Preliminary but close to final results on the Z lineshape and
Forward-Backward asymmetries from the four LEP experiments are presented.
Combined values extracted from ALEPH. DELPHI, L3 and OPAL data recorded at
energies around the Z pole are discussed.Comment: 5 pages, 6 figures, sunbmitted to the Vancouver conference, ICHEP'9

Bloch-Devaux, B.

English

arXiv

Preliminary but close to final results on the Z lineshape and Forward-Backward asymmetries from the four LEP experiments are presented. Combined values extracted from ALEPH. DELPHI, L3 and OPAL data recorded at energies around the Z pole are discussed.Preliminary but close to final results on the Z lineshape and Forward-Backward asymmetries from the four LEP experiments are presented. Combined values extracted from ALEPH. DELPHI, L3 and OPAL data recorded at energies around the Z pole are discussed

Bloch-Devaux, Brigitte

CERN Document Server

Z LINESHAPE AND FORWARD-BACKWARD ASYMMETRIESB. BLOCH-DEVAUXCEA,DAPNIA/Service de Physique des Particules, CE-Saclay, F-91191Gif-sur-Yvette Cedex,FRANCEE-mail: Brigitte.Bloch@cern.chPreliminary but close to nal results on the Z Lineshape and Forward-Backward asymmetries from the four LEP experimentsare presented. Combined values extracted from ALEPH,DELPHI,L3 and OPAL data recorded at energies around the Z pole arediscussed.1 IntroductionPreliminary results of the four LEP experiments1, includ-ing the whole data set recorded around the Z pole from1990 to 1995, are presented here. Emphasis will be givento changes since the last report presented at Winter Con-ferences and experimental systematic errors evaluation.The discussion of the results as a test of the StandardModel can be found in another talk of this session 2.2 Lineshape parametersThe parametrisation of the dominant contribution to thecross section at energies around the Z resonance is basedon a Breit-Wigner shape with an s-dependent width. Af-ter deconvolution of pure QED corrections, this is givenin the \improved Born approximation" byf f¯(s) = 0ff¯sΓ2Z(s−M2Z)2 + s2Γ2Z=M2Z; (1)where the parameters are the Z mass, MZ, the width, ΓZ,and the pole cross section, 0ff¯. The contributions from γexchange and from γ{Z interference are small at energiesps = MZ and are set to their Standard Model values.The pole cross section can be written in terms ofpartial decay widths of the initial and nal states, Γeeand Γff ,0ff¯ =12M2ZΓeeΓffΓ2Z: (2)The denition of the widths explicitly includes QED andQCD corrections,Γff =GFM3Z6p2N fc(g2Vf+ g2Af )(1 + QED + QCD) ; (3)gVf and gAf are eective vector and axial vector cou-plings of the Z to fermion species f, and N fc , the QCDcolour factor, is one for leptonic nal states and threefor hadrons. Due to the eect of radiative corrections,these eective couplings are complex numbers. As thepole cross sections, 0ff¯, have in common the statisticaland systematic error from the luminosity determination,it is more practical to use the ratios of pole cross sectionsin the parametrisation of the leptonic channels,Rf =ohad0ff¯ ΓhadΓfffor ff = e+e−; +−; +−: (4)The energy dependence of the leptonic Forward-Backward asymmetry depends on the axial couplingwhich is mainly determined by the leptonic width.Therefore, the measurements of the leptonic Forward-Backward asymmetries can be condensed into one singleparameter per lepton species in the nal state, the poleasymmetry A0, fFB. This is given by the following combina-tions of eective couplingsA0, fFB 34AeAf (5)with:Af  2gVfgAfg2Vf + g2Af: (6)The contributions from γ{Z interference, imaginaryparts of the photon vacuum polarisation, and the imagi-nary parts of the eective couplings are set to their Stan-dard Model expectations and not included in the deni-tion of A0, fFB.3 The fit procedureEach experiment provides a set of nine parameters (MZ,ΓZ, ohad, Re, Rµ, Rτ ,A0, eFB , A0, µFB , A0, τFB ) tted to the wholeset of cross sections and Forward-Backward lepton asym-metries accumulated by the four LEP experiments dur-ing the LEP 1 period. This is done with the latest ver-sions of the computer codes MIZA 3 and ZFITTER 4,5.These codes provide parametrisations of the fermion pairproduction cross sections and Forward-Backward asym-metries at energies around the Z resonance in terms ofeective couplings and also calculate pure QED correc-tions to full O(2) with exponentiation of the soft partor with leading O(3).The measured cross sections and Forward-Backwardasymmetries are treated in a 2 minimisation procedure1Table 1: Typical correlation matrix for a ve parameter t.MZ ΓZ ohad R` A0, `FBMZ 1. 