A summary of the W-boson properties measured by the four LEP collaborations is presented here. These properties are updated to take into account the most recent results presented at the ICHEP98 conference

Pepé-Altarelli, M

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Corfu Summer Institute on Elementary Particle Physics, 1998PROCEEDINGSW Physics at LEPMonica Pepe AltarelliINFN - Laboratori Nazionali di Frascati and CERN, EP DivisionE-mail: Monica.Pepe.Altarelli@CERN.CHAbstract: A summary of the W-boson properties measured by the four LEP collaborations is pre-sented here. These properties are updated to take into account the most recent results presented atthe ICHEP98 Conference.1. WW cross sections andW branch-ing fractionsAfter the period of running at the Z, the centre-of-mass energy of LEP has been progressively in-creased from 161 GeV, i.e., just above the Wpair production threshold to the current centre-of-mass energy of 189 GeV. Each LEP experi-ment has collected a luminosity of approximately10 pb−1 atps = 161 GeV, 10 pb−1 atps =172 GeV and 55 pb−1 atps = 183 GeV. The cur-rent run atps = 189 GeV is expected to yield aluminosity of  150 pb −1; preliminary results onthe W+W− cross section atps = 189 GeV basedon the data analysed for ICHEP98 (i.e., about36 pb −1 per experiment) are also reported.To lowest order, three Feynman diagrams con-tribute to W pair production at LEP II, the s-channel Z and γ exchange and the t-channel eexchange (the so-called CC03 diagrams displayedin Figure 1 for the ud nal state). The s-e+e-ZW-µ-ν-µW+ud-e+e-γW-µ-ν-µW+ud-e-W-µ-ν-µνee+W+ud-Figure 1: Signal diagrams for e+e− ! ud.channel diagrams arise as a consequence of thetrilinear gauge-boson vertices γWW and ZWW.The process which is experimentally relevant ise+e− ! W+W− ! f1f2f3f4. Many more dia-grams contribute to four-fermion production.Those with the same nal states as for W+W−production interfere with the signal processes.Therefore, to obtain the W+W− cross sectionscorresponding to the three CC03 diagrams, themeasurements have to be corrected for four-fermioneects.Table 1 gives the values of the cross sectionsfor the four experiments combined at the dier-ent centre-of-mass energies [1, 2, 3, 4]. Figure 2shows the measured cross sections as a functionof centre-of-mass energy together with the Stan-dard Model (SM) prediction (full line). Alsoshown are the predictions obtained assuming theexistence of the t-channel e-exchange diagramonly (dotted line) or if the ZWW vertex did notexist (dashed line). While contributions fromthe individual Feynman graphs grow with energy,an energy behaviour in agreement with data isonly obtained when the full amplitude is consid-ered, due to cancellations which can be tracedto the gauge theory relations between fermion-Table 1: W+W− cross sections for the four LEPexperiments combined for the various centre-of-massenergies. The results relative to the data taken atps = 183 GeV and 189 GeV are still preliminary.ps (GeV) W+W− (pb)161 3:69 0:45172 12:05 0:73183 15:86 0:40189 15:24 0:57Corfu Summer Institute on Elementary Particle Physics, 1998 Monica Pepe Altarelli√s   [GeV] σ(e+e−→W+W−(γ))   [pb]LEPνe exchangeno ZWW vertexStandard ModelDataPreliminary01020160 170 180 190 200Figure 2: W-pair cross section as a function ofps.The data points are the combined LEP cross sections.The curves show the Standard Model prediction (fullline), the calculated cross section if no ZWW vertexexisted (dashed line) and if both ZWW and γWWvertices did not exist (dotted line).gauge boson vertices and triple gauge couplings.In Table 2, the W decay branching ratios arereported with and without assuming lepton uni-versality [1, 2, 3]. Correlated errors between thevarious channels are taken into account in