Della Ricca, G

Holt, J

Olshevskii, A G

CERN Document Server

DELPHI Collaboration DELPHI 2002-04 CONF 545February 18, 2002Preliminary S-Matrix Fits to LEP 1 and LEP 2DELPHI DataG.Della Ricca1, J.Holt2, A.Olchevski3AbstractThe hadronic and leptonic cross-sections and leptonic forward-backward asymmetriesdetermined from the data collected with the DELPHI detector at energies near the Z0resonance peak (88-93 GeV) and above (130-209 GeV) during LEP operations between1990 and 2000 have been interpreted in terms of the S-matrix parameters.1INFN, Trieste, Italy2CERN, Geneva, Switzerland3Joint Institute for Nuclear Research, Dubna, Russia1 IntroductionThe published measurements of [1], [2], [3] and the preliminary results of [4] and [5] wereanalyzed in the framework of the S-matrix approach, achieving a substantial improvementin the precision of the γZ0 interference compared to the accuracy obtained from the Z0 dataalone [1], updating the results presented in [2].2 Interpretation of the results in the S-matrix formal-ismThe S-matrix formalism is a rigorous model independent approach to describe the cross-sections and the forward-backward asymmetries in the e+e− annihilations. In this model,the cross-sections can be parametrized as follows:σ0a(s) =43piα2gfas+jfa(s−MZ2) + rfa s(s−MZ2)2 + MZ2ΓZ2 with a = tot, fbf = had, e, µ, τ ,(1)while the forward-backward asymmetries are given by:A0fb(s) =34σ0fb(s)σ0tot(s), (2)where√s is the centre-of-mass energy. The parameters rf and jf scale the Z0 exchange and theγZ0 interference contributions to the total cross-section and forward-backward asymmetries.The contribution gf of the pure γ exchange was fixed to the value predicted by QED in allfits. The Z0 exchange term, the γZ0 interference term and the photon exchange term aregiven by:rtotf =κ2[aˆ2e + vˆ2e] [aˆ2f + vˆ2f]− 2κ vˆe vˆfCImjtotf =2κ vˆe vˆf (CRe + CIm)gtotf =Q2eQ2f |FA(MZ)|2rfbf =4κ2aˆe vˆe aˆf vˆf − 2κ aˆe aˆfCImjfbf =2κ aˆe aˆf (CRe + CIm)gfbf =0 ,(3)with the following definitions:κ =GF MZ22√2 piα≈ 1.50CIm =ΓZMZQeQf Im {FA(MZ)}CRe = QeQf Re {FA(MZ)}FA(MZ) =α(MZ)α ,(4)1where α(MZ) is the complex fine-structure constant, and α ≡ α(0). The photonic virtualand bremsstrahlung corrections are included through the convolution of Equation 1 with thephotonic flux function.Fits to the measured inclusive and non-radiative hadronic and leptonic cross-sectionsand leptonic forward-backward asymmetries were carried out in this framework using thecorresponding branch of the ZFITTER/SMATASY6.36 [6, 7, 8] program 1. The fits includedhadronic and leptonic DELPHI measurements performed near the Z0 resonance [1], andhadronic, muon and tau measurements at higher energies [2, 3, 4, 5].The usual definitions of the mass MZ and width ΓZ of a Breit-Wigner resonance wereused, the width being s-dependent:MZ ≡ MZ√1 + ΓZ2/MZ2 ≈ MZ+34.20 MeV/c2ΓZ ≡ ΓZ√1 + ΓZ2/MZ2 ≈ ΓZ + 0.94 MeV .