. The combination of these two cuts removed most of the semi-leptonic
WW decays and the 2-jet and 3-jet events of the qq̄(γ) background. The charged-particle
multiplicity distribution for the selected events at 189 GeV is given in Figure 2, with data
points compared to the histogram from simulation of signal and background processes.
0 10 20 30 40 50 60 70 80 90
DELPHI 189 GeV
WW WPHACT
WW semileptonic
Figure 2: Uncorrected charged-particle multiplicity distribution at a centre-of-mass en-
ergy of 189 GeV. Points represent the data and the histograms represent the contribution
from simulation for the different processes.
For the study of the charged-particle flow between jets, the initial quark configuration
should be well reconstructed with a good quark-jet association. At 183 GeV and above,
the produced W bosons are significantly boosted. This produces smaller angles in the
laboratory frame of reference between the jets into which the W decays, when compared
to these angles at threshold (back-to-back). Hence, this property tends to reduce the
ambiguity in the definition of the Between-W and Inside-W regions. The selection criteria
were designed in order to minimize the situation of one jet from one W boson appearing
in the Inside-W region of the other W boson.
The selection criteria are based on the event topology, with cuts in 4 of the 6 jet-jet
angles. The smallest and the second smallest jet-jet angle should be below 100◦ and not
adjacent (not have a common jet). Two other jet-jet angles should be between 100◦ and
140◦ and not adjacent (large angles).
In the case that there are two different combinations of jets satisfying the above criteria
for the large angles, the combination with the highest sum of large angles is chosen. This
selection increases the probability to have a correct pairing of jets to the same W boson.
s L Eff. Pur. Nsel MC tot. WW 4j qq̄(γ) ZZ W lep. εPAIR
183 52.7 22% 74% 127 114.2 84.4 22.3 0.7 7.0 69%
189 157.6 21% 75% 340 341.4 255.9 56.8 2.4 26.4 75%
192 25.9 21% 75% 61 56.1 41.9 9.4 0.4 4.4 77%
196 77.3 19% 74% 176 159.2 117.6 26.2 1.3 14.0 79%
200 83.4 18% 72% 173 165.0 119.5 27.8 1.3 16.4 82%
202 40.6 17% 72% 82 75.7 54.6 12.5 0.7 8.0 82%
206 163.9 15% 70% 282 274.7 193.1 47.8 2.7 31.1 79%
207 59.4 15% 70% 102 99.7 70.1 17.6 1.0 11.1 80%
Table 1: Centre-of-mass energy (
s in GeV), integrated luminosity (L in pb−1), efficiency
and purity of the data samples, number of selected events, number of expected events
from 4-jet WW and background processes (total and separated by process), and efficiency
of correct pairing of jets to the same W boson.
The integrated luminosity, the efficiency to select 4-jet WW events and the purity of
the selected data samples, estimated using simulation, and the number of selected events
are summarised for each centre-of-mass energy in Table 1. The numbers of expected
events are also given separately for the signal and the background processes, and were
estimated using simulation. The efficiency to select the correct pairing of jets to the
same W boson, estimated with simulation as the fraction of WW events for which the
selected jets 1 and 2 (see later) correspond indeed to the same W boson, is given in the
last column of the Table.
The efficiency of the event selection criteria decreases with increasing centre-of-mass
energy. This is primarily due to the ‘large’ angles being reduced as a result of the
increased boost (becoming lower than the cut value of 100◦) and ‘small’ angles being
increased due to the larger phase-space available (becoming higher than the cut value of
100◦). Much for the same reason, the efficiency to assign two jets to the same W boson in
the selected events increases slightly with increasing centre-of-mass energy, in opposition
to what would happen at threshold with the W boson decaying into two back-to-back
jets, that would never be selected to come from the same W boson by the requirement
that their interjet angle should be between 100◦ and 140◦.
In the following analysis the jets and planar regions are labeled as shown in Figure 3:
the planar region corresponding to the smallest jet-jet angle is region B in the plane
made by jets 2 and 3; the second smallest jet-jet angle corresponds to the planar region D
between jets 1 and 4 in the plane made by these two jets; the planar region corresponding
to the greatest of the large jet-jet angles in this combination is region A and spans
the angle between jets 1 and 2 in the plane made by these jets; and finally region C
corresponds to the planar region spanned by the second large angle, between jets 3 and
4 in the plane made by these two jets. In general, the planar regions are not in the same
plane, as the decay planes of the W bosons do not coincide, and the large angles in this
combination are not necessarily the largest jet-jet angles in the event.
The distribution of the reconstructed masses of the jet pairings (1,2) and (3,4), after
applying a 4C kinematic fit requiring energy and momentum conservation, is shown in
Figure 4 (two entries per event). In the figure, data at 189 GeV (points) are compared
to the expected distribution from the 4-jet WW signal without CR, plus background
processes, estimated using the simulation (histograms). The contribution from the 4-jet
Inside-W region
Inside-W region
Between-W region
Between-W region
jet 2
jet 1
jet 3
jet 4
Figure 3: Schematic drawing of the angular selection.
WW signal simulation is split between the case in which the two pairs of jets making the
large angles actually come from their parent W bosons and the case in which the jets of
a pair come from different W bosons (mismatch).
4.2 Particle Flow Distribution
The particle flow analysis uses the number of particles in the Inside-W and the
Between-W regions. An angular ordering of the jets is performed as in Figure 3. The
two large jet-jet angles in the event are used to define the Inside-W regions, and the two
smallest angles span the Between-W regions, the regions between the different Ws.
In general, the two W bosons will not decay in the same plane, and this must be
accounted for when comparing the particle production in the Inside-W and Between-W
regions. So, for each region (A, B, C and D) the particle momenta of all charged particles
are projected onto the plane spanned by the jets of that region: jets 1 and 2 for region
A; jets 2 and 3 for region B; jets 3 and 4 for region C; jets 4 and 1 for region D. Then,
for each particle the rescaled angle Φrescaled is determined as a ratio of two angles:
Φrescaled = Φi/Φr , (2)
when the particle momentum is projected onto the plane of the region r. The angle Φi is
then the angle between the projected particle momentum and the first mentioned jet in
the definition of the regions given above. The angle Φr is the full opening angle between
the jets. Hence Φrescaled varies between 0 and 1 for the particles whose momenta are
projected between the pair of jets defining the plane.
However, due to the aplanarity of the event about 9% of the particles in the data and in
the 4-jet WW simulation have projected angles outside all four regions. These particles
were discarded from further analysis. In the case where a particle could be projected
onto more than one region, with 0 < Φrescaled < 1, the solution with the lower momentum
transverse to the region was used. This happened for about 13% of the particles in data,
after background subtraction, and in the 4-jet WW simulation.