themeasurements; in particular the branching ratiofor the channel W!  has a correlation of -25% with the other two leptonic channels.The W hadronic branching ratio Bh can berelated to the six elements of the CKM matrix(VCKM) not involving the top quark via the for-mulaBh1− Bh =∑i=u;c j=d;s;bjVi;jj2(1 + s): (1.1)Since jVcsj is rather poorly measured (jVcsj =1:04  0:16 from data on branching ratios forDe3 and D lifetimes [5]) it can be determinedfrom the above expression by taking for the otherCKM matrices the current world averages [5],Table 2: Summary of W branching fractions fromW+W− cross section measurements up to 183 GeVcentre-of-mass energy [1, 2, 3].W! e W!  W!  W!hadronsExp. (%) (%) (%) (%)A 11:2 0:8 0:3 9:9 0:8 0:2 9:7 1:0 0:3 69:0 1:2 0:6D 9:9 1:1  0:5 11:4 1:1 0:5 11:2 1:7 0:7 67:5 1:5 0:9L 10:5 0:9 0:2 10:2 0:9 0:2 9:0 1:2 0:3 70:1 1:3 0:4O 11:7 0:9 0:3 10:1 0:8 0:3 10:3 1:0 0:3 67:9 1:2 0:6LEP 10:92 0:49 10:29 0:47 9:95 0:60 68:79 0:77LEPW! ‘ 10:40 0:26SM 10.8 67.5s = 0:118 0:03 [5] and not assuming unitarityof VCKM. The result is [1, 2, 3, 6]:jVcsj = 1:04 0:04: (1.2)The error on this result is dominated by the sta-tistical error on the W branching fractions. Theelement jVcsj can also be determined by directflavour tagging, based, for example, on a lifetimeor D tag. The result is however less precise inthis case [2, 6]:jVcsj = 0:99 0:11: (1.3)2. Triple gauge couplingsThe most general Lorentz invariant Lagrangiandescribing the triple gauge boson interactions hasfourteen terms which reduce to ve assuming elec-tromagnetic gauge invariance as well as P and Cconservation. Since we are interested in possi-ble deviations from the SM, the anomalous cou-plings g1Z , kZ , kγ , Z and γ , which areall zero in the SM at tree level, are chosen asfree parameters. The Triple Gauge boson Cou-plings ( TGCs) contribute via loops to observ-ables which are precisely measured at LEP I. Itis therefore convenient to choose combinationsof couplings not tightly constrained by existingLEP I data. This leads to the choice at LEP IIof the following parametrisation [7]:W = g1Zcos2W (2.1)W = γ (2.2)B = γ −g1Zcos2W (2.3)2Corfu Summer Institute on Elementary Particle Physics, 1998 Monica Pepe Altarelliwith the constraintsZ = γ and Z = −γtan2W +g1Zif SU(2)⊗SU(1) gauge invariance is also required.The -parameters are all zero in the SM at treelevel.Anomalous couplings increase the W+W−cross section and change the angular distribu-tion of the produced W bosons and of their decayproducts. The strongest information is providedby the semileptonic qq‘ decay for which thecharge assignment is unambiguous. On the con-trary, in the case of the hadronic channel, with-out quark charge or flavour tagging, the fermionand anti-fermion cannot be distinguished. Thedierential cross sections in the production anddecay angles are written in terms of the W helic-ity amplitudes, which are, in turn, well denedfunctions of the TGCs.Additional sensitivity to the WWγ couplingsis provided by single photon and especially singleW events. The dominant diagrams for single Wproduction in the e nal state are shown inFigure 3, the rst diagram being the one provid-ing sensitivity to the WWγ vertex. Since, typi-e-e+e-ν eµ +ν µγWWe-e+e-ν eµ +ν µγeWe-e+e-ν eµ +ν µγµWproduced by GRACEFIGFigure 3: Dominant diagrams for the e+e− !