0.05 -0.01 -0.02 0.06ΓZ 1. -0.16 0.00 0.00ohad 1. 0.14 0.00R` 1. 0.01A0, `FB 1.to extract the nine parameters and their errors and corre-lations. The full error matrix of the input measurementis constructed. The covariance matrix includes the sta-tistical and systematic errors as well as their correlations.Under the assumption of lepton universality, the nineparameters set reduces to a ve parameters one (MZ, ΓZ,ohad, R`, A0, `FB). The chosen parameters are almost un-correlated and thus well adapted to tting and averagingprocedures.Table 1 gives a typical correlation matrix.The only relevant correlations are between (ΓZ andohad) and (R` and ohad). They contain the sensitivity tothe Standard Model parameters MH and s.4 Statistics analysedAnalyses have been performed on data sets recorded from1990 to 1995. Several energy scans were archieved, rstin 1990 and 1991 within 3GeV of ps = MZ value,thenagain in 1993 and 1995 (within 2GeV ), while 1992 and1994 were devoted to peak energy only. In total thefour LEP experiments accumulated 4 times 4 Millionsof Z decays, corresponding to an integrated Luminosityof 120 pb−1 at the peak energy and 40 pb−1 o peak. Thestatistical error on ohad is therefore about 0:05% per ex-periment and about 0:15% per experiment for leptoniccross-sections. As no more running at the Z peak energyis foreseen before the end of LEP era, the results pre-sented here contain the nal word on statistical errors.The details of the improvements achieved in the exper-imental systematic errors will be discussed in the nextsections.5 Experimental errorsEach experiment provides a set of nine (ve) parametersvalues and the corresponding covariance matrix wherecommon systematic error sources are clearly identied.Their origine is of two types: rst, uncertainties in thetheoretical calculations, dominated by the uncertainty onthe small angle Bhabha cross section and the t-channelcontribution to the wide angle Bhabhas, second, a com-mon experimental error from the LEP beam energy un-certainties. All will be discussed below in the appropriateTable 2: MZ value per experiment and combined result in MeV.ALEPH 91188:4 3:1DELPHI 91186:6 2:9L3 91188:3 2:9OPAL 91184:8 3:0LEP 91186:7 2:1sections.Most of the correlations are specied via detailedcorrelation matrices constructed from the specic inter-dependencies of the various error contributions. Partic-ular care is given to the evaluation of the correlated anduncorrelated contribution of each source between datasets of dierent years as well as data sets of the sameyear recorded at dierent center of mass energies.6 MZThe very precise relative error obtained for MZ (about2:10−5) has been achieved after the impressive work ofthe LEP Energy Calibration group6. Starting with a45 MeV error from a simple on-line Field Display in1989, the breakthrough was obtained in 1991 with the useof the depolarization resonance method to calibrate thebeam energy. Later this technique was applied at severalenergy points and other internal (Radio Frequency cor-rections) and external sources causing geometrical defor-mations of the LEP ring (terrestrial tides) were correctedfor in 1992, leading to a 7 MeV uncertainty. Today the ul-timate precision on the beam energy achieved is 1.5 MeV.A correlation matrix has been carefully built describingthe contributions of the dierent terms between years andenergy points of the same year. The mass measurementis directly aected by the uncertainty of the absolute en-ergy scale, i.e., uncertainties correlated between energypoints. The combined result from the LEP experimentsis given in Table 2.7 ΓZThe Z width uncertainty is aected only by the erroron