This leads to the normalised particle flow distribution shown in Figure 5 at 189 GeV,
where the rescaled angle of region A is plotted from 0 to 1, region B from 1 to 2, region
0 20 40 60 80 100 120
DELPHI 189 GeV
WW WPHACT
WW wrong pairing
WW semileptonic
Mass (GeV/c
Figure 4: Reconstructed dijet masses (after a 4C kinematic fit) for the selected pairs at
189 GeV (2 entries per event)(see text).
C from 2 to 3 and region D from 3 to 4. The statistical error on the bin contents (the
average multiplicity per bin of Φrescaled divided by the bin width) was estimated using
the Jackknife method [27], to correctly account for correlations between different bins.
In this distribution the regions between the jets coming from the same W bosons (A and
C), and from different W bosons (B and D), have the same scale and thus can be easily
compared.
After subtracting bin-by-bin the expected background from the observed distributions,
we define the Inside-W (Between-W) particle flow as the bin-by-bin sum of regions A and
C (B and D). These distributions are compared by performing the bin-by-bin ratio of
the Inside-W particle flow to the Between-W particle flow. This ratio of distributions is
shown for 189 GeV and 206 GeV in Figure 6. The data points are compared to several
fully simulated WW MC samples with and without CR.
A good agreement was found between the predictions using the WPHACT WW MC sam-
ples and the predictions based on the KORALW WW MC samples, both for the scenario
without CR and for the scenario with CR (SK-I model with 100% probability of recon-
nection). For both sets of predictions the regions of greatest difference between the two
scenarios span the rescaled variable Φrescaled from 0.2 to 0.8.
4.3 Particle Flow Ratio
After summing the particle flow distributions for regions A and C, and regions B and
D, the resulting distributions are integrated from 0.2 to 0.8. The ratio R of the Inside-W
to the Between-W particle flow is then defined as (with Φ being the rescaled variable
Φrescaled):
0 0.5 1 1.5 2 2.5 3 3.5 4
A B C D
DELPHI 189 GeV
WPH. SK-I 100%
WW WPHACT
WW semilept.
Φrescaled
Figure 5: Normalised charged-particle flow at 189 GeV. The lines correspond to the sum
of the simulated 4-jet WW signal with the background contributions (estimated from
DELPHI MC samples), normalised to the total number of expected events (Nevents). The
dashed histogram corresponds to the sum with the simulated 4-jet WW signal generated
by WPHACT with 100% SK-I.
0 0.2 0.4 0.6 0.8 1
Φrescaled
DELPHI 189 GeV
KW. SK-I 100%WPH. SK-I 100%
WW KORALWWW WPHACT
0 0.2 0.4 0.6 0.8 1
Φrescaled
DELPHI 206 GeV
WPH. SK-I 100%
WW WPHACT
Figure 6: The ratio of the particle flow distributions (A+C)/(B+D) at 189 GeV (a) and at
206 GeV (b). The data (dots) are compared to WW MC samples generated with WPHACT
(DELPHI samples) and KORALW (Cetraro samples), both without CR and implementing
the SK-Imodel with 100% probability of reconnection. The lines corresponding to WPHACT
are hardly distinguishable from the lines corresponding to KORALW in the same condition
of implementation of CR.
s (GeV) RData Rno CR RSK-I:100%
183 0.889 ± 0.084 0.928 ± 0.005 -
189 1.025 ± 0.063 0.966 ± 0.006 0.864 ± 0.005
192 1.008 ± 0.150 0.970 ± 0.006 -
196 1.041 ± 0.093 0.995 ± 0.006 -
200 0.922 ± 0.084 1.022 ± 0.007 0.889 ± 0.006
202 0.952 ± 0.126 1.015 ± 0.008 -
206 1.116 ± 0.088 1.012 ± 0.008 0.889 ± 0.006
207 1.039 ± 0.135 1.019 ± 0.008 -
Table 2: Values of the ratio R for each energy (errors are statistical only), and expected
values with errors due to limited statistics of the simulation, all from DELPHI WPHACT
WW samples.
MC Sample χ2/DF α,A β,B γ
no CR 7.31/5 1.001± 0.003 (3.20± 0.36)× 10−3 (−1.35± 0.40)× 10−4
SK-I 100% 1.46/1 0.880± 0.003 (1.68± 0.44)× 10−3 -
Table 3: Results of the fit to the evolution of R with (
s(GeV)− 197.5).
∫ 0.8
dnch/dΦ(A+ C)dΦ
∫ 0.8
dnch/dΦ(B +D)dΦ
. (3)
To take into account possible statistical correlations between particles in the Inside-W
and Between-W regions, the statistical error on this ratio R was again estimated through
the Jackknife method [27].
The values forR obtained for the different centre-of-mass energies are shown in Table 2,
and compared to the expectations from the DELPHI WPHACT WW samples without CR
and implementing the SK-I model with 100% reconnection probability. These values for
data and MC are plotted as function of the centre-of-mass energy in Figure 7.
The changes in the value of R for the MC samples are mainly due to the dif-
ferent values of the boost of the W systems. In order to quantify this effect
a linear function R(
s− 197.5) = A + B · (
s− 197.5) was fitted to the MC points
with CR (with
s in GeV), while for the points without CR the quadratic func-
tion R(
s− 197.5) = α+ β · (
s− 197.5) + γ · (
s− 197.5)2 was assumed (with
GeV), giving reasonable χ2/d.o.f. values. The fits yielded the results shown in Table 3.
The MC without CR shows a stronger dependence on
s. The function fitted to this
sample was used to rescale the measured values of R for the data collected at different
energies to the energy of 189 GeV, the centre-of-mass energy at which the combination
of the results of the LEP experiments was proposed in [4]. All the rescaled values were
combined with a statistical error-weighted average. The average of the R ratios rescaled
to 189 GeV was found to be
〈R〉 = 0.979± 0.032(stat). (4)
180 185 190 195 200 205 210
WW no CR Fit to no CR
WW SK-I 100% Fit to SK-I 100%Fit to SK-I 100%
Combined Ratio
√s (GeV)
DELPHI
Figure 7: The ratio R as function of
s for data and MC (DELPHI WPHACTWW samples),
and fits to the MC with and without CR, and the combined ratio after rescaling all values
s = 189 GeV (see text). The value of the combined ratio at 189 GeV is shown at
a displaced energy (upwards by 1 GeV) for better visibility, as well as all the values
for the MC ‘WW no CR’ points and the corresponding fitted curve which are shown at
centre-of-mass energies shifted downwards by 0.5 GeV. All errors for the MC values are
smaller than the size of the markers.
Performing the same weighted average when using for the rescaling the fit to the MC
with CR, one obtains:
〈RCR rescale〉 = 0.987± 0.032(stat). (5)
Repeating the procedure, but now without rescaling the R ratios, the result is:
〈Rno rescale〉 = 0.999± 0.033(stat). (6)
4.4 Study of the Systematic Errors in the Particle Flow
The following effects were studied as sources of systematic uncertainties in this anal-
ysis.