(e) nal state.cally, the electron goes down the beam pipe, thesignatures are a single energetic lepton, or twoacoplanar jets and large missing energy. Figure 4shows the gain in sensitivity on γ (and there-fore on B) obtained when the \standard" WWanalysis is combined with the single W analy-sis [8].The results of ts to W, W and B areshown in Figure 5, assuming in each case thatthe other two anomalous couplings are zero.The combination is performed by adding the log-likelihood curves supplied by the LEP and D0 [9]experiments. The one standard deviation and00.511.522.53-2.5 0 2.5σ (pb)∆g1Z00.511.522.53-2.5 0 2.5∆κγWW+eνW+..WW00.511.522.53-2.5 0 2.5λγExcaliburgrc4fFigure 4: Sensitivity of the cross sections to g1Z ,γ and γ with and without inclusion of the singleW processes.95% condence limits are taken as the parame-ter values where −log L = 0:5 and 1.92, respec-tively. No discrepancy with the SM is observed,however the accuracy on the determination of the parameter is rather poor (in the SM, from ra-diative corrections, they are expected to be oforder 10−2, 10−3).3. Measurement of the W massThe data collected at centre-of-mass energy of161 GeV, i.e., just above the W pair productionthreshold, were used to obtain MW by compar-ing the measured cross section with a theoreti-cal calculation which has MW as a free param-eter. In fact, forps ’ 2MW, the value of thecross section is very sensitive to the W mass andthe precise value of 161 GeV was chosen as thebest compromise between sensitivity to MW andstatistics. Despite the fact that one relies on atheoretical calculation based on the SM to de-riveMW, the model dependence is small since atthreshold the cross section is dominated by thewell established e t-channel exchange diagram.From the LEP combined cross section at 161 GeVWW = 3:69  0:45 pb, the following result for3Corfu Summer Institute on Elementary Particle Physics, 1998 Monica Pepe AltarelliLEP+D0  COMBINATION00.250.50.7511.251.51.752-0.2 0 0.2 0.4 0.6αWφ-∆ln l00.250.50.7511.251.51.752-0.2 0 0.2αW00.511.522.533.54-2 -1 0 1 2αBφ-∆ln l αWφ=-0.03 αW =-0.03 αBφ=-0.05-0.06+0.06+0.08-0.08-0.20+0.22Figure 5: Results for the three  couplings combin-ing LEP (dark grey line), D0 (light grey line) andLEP+D0 (black line).MW is obtained:MW = 80:40 0:22GeV: (3.1)At higher energies MW is obtained by di-rect reconstruction of the jet-jet invariant massesfrom the channels:W+W− ! qqqq ( 45%of cases )W+W− ! qq‘ ( 44%of cases ):These topologies are selected with high eciencyand low background. Eciency and purity forthe fully hadronic events are approximately 85%.The semileptonic events are selected with typi-cally 85% ( 60%) eciency and 95% ( 85%) pu-rity for e and  (). The purely leptonic channelhas not been used so far due to the lack of su-cient constraints on the kinematics of the event,as it contains at least two neutrinos.A kinematic t requiring energy and momen-tum conservation is used to improve the invariantmass resolution. An additional constraint basedon the equality of the two W masses in an eventis also frequently used. In the four-jet case, threekinematic ts are performed for the three possi-ble jet-jet pairings and the resulting t probabil-Table 3: Summary of W mass measurements by di-rect reconstruction ( i.e. using data atps=172 and183 GeV) for the four LEP experiments in the vari-ous decay channels [1, 2, 10, 11]. The errors reportedinclude both statistical and systematic uncertainties.Semileptonic Hadronic CombinedExp. MW (GeV) MW (GeV) MW (GeV)ALEPH 80:34  0:18 80:53  0:18 80:44  0:13DELPHI 80:50  0:24 80:01  0:22 80:24  0:17L3 80:09  0:24 80:59  0:23 80:40  0:18OPAL 80:29  0:19 80:40  0:24 80:34  0:15Combined 80:31  0:11 80:39  0:14 80:36  0:09ities are used to discard, in general, at least oneof the three combinations.The invariant mass distribution has a Breit-Wigner shape which is distorted by several ef-fects such as initial state radiation, detector res-olution, misassignement of particles between thetwo W bosons, background, analysis biases, etc,which can only be evaluated by extensive MonteCarlo simulations. What is generally done toextract MW is to compare the measured invari-ant mass spectra with the corresponding distri-butions