(5)The results of the fits are presented in Table 1. The χ2 amounted to 162.2(236.9) in thecase of the 16-parameter fit (i.e. without assuming lepton universality) and to 176.5(246.5)for the 8-parameter fit (where lepton universality was assumed), for the line-shape and thecombined line-shape and high energy data, respectively, the number of fitted points being177(237). The correlation coefficients between the free parameters of the 16- and 8-parameterfits for the LEP1 and LEP1+LEP2 are shown in Tables 2, 3, 4 and 5. The data support thehypothesis of lepton universality. Overall, the measurements are in good agreement with theStandard Model predictions.The correlations between the parameters MZ and jtothad is shown in Figure 1. It can beseen that a significant improvement on the precision on the hadronic interference parameter,jtothad, is obtained when the high energy data are included in the fit.1The following values for the Standard Model parameters were used: MZ = 91.1875 GeV, mt = 175 GeV,MH = 150 GeV, αs = 0.118, ∆α(5)had = 2.8761 × 10−2 and GF = 1.166389 × 10−5 GeV−2. The followingZFITTER flags were used: AFBC: 1 SCAL: 0 SCRE: 0 AMT4: 4 BORN: 0 BOXD: 1 CONV: 1 FINR: 1FOT2: 3 GAMS: 1 DIAG: 1 INTF: 1 BARB: 2 PART: 0 POWR: 1 PRNT: 0 ALEM: 2 QCDC: 3 VPOL: 1WEAK: 1 FTJR: 1 EXPR: 0 EXPF: 0 HIGS: 0 AFMT: 1 CZAK: 0 PREC:10 HIG2: 0 ALE2: 3 GFER: 2ISPP: 2 FSRS: 1 MISC: 0 MISD: 1 IPFC: 5 IPSC: 0 IPTO: 3 FBHO: 0 FSPP: 0 FUNA: 0 ASCR: 1 SFSR: 1ENUE: 1 TUPV: 1 .2LEP1 LEP1+LEP2 SMMZ 91.1939 ± 0.0112 91.1826 ± 0.0094 91.1857 ± 0.0037 91.1841 ± 0.0036 –ΓZ 2.4861 ± 0.0048 2.4886 ± 0.0046 2.4890 ± 0.0041 2.4889 ± 0.0041 2.497rtothad 2.9490 ± 0.0110 2.9544 ± 0.0106 2.9557 ± 0.0096 2.9554 ± 0.0096 2.966rtote 0.14092 ± 0.00095 0.14125 ± 0.00091rtotµ 0.14274 ± 0.00072 0.14295 ± 0.00067rtotτ 0.14161 ± 0.00100 0.14201 ± 0.00096rtot` 0.14230 ± 0.00062 0.14235 ± 0.00058 0.1427jtothad −0.21 ± 0.64 0.54 ± 0.54 0.36 ± 0.14 0.39 ± 0.14 0.22jtote −0.095 ± 0.074 −0.050 ± 0.047jtotµ 0.056 ± 0.042 0.022 ± 0.020jtotτ 0.040 ± 0.046 −0.007 ± 0.026jtot` 0.047 ± 0.037 0.006 ± 0.016 0.004rfbe 0.00306 ± 0.00092 0.00298 ± 0.00091rfbµ 0.00275 ± 0.00051 0.00286 ± 0.00049rfbτ 0.00416 ± 0.00072 0.00428 ± 0.00070rfb` 0.00304 ± 0.00038 0.00326 ± 0.00037 0.00273jfbe 0.803 ± 0.073 0.805 ± 0.073jfbµ 0.711 ± 0.037 0.797 ± 0.024jfbτ 0.707 ± 0.047 0.822 ± 0.032jfb` 0.726 ± 0.027 0.804 ± 0.019 0.799Table 1: Results of the 16- and 8-parameter fits to the line-shape and combined line-shape and highenergy data. Also shown are the Standard Model predictions for the fit parameters.3ΓZ rtothad rtote rtotµ rtotτ jtothad jtote jtotµ jtotτ rfbe rfbµ rfbτ jfbe jfbµ jfbτMZ -0.50 -0.46 -0.29 -0.32 -0.25 -0.96 -0.81 -0.70 -0.64 0.13 0.25 0.16 -0.03 0.00 0.00ΓZ 0.90 0.52 0.67 0.49 0.53 0.41 0.38 0.35 -0.06 -0.11 -0.07 0.04 0.04 0.03rtothad 0.53 0.68 0.49 0.50 0.38 0.36 0.32 -0.05 -0.10 -0.06 0.04 0.05 0.04rtote 0.39 0.28 0.30 0.26 0.22 0.20 0.07 -0.06 -0.04 0.08 0.03 0.02rtotµ 0.36 0.34 0.26 0.33 0.23 -0.03 -0.05 -0.04 0.03 0.08 0.03rtotτ 0.26 0.20 0.19 0.25 -0.03 -0.05 0.00 0.02 0.03 0.09jtothad 0.79 0.70 0.64 -0.13 -0.24 -0.16 0.03 0.01 0.01jtote 