4.4.1 Fragmentation and Detector response
A direct comparison between the particle flow ratios measured in fully hadronic data
and MC samples, R4qData and R4qMC, respectively, is hampered by the uncertainties as-
sociated with the modelling of the WW fragmentation and the detector response. These
systematic uncertainties were estimated using mixed semi-leptonic events. In this tech-
nique, two hadronically decaying W bosons from semi-leptonic events were mixed together
to emulate a fully hadronic WW decay.
Mixing Technique
Semi-leptonic WW decays were selected from the data collected by DELPHI at centre-
of-mass energies between 189 and 206 GeV, by requiring two hadronic jets, a well isolated
identified muon or electron or, in case of a tau candidate, a well isolated particle, all
associated with missing momentum (corresponding to the neutrino) pointing away from
the beam pipe. A neural network selection, developed in [28], was used to select the
events. The same procedure was applied to the WPHACT samples fragmented with PYTHIA
and HERWIG at centre-of-mass energies of 189, 200 and 206 GeV and with ARIADNE at 189
and 206 GeV. The background to this selection was found to be of negligible importance
in this analysis. Samples of mixed semi-leptonic events were built separately at each
centre-of-mass energy for data and Monte Carlo semi-leptonic samples, following the
mixing procedure developed in [2].
In each semi-leptonic event, the lepton (or tau-decay jet) was stripped off and the
remaining particles constituted the hadronically decaying W boson. Two hadronically
decaying W bosons were then mixed together to emulate a fully hadronic WW decay.
The hadronic parts of W bosons were mixed in such a way as to have the parent W
bosons back-to-back in the emulated fully hadronic WW decay. To increase the statistics
of emulated events, and profiting from the cylindrical symmetry of the detector along
the z axis, the hadronic parts of W bosons were rotated around the z axis, but were not
moved from barrel to forward regions or vice-versa, as detailed in the following.
When mixing the hadronic parts of different W events it was required that the two Ws
had reconstructed polar angles back-to-back or equal within 10 degrees. In the latter case,
when both Ws are on the same side of the detector, the z component of the momentum
is sign flipped for all the particles in one of the Ws.
The particles of one W event were then rotated around the beam axis, in order to have
the two Ws also back-to-back in the transverse plane. Each semi-leptonic event was used
in the mixing procedure between 4 and 9 times, to minimize the statistical error on the
particle flow ratio R measured in the mixed semi-leptonic data sample.
The mixed events were then subjected to the same event selection and particle flow
analysis used for the fully hadronic events. The particle flow ratios Rmixed SLData and
Rmixed SLMC were measured in the mixed semi-leptonic data and MC samples, respectively,
and are plotted as function of the centre-of-mass energy in Figure 8.
The values of Rmixed SL measured in MC show a dependence on
s. This effect is
quantified by performing linear fits to the points measured with PYTHIA, ARIADNE and
HERWIG, respectively. The differences between the measured slopes were found to be small.
The function fitted to the PYTHIA points was used to rescale the values of R measured in
data at different energies to 189 GeV. The rescaled values were then combined using as
weights the scaled statistical errors. The weighted average R at 189 GeV for the mixed
semi-leptonic events built from data was found to be
〈Rmixed SLData〉 = 1.052± 0.027(stat). (7)
For each MC sample, the ratio Rmixed SLData/Rmixed SLMC was used to calibrate the
particle flow ratio measured in the corresponding fully hadronic sample, R4qMC, to
compare it to the ratio measured in the data, 〈R4qData〉. The correction factor
Rmixed SLData/Rmixed SLMC was computed from the values of R rescaled to 189 GeV, calcu-
lated from the fits to the mixed semi-leptonic samples built from the data and the MC.
185 190 195 200 205 210
Data Mixed SL
PYTHIA
Fit to PYTHIA
ARIADNE
Fit to ARIADNE
HERWIG
Fit to HERWIG
√s (GeV)
DELPHI
Figure 8: The ratio Rmixed SL as function of
s for data and MC, and fits to the MC (see
text). The ARIADNE points at 189 GeV and at 206 GeV have their centre-of-mass energy
shifted and the error bars on data are tilted for readability.
MC sample PYTHIA ARIADNE HERWIG
Rmixed SLData/Rmixed SLMC 1.053 1.044 0.997
RCalibrated4qMC 1.018 1.011 1.004
Table 4: Ratio of data to MC fitted values of R in mixed semi-leptonic samples, used
to calibrate the R4qMC values for different models (upper line), and calibrated values of
R4qMC. All values were computed at
s = 189 GeV.
The values for Rmixed SLMC are presented in Table 4, for the different models, along with
the calibrated values of R4q for the same models.
The calibration factors differ from unity by less than 6%, and the largest difference of
the calibrated R4qMC values when changing the fragmentation model, 0.014, was consid-
ered as an estimate of the systematic error due to simulation of the fragmentation and of
the detector response, and was added in quadrature to the systematic error. The error
in the calibrated R4qMC values due to the statistical error on 〈Rmixed SLData〉 value used
for the calibration, 0.026, was also added in quadrature to the systematic error.
4.4.2 Bose-Einstein Correlations
Bose-Einstein correlations (BEC) between identical pions and kaons are known to
exist and were established and studied in Z hadronic decays in [29]. They are expected
to exist with a similar behaviour in the W hadronic decays, and this is studied in [2].
They are implemented in the MC simulation samples with BEC via the BE32 model
of LUBOEI [21], which was tuned to describe the DELPHI data in [2]. However, the
situation for the WW (ZZ) fully hadronic decays is not so clear, i.e. whether there are
correlations only between pions and kaons coming from the same W(Z) boson or also
between pions and kaons from different W(Z) bosons. The analyses of Bose-Einstein
correlations between identical particles coming from the decay of different W bosons do
not show a significant effect [30] for three of the LEP experiments, whereas for DELPHI,
an effect was found at the level of 2.4 standard deviations [2]. Thus, a comparison was
made between the WPHACT samples without CR and with BEC only between the identical
pions coming from the same W boson (BEC only inside), to the samples without CR
and with BEC allowed for all the particles stemming from both W bosons, implemented
with the BE32 variant of the LUBOEI model (BEC all). The R values were obtained
at each centre-of-mass energy, after which a linear fit was performed for each model to
obtain a best prediction at 189 GeV. The fit values were found to be in agreement to the
estimate at 189 GeV alone, and for simplicity this estimate was used. The measurement
of BEC from DELPHI of 2.4 standard deviations above zero (corresponding to BEC only
inside), was used to interpolate the range of 4.1 standard deviations of separation between
BEC only inside and BEC all. To include the error on the measured BEC effect, one
standard deviation was added to the effect before the interpolation. The difference in the
estimated values of R at
s = 189 GeV, between the model with BEC only inside and
the model with partial BEC all (at the interpolated point of 3.4/4.1), -0.013, was added
in quadrature to the systematic error.