from simulated experiments based on dif-ferent input W masses. To avoid generating largeMonte Carlo samples at many dierent masses,starting from a few reference input W masses,the mass spectra corresponding to other choicesofMW are obtained by reweighting each event inthe reference Monte Carlo by the ratio of crosssections calculated with the new and the refer-ence W mass.Table 3 shows a summary of the W massmeasurement by direct reconstruction (at 172 and183 GeV) for the four LEP experiments in thevarious decay modes. The combined four-experimentW mass is [1, 2, 10, 11]:M leptW(172 − 183) = 80:31 0:10stat  0:03syst  0:025LEPMhadW (172 − 183) = 80:39 0:093stat  0:05syst  0:09FSI  0:025LEPMW(172 − 183) = 80:36 0:08 0:05FSI  0:025LEP :The semileptonic and hadronic channels havecomparable branching ratios and selection e-ciencies and give comparable mass resolution. How-ever, the hadronic mode has an additional sys-tematic error of 90 MeV associated to nal stateinteraction eects (FSI) which represents the largestsource of systematic uncertainty, as shown in Ta-4Corfu Summer Institute on Elementary Particle Physics, 1998 Monica Pepe AltarelliTable 4: \Typical" systematic uncertainties forthe semileptonic and hadronic channels. The upper(lower) part of the Table gives those errors which arenot correlated (correlated) between experiments.Systematic Semileptonic Hadronicsource MW (MeV)Detector calibration 40 30QCD background 10MC statistics 10 10Hadronisation 25 30ISR 15 15Beam energy 25 25Final State Interactions - 90TOTAL  60 110ble 4. Final state interactions may arise since theseparation of the W decay vertices at LEP II is 0:1 fm, a distance small with respect to thetypical hadronisation scale of 1 fm (or, in otherwords, ΓW  10QCD). As a result, interconnec-tion phenomena may obscure the separate iden-tities of the two W bosons distorting the massdetermination in the hadronic channel. These in-terconnection eects can be associated to colourelds stretched between quark lines from dier-ent W bosons (\Colour Reconnection") or to in-terference between identical bosons close in phasespace, but produced by dierentW decays (\Bose-Einstein correlations").The best test of colour reconnection is real-ized by comparing mean values of charged parti-cle multiplicity and event-shape distributions inthe fully hadronic and semileptonic modes sincemany systematic eects cancel in the dierence.The distributions for the qqqq mode should beequal to twice the qq‘ mode after removing thenal state lepton or its decay products. The fol-lowing result on the average charged multiplicitydierence between qqqq and qq‘ is obtained bycombining the four LEP experiments [2, 12]:nch  hnchqqqqi − 2hnchqq‘i = 0:20  0:50 : (3.2)At the current level of statistical precision, noevidence for colour reconnection eect is foundin the observables studied. Most models, suchas Sjo¨strand-Khoze [13], ARIADNE [14], HER-WIG [15], are consistent with the data and pre-dict shifts for MW smaller than 50 MeV. TheEllis-Geiger model [16] has not been used to es-timate the systematic error since, in its currentimplementation, does not reproduce a variety ofthe measured event shapes.The simplest method to analyse Bose-Einsteincorrelations is to measure the ratio of like-signto unlike-sign pion pairs as a function of Q2 =(p1 − p2)2 where p1 and p2 are the particle four-momenta. Contribution of pion pairs originatingfrom the same W are subtracted statistically, us-ing the distribution obtained from semileptonicevents. Bose-Einstein correlations are observedin hadronic and semileptonic W decays. How-ever, at the present level of statistics, there isno experimental evidence for Bose-Einstein cor-relations for pairs originating from dierent Wbosons [2, 17]. Phenomenological