the dierence in energy between energy points (1.3MeV), and not by the error on the absolute energy scale.An additionnal 0.2 MeV comes from the energy spreadaround the mean value. The combined result from theLEP experiments is given here and is shown in Figure 1,the overall relative precision achieved is 0:1%ΓZ = (2:4939 0:0019 0:015 (LEP ))GeV=c2: (7)2Total width ΓZALEPH 2495.0 ± 4.3 MeVDELPHI 2487.2 ± 4.1 MeVL3 2499.6 ± 4.3 MeVOPAL 2493.9 ± 4.0 MeVLEP 2493.9 ± 2.4 MeVmt = 175.6 ± 5.5 GeVαs = 0.123 ± 0.006mZ = 91 186 ± 2 MeVΓZ [MeV]mH [GeV]20040060080010002480 2490 2500Figure 1: ΓZ value for each LEP experiment and combined result.8 ohadThe main source of uncertainty comes here from the Lu-minosity error. All four experiments have decreased theirexperimental error at the 0:1% level. The common theo-retical error amounts to 0:11%. There are some hints of afurther decrease in its evaluation7. One should note thatan increased (with respect to reports at Winter Confer-ences) overall systematic error is quoted due to the the-oretical uncertainty (0.021 nb) on the third order termsintroduced in the lineshape description. The combinedresult from the LEP experiments is shown in Figure 2.9 R`The errors on Re, Rµ and Rτ do not depend on luminos-ity but on the knowledge of relative acceptance and selec-tion eciencies. They are entirely dominated by the totalerror on the lepton cross sections, with very small correla-tions of about 5% from the common normalisation to thenumber of hadrons. Substantial improvements have beenachieved by ALEPH and OPAL who decreased the sys-tematics uncertainty on R` by almost a factor 2. Alephhas developped a new global lepton analysis which re-duces the uncertainty on the flavour separation and is invery good agreement with the classical exclusive analysis.Therefore both analyses have been combined. Particularcare has been given to the t-channel subtraction, usingthe prescription from the authors of ALIBABA 8. TheσhadALEPH 41.519 ± 0.067DELPHI 41.553 ± 0.079L3 41.411 ± 0.074OPAL 41.474 ± 0.068LEP 41.490 ± 0.058mt = 175.6 ± 5.5 GeVαs = 0.123 ± 0.006mZ = 91 186 ± 2 MeVσhadmH [GeV]200400600800100041.4 41.6Figure 2: Pole hadronic cross-section value for each LEP experi-ment and combined result.Table 3: R` ratio value for each experiment and each lepton specie.Re Rµ RτALEPH 20:69 0:07 20:81 0:06 20:72 0:06DELPHI 20:87 0:12 20:67 0:08 20:78 0:12L3 20:78 0:11 20:84 0:10 20:75 0:14OPAL 20:92 0:09 20:82 0:06 20:85 0:09LEP 20:78 0:05 20:79 0:03 20:76 0:05combined result from the LEP experiments assuming lep-ton universality is shown in Figure 3. The splitting intoindividual lepton species is given in Table 310 A0, `FBThe dierential cross section for the reaction e+e− !‘+‘− is expected to have an approximate quadratic de-pendence on the cosine of the polar angle:ddcos /(1 + cos2  +83AFBcos ); (8)where  is the angle between the incoming electron andthe outgoing negative lepton. The LEP experiments havenalized the lepton asymmetry analyses including peri-ods in 1993,1994 and 1995 where precise LEP energy cali-bration was not available but data could be used howeverfor asymmetry measurements. In the case of muons andtaus, the selection has been designed to minimize any3RlALEPH 20.738 ± 0.038DELPHI 20.728 ± 0.060L3 20.788 ± 0.066OPAL 20.828 ± 0.045LEP 20.767 ± 0.026mt = 175.6 ± 5.5 GeVαs = 0.123 ± 0.006mZ = 91 186 ± 2 MeVRlmH [GeV]200400600800100020.7 20.8 20.9Figure 3: R` ratio value for each LEP experiment and combinedresult, assuming lepton universality.Table 4: A0, `FBvalue for each experiment and each lepton specie.Unit is 10−4 A0, eFB A0, µFB A0, τFBALEPH 181: 33: 170: 25: 166: 28:DELPHI 189: 48: 160: 25: 244: 37:L3 148: 63: 176: 35: 233: 49:OPAL 70: 51: 156: 25: 143: 30:LEP 153: 25: 164: 13: 183: 17:nal state invariant mass dependence as an acolinearitycut between the two nal leptons is equivalent to an in-variant mass dependent cut. For the electron nal state,the nal error is dominated by the uncertainty on thet-channel subtraction. The error correlation between theR` and the A0, `FB parameters is also taken into account.The combined