4.4.3 qq̄(γ) Background Shape
The fragmentation effects, in the shape of the qq̄(γ) background, were estimated by
comparing the values of R obtained when the subtracted qq̄(γ) sample was fragmented
with ARIADNE instead of PYTHIA at the centre-of-mass energy of 189 GeV, and the differ-
ence, 0.003, was added in quadrature to the systematic error.
4.4.4 qq̄(γ) and ZZ Background Contribution
At the centre-of-mass energy of 189 GeV, the qq̄(γ) cross-section in the 4-jet region
is poorly known, due to the difficulty in isolating the qq̄(γ) → 4-jet signal from other
4-jet processes such as WW and ZZ. The study performed in [31] has shown that the
maximal difference in the estimated qq̄(γ) background rate is 10% coming from changing
from PYTHIA to HERWIG as the hadronization model, with the ARIADNE model giving
intermediate results. Conservatively, at each centre-of-mass energy a variation of 10%
on the qq̄(γ) cross-section was assumed, and the largest shift in R, 0.011, was added in
quadrature to the systematic error.
The other background process considered is the Z pair production. The Standard
Model predicted cross-sections are in agreement with the data at an error level of 10% [32].
The cross-section was thus varied by ±10% at each energy and the effect in R was found
to be negligible.
4.4.5 Evolution of R with Energy
The R ratios were rescaled to
s = 189 GeV using the fit to the MC without CR,
however the correct behaviour might be given by the MC with CR. Hence, the difference of
0.009 between the R values obtained using the two rescaling methods, using MC without
CR 〈R〉 and with CR 〈RCR rescale〉, was added in quadrature to the systematic error.
4.5 Results of the Particle Flow Analysis
The final result for the average of the ratios R rescaled to 189 GeV is
MC Sample R
PYTHIA no CR 1.037± 0.004
PYTHIA SK-I 100% 0.917± 0.003
ARIADNE no CR 1.053± 0.004
ARIADNE AR2 1.021± 0.004
HERWIG no CR 1.059± 0.004
HERWIG 1/9 CR 1.040± 0.003
Table 5: R ratios for the Cetraro samples at 189 GeV, calibrated with the mixed semi-lep-
tonic events.
〈R〉 = 0.979± 0.032(stat)± 0.035(syst). (8)
In order to facilitate comparisons between the four LEP experiments, this value can
be normalised by the one determined from simulation samples produced with the full
detector simulation and analysed with the same method. The LEP experiments agreed
to use for this purpose the Cetraro PYTHIA samples. These events were generated with the
ALEPH fragmentation tuning but have been reconstructed with the DELPHI detector
simulation and analysed with this analysis. The values of the R ratios obtained from the
Cetraro samples at 189 GeV, calibrated using the mixed semi-leptonic events from these
samples, are given in Table 5.
The value of 〈R〉 measured from data is between the expected R ratios from PYTHIA
without CR and with the SK-I model with 100% fraction of reconnection. The error
of this measurement is larger than the difference between the values of R from ARIADNE
samples without and with CR, and than the difference between values of R from the
HERWIG samples without CR and with 1/9 of reconnected events.
The following normalised ratios are obtained for the sample without CR and imple-
menting the SK-I model with 100% CR probability, respectively:
rdatano CR =
〈R〉data
Rno CR
= 0.944± 0.031(stat)± 0.034(syst), (9)
rdataCR =
〈R〉data
= 1.067± 0.035(stat)± 0.039(syst). (10)
In the above expressions, the statistical errors in the MC predicted values were propagated
and added quadratically to the systematic errors on the ratios.
It is also possible to define the following quantity, taking the predictions for RCR and
Rno CR at
s = 189 GeV from the PYTHIA samples in Table 5,
〈Rdata〉 −Rno CR
RCR − Rno CR
= 0.49± 0.27(stat)± 0.29(syst) , (11)
from which it can be concluded that the measured 〈Rdata〉 is compatible with intermediate
probability of CR, and differs from the CR in the SK-I model at 100% at the level of
1.3 standard deviations. The ability to distinguish between these two models can be
computed from the inverse of the sum in quadrature of the statistical and systematic
errors; it amounts to be 2.5 standard deviations. In Figure 9 the result of δr is compared
to the predicted values, in the scope of the SK-I model, as a funtion of the fraction of
reconnected events.
Fraction of reconnected events %
DELPHI
0 20 40 60 80 100
Figure 9: Comparison of the measurement of the δr observable to the predictions from
the SK-I model as a function of the fraction of reconnected events.
The result for the value of 〈R〉 can also be used to test for consistency with the SK-I
model as a function of κ and a log-likelihood curve was obtained. This also facilitates
combination with the result obtained in the analysis in the following section, and for this
reason the value of 〈R〉 is rescaled with PYTHIA without CR to a centre-of-mass energy
of 200 GeV: the value obtained at 200 GeV is 〈R〉(200 GeV) = 1.024 ± 0.050. The
values obtained for the predicted ratios RN at 200 GeV and the log-likelihood curve, as
a function of κ, are shown in Figure 10. The value of κ most compatible with the data
within one standard deviation is
κSK-I = 4.13
+20.97
−3.46 . (12)
5 Different MW Estimators as Observables
It has been shown [12] that the MW measurement inferred from hadronically decaying
W+W− events at LEP-2, by the method of direct reconstruction, is influenced by CR
effects, most visible when changing the value of κ in the SK-I model. For the MW(4q)
estimator within DELPHI this is shown in [33]. Other published MW estimators in LEP
experiments are equally sensitive to κ [34].
To probe this sensitivity to CR effects, alternative estimators for the MW measure-
ment were designed which have different sensitivity to κ. In the following, the standard
estimator and two alternative estimators, studied in this paper, are presented. The stan-
dard estimator corresponds to that previously used in the measurement of the W mass
by DELPHI [33]. Note that in the final DELPHI W mass analysis [35] results are given
0. 0.
Fraction of reconnected events %
DELPHI
DELPHI
Fraction of reconnected events %
DELPHI
DELPHI
0 20 40 60 80 100
0 20 40 60 80 100
Figure 10: a) Estimated ratio RN at 200 GeV plotted as a function of different κ values
(top scale), or as function of the corresponding reconnection probabilities (bottom scale),
compared to 〈R〉 measured from data after rescaling to 200 GeV (horizontal lines marked
with R for the value and with 1σ(2σ) for the 〈R〉 value added/subtracted by one(two)
standard deviations); the last three marks on the x axis, close to 100% of reconnection
probability, correspond respectively to the values κ = 100, 300, 800; b) corresponding
log-likelihood curve for the comparison of the estimated values (RN ) with the data (〈R〉).
for the standard and hybrid cone estimators, with the hybrid cone estimator used to
provide the primary result. The data samples, efficiencies and purities for the analysis
corresponding to the standard estimator are provided in [33, 35].