studies indi-cate that this eect could introduce a shift toMW smaller than 50 MeV. On the basis of thepresent experimental and phenomenological re-sults, the error of 90 MeV which is currentlyassigned as common systematic uncertainty be-tween the LEP experiments due to nal state in-teractions (Bose-Einstein and Colour Reconnec-tion eects) is probably a rather conservative es-timate.Since the systematic uncertainties of the di-rect reconstruction technique and threshold methodare largely independent, the two measurementscan be combined, yielding the following result:MW = 80:37 0:09GeV: (3.3)Figure 6 shows a summary of direct determina-tions of MW from LEP and the TEVATRON, aswell as the indirect estimates from N scatter-ing and from radiative corrections using all elec-troweak data [2, 11]. Direct MW measurementsprovide a precision which is approaching the oneobtained by radiative corrections, allowing a fur-ther important test of the SM. The goal of mea-suring by the end of the LEP II programme in theyear 2000 the W mass with a precision of 30-40 MeV seems to be in reach. SinceMW is an ob-servable which is sensitive to MH, this measure-ment will allow to put additional constraints onthe Higgs mass. The real break-through wouldbe of course the discovery of the Higgs in the10 GeV mass window which is still accessibleto LEP II.5Corfu Summer Institute on Elementary Particle Physics, 1998 Monica Pepe AltarelliW-Boson Mass  [GeV]mW  [GeV]χ2/DoF: 0.1 / 180.0 80.2 80.4 80.6 80.8pp−-colliders 80.41 ± 0.09LEP2 80.37 ± 0.09Average 80.39 ± 0.06NuTeV/CCFR 80.25 ± 0.11LEP1/SLD/νN/mt 80.365 ± 0.030Figure 6: Summary of MW measurements fromLEP, the TEVATRON experiments and N scatter-ing as well as the indirect determination derived fromall other electroweak data.References[1] LEPEWWG/MW/98-02, LEP WW cross sec-tion and W mass for ’98 Summer conferences,The LEP Electroweak W Mass Working Group,available at the following WWW address:http://www.cern.ch/LEPEWWG/wmass/ ,and references herein.[2] D.Karlen, Experimental Status of the StandardModel, Plenary talk presented at ICHEP98.[3] L.Malgeri, WW Cross Section and BranchingFraction Measurements at LEP, Talk presentedat ICHEP98.[4] The LEP Collaborations ALEPH, DELPHI,L3, OPAL and the LEP Electroweak WorkingGroup and the SLD Heavy Flavour Group, Acombination of Preliminary LEP ElectroweakMeasurements and Constraints on the StandardModel, CERN-PPE/97-154.[5] R.M.Barnett et al, Review of particle properties,Phys. Rev. D54 (1996) 1.[6] V.Obraztsov, Measurements of jVcsj in W de-cays at LEP II, Talk presented at ICHEP98.[7] Physics at LEP2, Edited by G.Altarelli,T.Sjo¨strand and F.Zwirner, Report on the LEP2workshop 1995, CERN 96-01 (1996) Vol 1,p.525.[8] R.Tanaka, Single W Production at LEP2, Talkpresented at ICHEP98.[9] LEPEWWG/TGC/98-01, A Combination ofPreliminary Measurements of Triple GaugeBoson Coupling Parameters Measured bythe LEP and D0 Experiments, TGC Com-bination Group, Prepared from Contribu-tions of the LEP and D0 experiments tothe 1998 winter conferences. Available at:http://www.cern.ch/LEPEWWG/tgc/ .[10] H.Przysiezniak, MW by direct reconstruction atLEP in the semileptonic channel, Talk presentedat ICHEP98.[11] M.Thomson, MW by direct reconstruction atLEP in the hadronic channel, Talk presented atICHEP98.[12] N.K.Watson, Hadronic Decay Properties, Talkpresented at ICHEP98.[13] T.Sjo¨strand and V.A.Khoze, Z. Phys. C62(1994) 281;T.Sjo¨strand and V.A.Khoze, CERN-TH/98-74.[14] L.Lo¨nnblad, Z. Phys. C70 (1996) 107.[15] G.Marchesini et al, Comput. Phys. Commun 67(1992) 465.[16] J.Ellis and K.Geiger, Phys. Lett. B404 (1997)230.[17] R.Moller, Bose-Einstein Correlations in WWevents, Talk presented at ICHEP98.6

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