0.58 0.53 -0.08 -0.20 -0.13 0.11 0.00 0.00jtotµ 0.46 -0.09 -0.15 -0.12 0.02 -0.04 0.00jtotτ -0.08 -0.16 -0.08 0.02 0.00 -0.04rfbe 0.04 0.03 0.09 0.00 0.00rfbµ 0.05 -0.01 0.19 0.00rfbτ -0.01 0.00 0.18jfbe 0.00 0.00jfbµ 0.00Table2:Correlationmatrixforthe16-parametersfitatLEP1data.4ΓZ rtothad rtote rtotµ rtotτ jtothad jtote jtotµ jtotτ rfbe rfbµ rfbτ jfbe jfbµ jfbτMZ 0.00 0.03 -0.01 0.02 0.01 -0.62 -0.38 -0.18 -0.16 0.04 0.08 0.06 0.00 -0.07 -0.06ΓZ 0.87 0.44 0.61 0.42 0.06 -0.01 0.03 0.03 0.01 0.02 0.02 0.03 0.05 0.05rtothad 0.45 0.62 0.43 0.04 -0.02 0.02 0.02 0.01 0.02 0.02 0.03 0.05 0.04rtote 0.32 0.22 0.03 0.04 0.01 0.01 0.11 0.01 0.01 0.07 0.03 0.02rtotµ 0.30 0.02 -0.02 0.09 0.01 0.01 0.03 0.02 0.02 0.11 0.03rtotτ 0.02 -0.01 0.01 0.09 0.01 0.01 0.04 0.01 0.03 0.12jtothad 0.27 0.15 0.14 -0.03 -0.06 -0.04 0.00 0.06 0.05jtote 0.08 0.07 0.02 -0.03 -0.02 0.13 0.03 0.03jtotµ 0.04 -0.01 0.07 -0.01 0.00 0.34 0.02jtotτ -0.01 -0.01 0.08 0.00 0.02 0.34rfbe 0.01 0.01 0.09 0.00 0.00rfbµ 0.02 0.00 0.12 0.00rfbτ 0.00 0.00 0.11jfbe 0.00 0.00jfbµ 0.01Table3:Correlationmatrixforthe16-parametersfitatLEP1+LEP2data.5ΓZ rtothad rtot` jtothad jtot` rfb` jfb`MZ -0.42 -0.39 -0.32 -0.95 -0.82 0.26 0.04ΓZ 0.90 0.74 0.45 0.38 -0.09 0.05rtothad 0.75 0.43 0.35 -0.08 0.05rtot` 0.35 0.33 -0.04 0.09jtothad 0.81 -0.26 -0.03jtot` -0.20 -0.04rfb` 0.17Table 4: Correlation matrix for the 8-parameter fit at LEP1 data.ΓZ rtothad rtot` jtothad jtot` rfb` jfb`MZ 0.00 0.03 0.01 -0.60 -0.33 0.10 -0.11ΓZ 0.87 0.70 0.06 0.03 0.03 0.07rtothad 0.71 0.05 0.02 0.03 0.07rtot` 0.03 0.08 0.05 0.12jtothad 0.26 -0.07 0.09jtot` 0.04 0.34rfb` 0.10Table 5: Correlation matrix for the 8-parameter fit at LEP1+LEP2 data.6-0.4-0.200.20.40.60.811.21.491.165 91.17 91.175 91.18 91.185 91.19 91.195MZ (GeV/c 2)jtot hadDELPHI LEP1 dataDELPHI LEP1+LEP2 dataFigure 1: Contour plot in the MZ -jtothad plane. The dotted curve shows the region accepted at the 68%confidence level from a fit to data taken at the energies around Z0; the solid curve shows the regionaccepted at the same confidence level when the high energy data are also included in the fit.7References[1] P. Abreu et al., Nucl. Phys. B417 (1994) 3;P. Abreu et al., Nucl. Phys. B418 (1994) 403;P. Abreu et al., E. Phys. J. C16 (2000) 371.[2] P. Abreu et al., E. Phys. J. C11 (1999) 383.[3] P. Abreu et al., Phys. Lett. B485 (2000) 45.[4] P. Abreu et al., contributed paper to ICHEP (Osaka, July 2000), DELPHI 2000-128CONF 427.[5] A. Behrmann et al., contributed paper to EPS HEP 2001 (Budapest, July 2001) andLP01 (Rome, July 2001), DELPHI 2001-094 CONF 522.[6] D. Bardin et al., Z. Phys. C44 (1989) 493;D. Bardin et al., Comput. Phys.Comm. 59 (1990) 303;D. Bardin et al., Nucl. Phys. B351 (1991) 1;D. Bardin et al., Phys. Lett. B255 (1991) 290;D. Bardin et al., CERN-TH 6443/92 (May 1992);D. Bardin et al., Comput. Phys. 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Preliminary S-Matrix Fits to LEP 1 and LEP 2 DELPHI Data

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