The cross section of the pure QED process e + e − → γγ has been measured using data accumulated during the 1989 and 1990 scans of the Z 0 resonance at LEP. Both the energy dependence and the angular distribution are in good agreement with the QED prediction. Upper limits on the branching ratios of Z 0 → γγ , Z 0 → π 0 γ and Z 0 → ηγ have been set at 1.4×10 −4 , 1.4×10 −4 and 2.0×10 −4 respectively. Lower limits on the cutoff parameters of the modified electron propagator have been found to be Λ + > 117 GeV and Λ − > 110 GeV. The reaction e + e − → γγγ has also been studied and was found to be consistent with the QED prediction. An upper limit on the branching ratio of Z 0 → γγγ has been set at 6.6 × 10 −5 . All the limits are given at 95% confidence level.

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 analysis of the production ofKS0KS0 andK±Ks0π∓ by two quasi-real photons is presented. The cross section forγγ→K0\(\overline {K^0 } \), which is given for the γγ invariant mass range fromK\(\bar K\) threshold to 2.5 GeV, is dominated by thef′(1525) resonance and an enhancement near theK\(\bar K\) threshold. Upper limits on the product of the two-photon width times the branching ratio intoK\(\bar K\) pairs are given forΘ(1700),h(2030), and ξ(2220). For exclusive two-photon production ofK±Ks0π∓ no significant signal was observed. Upper limits are given on the cross section ofγγ→K+\(\overline {K^0 } \)π− orK−K0π+ between 1.4 and 3.2 GeV and on the product of the γγ width times the branching ratio into theK\(\bar K\)π final states for theηc(2980) and the ι(1440), yieldingΓ(γγ)→i(1440))·BR(i(1440)→K\(\bar K\)π<2.2 keV at 95% C.L.

We have measured, at an average centre-of-mass energy of 34.22 GeV a forward-backward charge asymmetry in the reaction e + e − → μ + μ − of value −0.161 ± 0.032. This demonstrates the existence of an axial vector neutral current with coupling strength of g e a g μ a =0.53 ± 0.10. We have also obtained a limit on the vector coupling strength of g e v g μ v <0.12. The Weinberg angle is found to be sin 2 θ W =0.29 +0.09 −0.11 . From the reaction e + e − → τ + τ − we have found g e a g τ a <0.34, g e v g τ v <0.55.

Exclusive production of proton-antiproton pairs by two photon scattering at CM energies between 2.0 GeV and 3.1 GeV has been measured with the TASSO detector at the e + e − storage ring PETRA. The angular distribution is flat within the accepted CM angular range | cos Θ ∗ |⩽0.7 . The integrated cross section (| cos Θ ∗ |⩽0.6) drops from about 4 nb at 2 GeV to less than 0.5 nb above 3 GeV. For the two-photon production of the η c (2984) and its subsequent decay into proton-antiproton the upper limit Γ(η c →γγ)· B (η c → p p )<0.32 keV (95% CL) is found.

The pure QED reaction e + e − → γγ has been studied at centre of mass energies around the mass of the Z 0 boson using data recorded by the OPAL detector at LEP. The results are in good agreement with the QED prediction. Lower limits on the cutoff parameters of the modified electron propagator are found to be Λ + >89 GeV and Λ. The lower limit on the mass of an excited electron is 82 GeV assuming the coupling constant λ =1. Upper limits on the branching ratios of Z 0 → γγ , Z 0 → π 0 γ and Z 0 → ηγ are set at 3.7×10 −4 , 3.9×10 −4 and 5.8×10 −4 respectively. Two events from the reaction e + e − → γγγ have been observed, consistent with the QED prediction. An upper limit on the branching ratio of Z 0 → γγγ is set at 2.8×10 −4 . All the limits are given at 95% confidence level.

Production of the p p π + π − final state by two-photon scattering was observed. The cross section for γγ→p p π + π − was determined assuming phase space production. No evidence was found for the production or formation of resonances. Upper limits are given for Λ and Δ pair production, for production of p p ϱ 0 and for the two-photon excitation of c c bound states.

We present the general properties of jets produced bye+e− annihilation. Their production and fragmentation characteristics have been studied with charged particles for c.m. energies between 12 and 43 GeV. In this energy rangee+e− annihilation into hadrons is dominated by pair production of the five quarksu, d, s, c andb. In addition, hard gluon bremsstrahlung effects which are invisible at low energies become prominent at the high energies. The observed multiplicity distributions deviate from a Poisson distribution. The multiplicity distributions for the overall event as well as for each event hemisphere satisfy KNO scaling to within ∼20%. The distributions ofxp=2p/W are presented; scale breaking is observed at the level of 25%. The quantityxpdδ/dxp is compared with multigluon emission calculations which predict a Gaussian distribution in terms of ln(1/x). The observed energy dependence of the maximum of the distributions is in qualitative agreement with the calculations. Particle production is analysed with respect to the jet axis and longitudinal and transverse momentum spectra are presented. The angular distribution of the jet axis strongly supports the idea of predominant spin 1/2 quark pair production. The particle distributions with respect to the event plane show clearly the growing importance of planar events with increasing c.m. energies. They also exclude the presence of heavy quark production,e+e−→Q\(\bar Q\) for quark masses up to 5<mQ<20.3 GeV (|eQ|=2/3) and 7<mQ<19 GeV (|eQ|=1/3). The comparison of 1/σtotdδ/dpT measured at 14, 22 and 34 GeV suggests that hard gluon bremsstrahlung contributes mainly to transverse momenta larger than 0.5 GeV/c. The rapidity distribution forW≧22 GeV shows an enhancement away fromy=0 which corresponds to an increase in yield of 10–15% compared to the centre region (y=0). The enhancement probably results from heavy quark production and gluon bremsstrahlung. The particle flux around the jet axis shows with increasing c.m. energy a rapidly growing number of particles collimated around the jet axis, while at large angles to the jet axis almost noW dependence is observed. For fixed longitudinal momentump‖ approximate “fan invariance” is seen: The shape of the angular distribution around the jet axis is almost independent ofW. The collimation depends strongly onp‖. For smallp‖,p‖<0.2 GeV/c, isotropy is observed. With increasingp‖ the particles tend to be emitted closer and closer to the jet axis.

Production of events with hadronic and leptonic final states has been measured in e^+e^- collisions at centre-of-mass energies of 130-172 GeV, using the OPAL detector at LEP. Cross-sections and leptonic forward-backward asymmetries are presented, both including and excluding the dominant production of radiative Z \gamma events, and compared to Standard Model expectations. The ratio R_b of the cross-section for bb(bar) production to the hadronic cross-section has been measured. In a model-independent fit to the Z lineshape, the data have been used to obtain an improved precision on the measurement of \gamma-Z interference. The energy dependence of \alpha_em has been investigated. The measurements have also been used to obtain limits on extensions of the Standard Model described by effective four-fermion contact interactions, to search for t-channel contributions from new massive particles and to place limits on chargino pair production with subsequent decay of the chargino into a light gluino and a quark pair.

The process γγ→π+π−π+π− has been investigated in reactions of the typee+e−→e+e−π+π−π+π− in the single tag mode. The range of the four momentum squared of one of the virtual photons was 0.28 GeV2/c2≦Q2≦3.6 GeV2/c2, the average being 〈Q2〉=0.92 GeV2/c2; the other photon was quasi real. The reaction is mainly described by the channels γγ→ρ0ρ0 and γγ→4π (phase space), occuring with about equal probability. TheQ2-dependence of the cross section is in agreement with the ρ form factor.