The forward-backward asymmetry of bottom quarks is measured with statistics of approximately 80 000 hadronic Z 0 decays produced in e + e − collisions at a centre of mass energy of √ s ≈ M z . The tagging of b quark events has been performed using the semileptonic decay channel b→X+ μ . Because the asymmetry depends on the weak coupling, this leads to a precise measurement of the electroweak mixing angle sin 2 θ w . The experimental result is A FB b = 0.115±0.043(stat.)±0.013(syst.). After correcting the value for the B 0 B 0 mixing this becomes A FB b =0.161±0.060(stat.)±0.021(syst.) corresponding to sin 2 θ W MS =0.221±0.011( stat. )±0.004( syst. ) .

We present a measurement of the forward-backward charge asymmetry in hadronic decays of the Z 0 using data collected with the OPAL detector at LEP. The forward-backward charge asymmetry was measured using a weight function method which gave the number of forward events on a statistical basis. In a data sample of 448 942 hadronic Z 0 decays, we have observed a charge asymmetry of A h = 0.040±0.004 (stat.)±0.006 (syst.)±0.002 (B 0 B 0 mix.), taking into account the effect of B 0 B 0 mixing. In the framework of the standard model, this asymmetry corresponds to an effective weak mixing angle averaged over five quark flavours of sin 2 θ W = 0.2321 ± 0.0017 ( stat. ) ± 0.0027 ( syst. ) ± 0.0009 (B 0 B 0 mix.). The result agrees with the value obtained from the Z 0 line shape and lepton pair forward-backward asymmetry.

Measurements of the cross section and forward-backward asymmetry for the reaction e + e − → μ + μ − using the DELPHI detector at LEP are presented. The data come from a scan around the Z 0 peak at seven centre of mass energies, giving a sample of 3858 events in the polar angle region 22° < θ < 158°. From a fit to the cross section for 43° < θ < 137°, a polar angle region for which the absolute efficiency has been determined, the square root of the product of the Z 0 → e + e − and Z 0 → μ + μ − partial widths is determined to be (Γ e Γ μ ) 1 2 = 85.0 ± 0.9( stat. ) ± 0.8( syst. ) MeV . From this measurement of the partial width, the value of the effective weak mixing angle is determined to be sin 2 ( θ w ) = 0.2267 ± 0.0037 . The ratio of the hadronic to muon pair partial widths is found to be Γ h / Γ μ = 19.89 ± 0.40(stat.) ± 0.19(syst.). The forward-backward asymmetry at the resonance peak energy E CMS = 91.22 GeV is found to be A FB = 0.028 ± 0.020(stat.) ± 0.005(syst.). From a combined fit to the cross section and forward-backward asymmetry data, the products of the electron and muon vector and axial-vector coupling constants are determined to be V e V μ = 0.0024 ± 0.0015(stat.) ± 0.0004(syst.) and A e A μ = 0.253 ± 0.003(stat.) ± 0.003 (syst.). The results are in good agreement with the expectations of the minimal standard model.

A measurement of the charm and bottom forward-backward asymmetry in e+e− annihilations is presented at energies on and around the peak of the Z0 resonance. Decays of the Z0 into charm and bottom quarks are tagged using D mesons identified in about 4 million hadronic decays of the Z0 boson recorded with the OPAL detector at LEP between 1990 and 1995. Approximately 33000 D mesons are tagged in seven different decay modes. From these the charm and bottom asymmetries are measured in three energy ranges around the Z0 peak: \(\matrix {A_{\rm FB}^{\rm c}=0.039\pm 0.051\pm 0.009\cr A_{\rm FB}^{\rm c}=0.063\pm 0.012\pm 0.006\cr A_{\rm FB}^{\rm c}=0.158\pm 0.041\pm 0.011}\)\(\matrix {A_{\rm FB}^{\rm b}=0.086\pm 0.108\pm 0.029\cr A_{\rm FB}^{\rm b}=0.094\pm 0.027\pm 0.022\cr A_{\rm FB}^{\rm b}=0.021\pm 0.090\pm 0.026}\)\(\matrix{\langle E_{cm}\rangle =89.45\ {\rm GeV}\cr \langle E_{cm}\rangle =91.22\ {\rm GeV}\cr \langle E_{cm}\rangle =93.00\ {\rm GeV}}\) The results are in agreement with the predictions of the standard model and other measurements at LEP.