• The standard MW estimator :
This estimator is described in [33] and was optimised to obtain the smallest sta-
tistical uncertainty for the W mass measurement. It results in an event-by-event
likelihood Li(MW) for the parameter MW.
• The momentum cut MW estimator :
For this alternative MW estimator the event selection was performed in exactly
the same way as for the standard MW estimator. The particle-jet association was
also taken from this analysis. However, when reconstructing the event for the MW
extraction a tighter track selection was applied. The momentum and energy of the
jets were calculated only from those tracks having a momentum higher than a certain
pcut value. An event-by-event likelihood L
i (MW) was then calculated.
• The hybrid cone MW estimator :
In this second alternative MW estimator the reconstruction of the event is the same
as for the standard analysis, except when calculating the jet momenta used for the
MW extraction.
coneR
(cone) (std)
Figure 11: Illustration of the iterative cone algorithm within a predefined jet as explained
in the text.
An iterative procedure was used within each jet (defined by the clustering algorithm
used in the standard analysis) to find a stable direction of a cone excluding some
particles in the calculation of the jet momentum, illustrated in Figure 11. Starting
with the direction of the original jet ~p
std , the jet direction was recalculated (direction
(1) on the Figure) only from those particles which have an opening angle smaller
than Rcone with this original jet. This process was iterated by constructing a second
cone (of the same opening angle) around this new jet direction and the jet direction
was recalculated again. The iteration was continued until a stable jet direction ~p jetcone
was found. The jet momenta obtained, ~p jetcone, were rescaled to compensate for the
lost energy of particles outside the stable cone,
~p jetcone → ~p jetcone ·
Ejetcone
. (13)
The energies of the jets were taken to be the same as those obtained with the
standard clustering algorithm (E jetcone → E jet). This was done to increase the
correlation of this estimator with the standard one. The rescaling was not done
for the pcut estimator as it will be used in a cross-check observable with different
systematic properties. Again the result is an event-by-event likelihood LRconei (MW).
Each of these previously defined MW likelihoods had to be calibrated. The slope of
the linear calibration curve for the MW estimators is tuned to be unity, therefore only
a bias correction induced by the reconstruction method has to be applied. This bias
is estimated with the nominal WPHACT Monte Carlo events and the dependence on the
value of κ is estimated with the EXCALIBUR simulation. It was verified for smaller subsets
that the results using these large EXCALIBUR samples and the samples generated with
WPHACT are compatible. Neglecting the possible existence of Colour Reconnection (CR) in
the Monte Carlo simulation results in event likelihoods Li(MW|event without CR), while
Li(MW|event with CR) are the event likelihoods obtained when assuming the hypothesis
that events do reconnect (100% CR in the scope of the SK-I model). To construct the
event likelihoods for intermediate CR (values of κ larger than 0) the following weighting
formula is used :
Li(MW|κ) = [1−Pi(κ)]·Li(MW|event without CR)+Pi(κ)·Li(MW|event with CR) (14)
where Pi(κ) is defined in Equation 1. The combined likelihood is produced for
the event sample; the calibrated values for MW(κ) were obtained for different val-
ues of κ using the maximum likelihood principle. In Figure 12 the difference
dMW(κ) = MW(κ)−MW(κ = 0) or the influence of κ on the bias of the MW estimator is
presented as function of κ.
The uncertainty on this difference is estimated with the Jackknife method [27] to
take the correlation between MW(κ) and MW(κ = 0) into account. It was observed from
simulations that the estimators dependency on κ, for κ below about 5, was not signifi-
cantly different in the centre-of-mass range between 189 and 207 GeV. Therefore in the
determination of κ the dependency at 200 GeV was taken as default for all centre-of-
mass energies. This value of centre-of-mass energy is close to the integrated luminosity
weighted centre-of-mass energy of the complete data sample, which is 197.1 GeV.
When neglecting the information content of low momentum particles or when using
the hybrid cone algorithm, the influence of Colour Reconnection on the MW estimator is
decreased. The dependence ∂MW
of the estimator to κ is decreased when increasing the
value of pcut or when working with smaller cone opening angles Rcone.
5.1 The Measurement of κ
The observed difference ∆MW(std, i) = MW
std − MWi in the event sample, where i
is a certain alternative analysis, provides a measurement of κ. When both estimators
std and MW
i are calibrated in the same hypothesis of κ, the expectation values of
∆MW(std, i) will be invariant under a change of pcut or Rcone.
When neglecting part of the information content of the events in these alternative MW
analyses, by increasing pcut or decreasing Rcone, the statistical uncertainty on the value of
1 10 10
Standard MW analysis    DELPHI
pcut = 1 GeV/c
pcut = 2 GeV/c
pcut = 3 GeV/c
Cone R=1.00 rad
Cone R=0.75 rad
Cone R=0.50 rad
Cone R=0.25 rad
SK-I Model parameter κ
κ = 0.66
Figure 12: The difference dMW(κ) = MW(κ)−MW(κ = 0) is presented as a function of
κ, for different MW estimators. The curve for the standard MW estimator is the curve
at the top. The curves obtained with the hybrid cone analysis for different values of the
cone opening angle, starting from the top with 1.00 rad down to 0.75 rad, 0.50 rad and
0.25 rad are indicated with dotted lines. The curves obtained with the momentum cut
analysis for different values of pcut, starting from the top with 1 GeV/c, down to 2 GeV/c
and 3 GeV/c are dashed. The vertical line indicates the value of κ preferred by the SK-I
authors [5] and commonly used to estimate systematic uncertainties on measurements
using e+e− → W+W− → q1q̄2q3q̄4 events.
the MW estimator is increased. Therefore a balance must be found between the statistical
precision on ∆MW(std, i) and the dependence of this difference to κ in order to obtain
the largest sensitivity for a κ measurement. This optimum was found using the Monte
Carlo simulated events and assuming that the data follow the κ = 0 hypothesis, resulting
in the smallest expected uncertainty on the estimation of κ.
For the pcut analysis an optimal sensitivity was found when using the difference
∆MW(std, pcut) with pcut equal to 2 GeV/c or 3 GeV/c. Even more information about
κ could be extracted from the data, when using the difference ∆MW(std,Rcone), which
was found to have an optimal sensitivity around Rcone = 0.5 rad. No significant im-
provement in the sensitivity was found when combining the information from these two
observables. Therefore the best measure of κ using this method is extracted from the
∆MW(std,Rcone = 0.5 rad) observable. Nevertheless, the ∆MW(std, pcut = 2GeV/c) ob-
servable was studied as a cross-check.