result from the LEP experiments is shownin Figure 4, assuming lepton universality. The splittinginto individual lepton species is given in Table 4.Figure 5 shows for each lepton species and for thecombination assuming lepton universality, the resulting68% probability contours in the (R`; A0, `FB) plane.11 Derived quantitiesThe partial decay widths into hadrons and leptons canbe obtained by parameter transformation from the orig-inal nine and ve parameters. Since the total Z width isA0FBALEPH 0.0169 ± 0.0016DELPHI 0.0187 ± 0.0019L3 0.0187 ± 0.0026OPAL 0.0141 ± 0.0018LEP 0.0168 ± 0.0010χ2/dof = 3.8/3mt = 175.6 ± 5.5 GeVα-1 = 128.90 ± 0.09mZ = 91 186 ± 2 MeVA0FBmH [GeV]20040060080010000.01250.0150.0175 0.02Figure 4: A0, `FB value assuming lepton universality, for each LEPexperiment and combined result.0.01080.01480.01880.022820.6 20.7 20.8 20.9RlA0,l fbPreliminary68% CLl+l−e+e−µ+µ−τ+τ−αsmtmHFigure 5: 68% probability contours in the (R`, A0, `FB ) plane with andwithout the assumption of lepton universality. The SM predictionshown by the arrows was computed for Mt = 173.8 ± 5.0 GeV ,90 GeV < MH < 1000 GeV and αs(M2Z) = 0.119 ± 0.002.4LEP averages of leptonic widthsΓe 83.87 ± 0.14 MeVΓµ 83.84 ± 0.18 MeVΓτ 83.94 ± 0.22 MeVΓl 83.90 ± 0.10 MeVmt = 175.6 ± 5.5 GeVmZ = 91 186 ± 2 MeVΓl [MeV]mH [GeV]200400600800100083.5 84 84.5Figure 6: Partial leptonic width values from combined LEP exper-iments.the sum of all partial widths, the decay width into invis-ible particles, Γinv = ΓZ − Γhad − Γ`` (3 + m), can alsobe determined; here, m = −0:0023 is a small correctionwhich accounts for the  mass eect. The results are sum-marised in Figure 6. The comparison of the partial decaywidths of the Z into e,  and  shows good consistencywith lepton universality. To check whether the invisiblewidth is completely explained by decays into the threeneutrino species, the \number of neutrinos", Nν can becalculated according toΓinvΓ``= Nν(ΓνΓ``)SM: (9)The Standard Model value for the ratio of the partialwidths to neutrinos and to charged leptons is 1:991 0:001, where the uncertainty arises from variations of thetop quark mass within Mt = 174  5 GeV and of theHiggs mass within 70 GeV < MH < 1000 GeV . Thenumber of neutrinos from all experiments are shown inTable 5.12 ConclusionThe four LEP experiments have provided very precisemeasurements of the lineshape parameters and Forward-Backward asymmetries. Many results are still prelimi-nary but will become nal soon. They will provide, to-gether with results from SLD and NUTEV experimentsTable 5: Number of light neutrino species detemined by each ex-periment and combined result.ALEPH 2:993 0:015DELPHI 2:988 0:018L3 3:005 0:018OPAL 2:988 0:015LEP 2:994 0:011further constraints on the Standard Model.AcknowledgementsThe averaging of the results was done inside the four-LEPexperiments electroweak group. The impressive achieve-ment of the LEP energy calibration group is also to beaknowledged. Therefore it is a pleasure to thank all mycolleagues from the two groups who helped me in prepar-ing this talk.References1. abstract 284 : Final results of the Z resonance pa-rameters and lepton Forward-Backward asymme-tries at LEP1 (ALEPH),abstract 438 : Cross Sections and LeptonicForward-Backward Asymmetries from the Z0 Run-ning of LEP (DELPHI),abstract 508 : Precise Determination of Elec-troweak Parameters with the L3 Detector at LEP(L3),abstract 229 : A Precision Measurement of the Z0Lineshape and Lepton Forward-Backward Asym-metry (OPAL).2. M.Gru¨newald,these proceedings .3. M.Martinez et al., Z. Phys. C 49, 645 (1991), Z.Phys. C 65, 267 (1995).4. D.Bardin et al., Z. Phys. C 44, 493 (1989), Nucl.Phys. B 351, 1 (1991), Phys. Lett. B 255, 290(1991).5. W.Hollik and G.Passarino, CERN YellowReport/95-03,(1995).6. L.Arnaudon et al., CERN-PPE/92-125,Phys. Lett. B 307, 187 (1993),CERN-SL/93-21,R.Assman et al.,Z. Phys. C 66, 567 (1995),CERN-EP/98-40.7. B.F.L.Ward,these proceedings .8. W.Beenakker et al., Phys. Lett. B 296, 241 (1992),Phys. Lett. B 304, 366 (1993).5

Z lineshape and forward-backward asymmetries

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