The$\tau$polarisation has been studied with the${\rm e^+e^-}\to \tau^+\tau^-$data collected by the DELPHI detector at LEP in

A measurement of theτ lepton polarization and its forward-backward asymmetry at the Z0 resonance using the OPAL detector is described. The measurement is based on analyses of τ→ρντ, ττπ(K)ντ,\(\tau\to e\bar \nu _e \nu _\tau\),\(\tau\to \mu \bar \nu _\mu\nu _\tau\) andτ→a1ντ decays from a sample of 89075 e+e−→τ+τ− candidates corresponding to an integrated luminosity of 117 pb−1. Assuming that theτ lepton decays according to V-A theory, we measure the averageτ polarization at √s=MZ to be 〈P〉=(−13.0±0.9±0.9)% and theτ polarization forward-backward asymmetry to be ApolFB=(−9.4±1.0±0.4)%, where the first error is statistical and the second systematic. These results are consistent with the hypothesis of lepton universality and, when combined, can be expressed as a measurement of sin2θefflept=0.2334±0.0012 within the context of the Standard Model.

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The couplings of the Z 0 to charged leptons are studied using measurements of the lepton pair cross sections and forward-backward asymmetries at centre of mass energies near to the mass of the Z 0 . The data are consistent with lepton universality. Using a parametrisation of the lepton pair differential cross section which assumes that the Z 0 has only vector and axial couplings to leptons, the charged leptonic partial decay width of the Z 0 is determined to be Г ol+ol− = 83.1±1.9 MeV and the square of the product of the effective axial vector and vector coupling constants of the Z 0 to charged leptons to be a ̌ 2 ol v ̌ 2 ol = 0.0039± 0.0083 , in agreement with the standard model. A parametrisation in the form of the improved Born approximation gives effective leptonic axial vector and vector coupling constants a ̌ 2 ol = 0.998±0.024 and v ̌ 2 ol = 0.0044±0.0083 . In the framework of the standard model, the values of the parameters ϱ z and sin 2 θ w are found to be 0.998±0.024 and 0.233 +0.045 −0.012 respectively. Using the relationship in the minimal standard model between ϱ z and sin 2 θ w , the results sin 2 θ SM w = 0.233 +0.007 −0.006 is obtained. Our previously published measurement of the ratio of the hadronic to the leptonic partial width of the Z 0 is update: R z = 21.72 +0.71 −0.65 .

An angular analysis and a measurement of the differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$ are presented, using data corresponding to an integrated luminosity of $3.0\, {\rm fb^{-1}}$ of $pp$ collisions recorded by the LHCb experiment at $\sqrt{s} = 7$ and $8\, {\rm TeV}$. Measurements are reported as a function of $q^{2}$, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range $1<q^2<6\, {\rm GeV}^{2}/c^{4}$, where precise theoretical calculations are available, the differential branching fraction is found to be more than $3\,\sigma$ below the Standard Model predictions.

An angular analysis of the $B^{0}\rightarrow K^{*0}(\rightarrow K^{+}\pi^{-})\mu^{+}\mu^{-}$ decay is presented. The dataset corresponds to an integrated luminosity of $3.0\,{\mbox{fb}^{-1}}$ of $pp$ collision data collected at the LHCb experiment. The complete angular information from the decay is used to determine $C\!P$-averaged observables and $C\!P$ asymmetries, taking account of possible contamination from decays with the $K^{+}\pi^{-}$ system in an S-wave configuration. The angular observables and their correlations are reported in bins of $q^2$, the invariant mass squared of the dimuon system. The observables are determined both from an unbinned maximum likelihood fit and by using the principal moments of the angular distribution. In addition, by fitting for $q^2$-dependent decay amplitudes in the region $1.1<q^{2}<6.0\mathrm{\,Ge\kern -0.1em V}^{2}/c^{4}$, the zero-crossing points of several angular observables are computed. A global fit is performed to the complete set of $C\!P$-averaged observables obtained from the maximum likelihood fit. This fit indicates differences with predictions based on the Standard Model at the level of 3.4 standard deviations. These differences could be explained by contributions from physics beyond the Standard Model, or by an unexpectedly large hadronic effect that is not accounted for in the Standard Model predictions.