5.2 Study of the Systematic Errors in the ∆MW Method
The estimation of systematic uncertainties on the observables ∆MW(std, i) follows
similar methods to those used within the MW analysis. Here the double difference is a
measure of the systematic uncertainty between Monte Carlo simulation (‘MC’) and real
data (‘DA’):
∆syst(MC,DA) =
std(MC)−MWstd(DA)]− [MWi(MC)−MWi(DA)]
∣ (15)
where i is one of the alternative MW estimators. The systematic error components are
described below and summarised in Table 6.
5.2.1 Jet Reconstruction systematics with MLBZs
A novel technique was proposed in [36] to study systematic uncertainties on jet recon-
struction and fragmentation in W physics measurements with high statistical precision
through the use of Mixed Lorentz Boosted Z events (MLBZs). The technique is similar to
the one described in section 4.4.1. The main advantage of this method was that Monte
Carlo simulated jet properties in W+W− events could be directly compared with the
corresponding ones from real data using the large Z statistics.
The main extension of the method beyond that described in [36] consisted in an
improved mixing and boosting procedure of the Z events into MLBZs, demonstrated
in Figure 13.
The 4-momenta of the four primary quarks in WPHACT generated W+W− → q1q̄2q3q̄4
events were used as event templates. The Z events from data or simulation were chosen
such that their thrust axis directions were close in polar angle to one of the primary quarks
of the W+W− event template. Each template W was then boosted to its rest frame. The
particles in the final state of a selected Z event were rotated so that the thrust axis matches
the rest frame direction of the primary quarks in the W+W− template. After rescaling the
kinematics of the Z events to match the W boson mass in the generated W+W− template,
the two Z events were boosted to the lab frame of the W+W− template. All particles
having an absolute polar angle with the beam direction smaller than 11◦ were removed
from the event. The same generated WPHACT events were used for the construction of both
the data MLBZs and Monte Carlo MLBZs in order to increase the correlation between
both emulated samples to about 31%. This correlation was taken into account when
boost
lab frame WW
"re−boost" rotate
rest frame WW
lab frame  MLBZ
boost
Figure 13: Illustration of the mixing and boosting procedure within the MLBZ method
(see text for details).
quoting the statistical uncertainty on the systematic shift on the observables between
data and Monte Carlo MLBZs.
It was verified that when introducing a significant mass shift of 300 MeV/c2 on MW
by using the cone rejection algorithm, it was reproduced within 15% by applying the
MLBZ technique. Because the expected systematic uncertainties on the ∆MW(std, i)
observables of interest are one order of magnitude smaller than 300 MeV/c2, this method
is clearly justified.
The double difference of Equation 15 was determined with the MLBZ method using
Z events selected in the data sets collected during the 1998 calibration runs and Z events
from the corresponding Monte Carlo samples. The following results were obtained for
the ∆MW(std,Rcone = 0.5 rad) observable:
∆syst(ARIADNE ,DA) = −1.9 ± 3.9(stat)MeV/c2
∆syst(PYTHIA ,DA) = −5.7 ± 3.9(stat)MeV/c2
∆syst(HERWIG ,DA) = −10.6 ± 3.9(stat)MeV/c2
where the statistical uncertainty takes into account the correlation between the Monte
Carlo and the data MLBZ events, together with the correlation between the two MW
estimators. This indicates that most of the fragmentation, detector and Between-W
Bose-Einstein Correlation systematics are small. The study was not performed for the
∆MW(std, pcut) observable.
Other systematic sources on the reconstructed jets are not considered as the MW
estimators used in the difference ∆MW(std, i) have a large correlation.
5.2.2 Additional Fragmentation systematic study
The fragmentation of the primary partons is modelled in the Monte Carlo simulation
used for the calibration of the MW
i observables.
The expected values on the MW estimators from simulation (in the κ = 0 hypothe-
sis) are changed when using different fragmentation models [33], resulting in systematic
uncertainties on the measured MW
i observables and hence possibly also on our esti-
mated κ. In Figure 14 the systematic shift δMW in the different MW
i observables is
shown when using HERWIG or ARIADNE rather than PYTHIA as the fragmentation model
in the no Colour Reconnection hypothesis. When inferring κ from the data difference,
∆MW(std, i), the PYTHIA model is used to calibrate each MW
i observable. This data
difference for MW
pcut=2GeV/c, ∆MW(std, pcut = 2GeV/c), changes
3 by (27 ± 12) MeV/c2
or (8 ± 12) MeV/c2 when replacing PYTHIA by respectively HERWIG or ARIADNE. Simi-
larly, the observable ∆MW(std,Rcone = 0.5 rad) changes by (-4 ± 10) MeV/c2 or (-6 ±
10) MeV/c2 when replacing PYTHIA by respectively HERWIG or ARIADNE. The largest
shift of the observable when changing fragmentation models (or the uncertainty on this
shift if larger) is taken as systematic uncertainty on the value of the observable. Hence,
systematic errors of 27 MeV/c2 for the ∆MW(std, pcut = 2GeV/c) observable and 10
MeV/c2 for the ∆MW(std,Rcone = 0.5 rad) observable were assumed as the contribution
from fragmentation uncertainties. The MLBZ studies (see above) are compatible with
these results, hence no additional systematic due to fragmentation was quoted for the
∆MW(std,Rcone = 0.5 rad) observable.
3This change, ∆MW(std, pcut = 2GeV/c)
PYTHIA
− ∆MW(std, pcut = 2GeV/c)
HERWIG
, is given by
δMW(std ≡ pcut = 0.2GeV/c)
PYTHIA−HERWIG
− δMW(pcut = 2GeV/c)
PYTHIA−HERWIG, and similar expressions for the
ARIADNE and Rcone cases (for Rcone, std ≡ Rcone = π).
0 0.5 1 1.5 2 2.5 3 3.5 4
PYTHIA-ARIADNE         DELPHI
PYTHIA-HERWIG
pcut / GeV/c
0 0.2 0.4 0.6 0.8 1 1.2
PYTHIA-ARIADNE         DELPHI
PYTHIA-HERWIG
Rcone / rad
Figure 14: Systematic shifts δMW, on MW observables, when applying different fragmen-
tation models as a function of the pcut or Rcone values used in the construction of the
MW observable. These Monte Carlo estimates were obtained at a centre-of-mass energy
of 189 GeV. The uncertainties are determined with the Jackknife method.
5.2.3 Energy Dependence
The biases of the different MW estimators have a different dependence on the centre-
of-mass energy, hence the calibration of ∆MW(i, j) will be energy dependent. The energy
dependence of each individual MW estimator was parameterised with a second order poly-
nomial. Since WPHACT event samples were used at a range of centre-of-mass energies
the uncertainty on the parameters describing these curves are small. Therefore a small
systematic uncertainty of 3 MeV/c2 was quoted on the ∆MW(i, j) observables due to the
calibration.
5.2.4 Background
The same event selection criteria were applied for all the MW estimators, hence the
same background contamination is present in all analyses. The influence of the qq̄(γ)
background events on the individual MW estimators is small [33] and was taken into
account when constructing the centre-of-mass energy dependent calibration curves of
the individual MW estimators. The residual systematic uncertainty on both ∆MW(i, j)
observables is 3 MeV/c2.
5.2.5 Bose-Einstein Correlations
As for the particle flow method, the systematic uncertainties due to possible Bose-
Einstein Correlations are estimated via Monte Carlo simulations. The relevant values
for the systematic uncertainties on the observables are the differences between the ob-
servables obtained from the Monte Carlo events with Bose-Einstein Correlations inside
individual W’s (BEI) and those with, in addition, Bose-Einstein Correlations between
identical particles from different W’s (BEA). The values were estimated to be (6.4 ±
9.3) MeV/c2 for the ∆MW(std, pcut = 2GeV/c) observable, and (7.2 ± 8.2) MeV/c2 for
the ∆MW(std,Rcone = 0.5 rad) observable. As the uncertainties in the estimated contri-
butions were larger than the contributions themselves, these uncertainties were added in
quadrature to the systematic errors on the relevant observables.
5.2.6 Cross-check in the Semi-leptonic Channel
Colour Reconnection between the decay products originating from different W boson
decays can only occur in the W+W− → q1q̄2q3q̄4 channel. The semi-leptonic W+W−
decay channel (i.e, qq̄′ℓνℓ) is by definition free of those effects. Therefore the determi-
nation of Colour Reconnection sensitive observables, like ∆MW(std,Rcone = 0.5 rad), in
this decay channel could indicate the possible presence of residual systematic effects. A
study of the ∆MW(std,Rcone = 0.5 rad) observable was performed in the semi-leptonic
decay channel. The semi-leptonic MW analysis in [33] was used and the cone algorithm
was implemented in a similar way as for the fully hadronic decay channel. The same
data sets have been used as presented throughout this paper and the following result was
obtained:
∆MW(std,Rcone) = MW
std − MWRcone = (8 ± 56(stat))MeV/c2 (17)
where the statistical uncertainty was computed taking into account the correlation be-
tween both measurements. Although the statistical significance of this cross-check is
small, a good agreement was found for both MW estimators.
5.3 Results from the MW Estimators Analyses
The observable ∆MW(std,Rcone) with Rcone equal to 0.5 rad (defined above), was
found to be the most sensitive to the SK-I Colour Reconnection model, and the
∆MW(std, pcut = 2GeV/c) observable was measured as a cross-check. The analyses were
calibrated with PYTHIA κ = 0 WPHACT generated simulation events. The values measured
from the combined DELPHI data at centre-of-mass energies ranging between 183 and
208 GeV are:
∆MW(std,Rcone) = MW
std − MWRcone = (59 ± 35(stat) ± 14(syst))MeV/c2
∆MW(std, pcut) = MW
std − MWpcut = (143 ± 61(stat) ± 29(syst))MeV/c2
where the first uncertainty numbers represent the statistical components and the sec-
ond the combined systematic ones. The full breakdown of the uncertainties on both
observables can be found in Table 6.
Uncertainty contribution (MeV/c2)
Source ∆MW(std,Rcone = 0.5 rad) ∆MW(std, pcut = 2GeV/c)
Fragmentation 11 27
Calibration 3 3
Background 3 3
BEI-BEA 8 9
Total systematic 14 29
Statistical Error 35 61
Total 38 67
Table 6: Breakdown of the total uncertainty on both relevant observables.
From these values estimates were made for the κ parameter by comparing them with
the Monte Carlo expected values in different hypothesis of κ, shown in Figure 15 for the
observable ∆MW(std,Rcone = 0.5 rad).
The Gaussian uncertainty on the measured observables was used to construct a log-
likelihood function L(κ) = −2 log L(κ) for κ. The log-likelihood function obtained is
shown in Figure 16 for the first and in Figure 17 for the second observable.
The result shown in Figure 16 is the primary result of this analysis, because of the
larger sensitivity of the ∆MW(std,Rcone = 0.5 rad) observable to the value of κ (see sec-
tion 5.1). The value of κ most compatible with the data within one standard deviation
of the measurement is
κSK-I = 1.75
+2.60
−1.30 . (19)
The result on κ extracted from the cross-check ∆MW(std, pcut = 2GeV/c) observable
is found not to differ significantly from the quoted result obtained with the more opti-
mal ∆MW(std,Rcone = 0.5 rad) observable. The significance can be determined by the
difference between both MW estimators :
pcut − MWRcone = (−84 ± 59(stat))MeV/c2 . (20)
Taking into account that the expectation of this difference depends on κ, we find a sta-
tistical deviation of about 1 to 1.5σ between the measurements. No improved sensitivity
is obtained by combining the information of both observables.
200 DELPHI
at 188.6 GeV
at 199.5 GeV
at 206.5 GeV
SK-I Model parameter κ
κ = 0.66
Figure 15: The dependence of the observable ∆MW(std,Rcone = 0.5 rad) from simulation
events on the value of the SK-I model parameter κ. The dependence is given at three
centre-of-mass energies.
1 10 10
Likelihood of indirect measurement of κ SK-I
DELPHI measured : std - R=0.50 (stat+syst)
DELPHI measured : std - R=0.50 (stat)
SK-I Model parameter κ
Figure 16: The log-likelihood function −2 log L(κ) obtained from the DELPHI data mea-
surement of ∆MW(std,Rcone = 0.5 rad). The bottom curve (full line) gives the final result
including the statistical uncertainty on ∆MW(std,Rcone = 0.5 rad) and the investigated
systematic uncertainty contributions. The top curve (dashed) is centred on the same min-
imum and reflects the log-likelihood function obtained when only statistical uncertainties
are taken into account.
1 10 10
Likelihood of indirect measurement of κ SK-I
DELPHI measured : std - pcut=2 (stat+syst)
DELPHI measured : std - pcut=2 (stat)
SK-I Model parameter κ
Figure 17: The log-likelihood function −2 log L(κ) obtained from the DELPHI data mea-
surement of ∆MW(std, pcut = 2GeV/c). The bottom curve (full line) gives the final result
including the statistical uncertainty on ∆MW(std, pcut = 2GeV/c) and the investigated
systematic uncertainty contributions. The top curve (dashed) is centred on the same min-
imum and reflects the log-likelihood function obtained when only statistical uncertainties
are taken into account.
In this paper the SK-I model for Colour Reconnection implemented in PYTHIA was
studied because it parameterizes the effect as function of the model parameter κ. Other
phenomenological models implemented in the ARIADNE [7,8] and HERWIG [6] Monte Carlo
fragmentation schemes exist and are equally plausible. Unfortunately their effect in
W+W− → q1q̄2q3q̄4 events cannot be scaled with a model parameter, analogous to κ
in SK-I, without affecting the fragmentation model parameters. Despite this non-
factorization property, the consistency of these models with the data can still be ex-
amined. The Monte Carlo predictions of the observables in the hypothesis with Colour
Reconnection (calibrated in the hypothesis of no Colour Reconnection) give the following
values:
ARIADNE → MWstd − MWRcone = (7.2 ± 4.1) MeV/c2
ARIADNE → MWstd − MWpcut = (9.4 ± 7.0) MeV/c2
HERWIG → MWstd − MWRcone = (19.7 ± 4.0) MeV/c2
HERWIG → MWstd − MWpcut = (22.8 ± 6.9) MeV/c2 .
The small effects on the observables with the HERWIG implementation of Colour Reconnec-
tion compared to those predicted by SK-I are due to the fact that the fraction of events
that reconnect is smaller in HERWIG (1/9) compared to SK-I (& 25% at
s = 200 GeV).
After applying this scale factor between both models, their predicted effect on the W
mass and on the ∆MW(i, j) observables becomes compatible. The ARIADNE implementa-
tion of Colour Reconnection has a much smaller influence on the observables compared
to those predicted with the SK-I and HERWIG Monte Carlo.
5.4 Correlation with Direct MW Measurement
When using a data observable to estimate systematic uncertainties on some measur-
and inferred from the same data sample, the correlation between the estimator used to
measure the systematic bias and the estimator of the absolute value of the measurand
should be taken into account. Therefore the correlation between the Colour Reconnection
sensitive observables ∆MW(std,Rcone = 0.5 rad) and ∆MW(std, pcut = 2GeV/c) and the
absolute MW(std) estimator was calculated. The correlation was determined from the
Monte Carlo events and with κ = 0 or no Colour Reconnection. The values obtained
were found to be stable as a function of κ within the statistical precision. The correlation
between ∆MW(std,Rcone = 0.5 rad) and MW(std) was found to be 11%, while for the one
between ∆MW(std, pcut = 2GeV/c) and MW(std) a value of 8% was obtained. Also the
correlation between the different MW estimators was estimated and found to be stable
with the value of κ. A value of 83% was obtained for the correlation between MW(std)
and MW
Rcone=0.5 rad, while 66% was obtained between MW(std) and MW
pcut=2GeV/c.
6 Combination of the Results in the Scope of the
SK-I Model
The log-likelihood curve from the particle flow method was combined with the curve
from the ∆MW method and the result is shown in Figure 18. The correlations between the
analyses were neglected because the overlap between the samples is small and the nature
of the analyses is very different. The total errors were used (statistical and systematic
added in quadrature) in the combination.
1 10 10
Log-Likelihood of measurement    of κ SK-I
from ∆MW
from particle flow
∆MW+part.flow combined
SK-I Model parameter κ
DELPHI
Figure 18: The log-likelihood function −2 log L(κ) obtained from the combined DELPHI
measurement via ∆MW(std,Rcone = 0.5 rad) and the particle flow. The full line gives
the final result including the statistical and systematic uncertainties. The log-likelihood
functions are combined in the hypothesis of no correlation between the statistical and
systematic uncertainties of both measurements.
The best value for κ from the minimum of the curve, with its error given by the width
of the curve at the value −2 log L = (−2 log L)min + 1, is:
κSK-I = 2.2
−1.3 . (22)
7 Conclusions
Colour Reconnection (CR) effects in the fully hadronic decays of W pairs, produced
in the DELPHI experiment at LEP, were investigated using the methods of the particle
flow and the MW estimators, notably the ∆MW(std,Rcone = 0.5 rad) observable.
The average of the ratios R of the integrals between 0.2 and 0.8 of the particle distri-
bution in Inside-W regions to the Between-W regions was found to be
〈R〉 = 0.979± 0.032(stat)± 0.035(syst) . (23)
The values used in this average were obtained after rescaling the value at each energy to
the value at a centre-of-mass energy of 189 GeV using a fit to the MC without CR.
The effects of CR on the values of the reconstructed mass of the W boson, as imple-
mented in different Monte Carlo models, were studied with different estimators. From
the estimator of the W mass with the strongest sensitivity to the SK-I model of CR, the
∆MW(std,Rcone = 0.5 rad) method, the difference in data was found to be
∆MW(std,Rcone) = MW
std −MWRcone=0.5 rad = ( 59± 35(stat)± 14(syst) )MeV/c2 . (24)
From the combination of the results from particle flow and MW estimators, corre-
sponding to the curve in full line shown in Figure 18, the best value and total error for
the κ parameter in the SK-I model was extracted to be:
κSK-I = 2.2
−1.3 (25)
which corresponds to a probability of reconnection of Preco = 52% and lies in the range
31% < Preco < 68% at 68% confidence level.
The two analysis methods used in this paper are complementary: the method of parti-
cle flow provides a model-independent measurement but has significantly less sensitivity
towards the SK-I model of CR than the method of ∆MW estimators.
The obtained value of κ in equation (25) can be compared with similar values obtained
by other LEP experiments, and it was found to be compatible with, but higher than, the
values obtained with the particle flow by L3 [37] and OPAL [38]. It is also compatible
with, but higher than, the values obtained with the method of different MW estimators
by OPAL [39] and ALEPH [40].
Acknowledgements
We thank the ALEPH Collaboration for the production of the simulated “Cetraro
Samples”.
We are greatly indebted to our technical collaborators, to the members of the CERN-
SL Division for the excellent performance of the LEP collider, and to the funding agencies
for their support in building and operating the DELPHI detector.
We acknowledge in particular the support of
Austrian Federal Ministry of Education, Science and Culture, GZ 616.364/2-III/2a/98,
FNRS–FWO, Flanders Institute to encourage scientific and technological research in the
industry (IWT) and Belgian Federal Office for Scientific, Technical and Cultural affairs
(OSTC), Belgium,
FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil,
Czech Ministry of Industry and Trade, GA CR 202/99/1362,
Commission of the European Communities (DG XII),
Direction des Sciences de la Matière, CEA, France,
Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Germany,
General Secretariat for Research and Technology, Greece,
National Science Foundation (NWO) and Foundation for Research on Matter (FOM),
The Netherlands,
Norwegian Research Council,
State Committee for Scientific Research, Poland, SPUB-M/CERN/PO3/DZ296/2000,
SPUB-M/CERN/PO3/DZ297/2000, 2P03B 104 19 and 2P03B 69 23(2002-2004)
FCT - Fundação para a Ciência e Tecnologia, Portugal,
Vedecka grantova agentura MS SR, Slovakia, Nr. 95/5195/134,
Ministry of Science and Technology of the Republic of Slovenia,
CICYT, Spain, AEN99-0950 and AEN99-0761,
The Swedish Research Council,
Particle Physics and Astronomy Research Council, UK,
Department of Energy, USA, DE-FG02-01ER41155,
EEC RTN contract HPRN-CT-00292-2002.
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