The total and the differential cross-sections for the reaction e + e − → γγ ( γ ) have been measured with the DELPHI detector at LEP at centre-of-mass energies from 130 to 183 GeV for an integrated luminosity of 78.19 pb −1 . The results agree with the QED predictions. The lower limits (obtained including previously published results at the Z 0 energies) on the QED cutoff parameters are Λ + >253 GeV and Λ − >225 GeV and the lower bound on the mass of an excited electron with an effective coupling constant λ γ =1 is 231 GeV/ c 2 . All the limits are at the 95% confidence level.
The reactionp→Δ(1236)\(\bar \Delta \)(1236) is studied at 7.23 GeV/c and at 12GeV/c in terms of the OPE model of Wolf. Good agreement between the model and experimental data is found for the mass andt distributions whereas for decay angular distributions the agreement is less satisfactory. A modified model, allowing for a spin orbit coupling, gives good agreement also for the angular distribution.
The total and differential cross-sections for the reaction e + e − → γγ ( γ ) are measured at centre of mass energies around 91 GeV using an integrated luminosity of 4.7 pb −1 . The aggreement with QED prediction is good. Consequently there is no evidence for non-standard channels which would have the same experimental signature. The lower limits on the QED cuttoff parameters are Λ + > 113 GeV and Λ − > 95 GeV. An upper limit on the effective coupling between a possible excited electron and the gamma is derived. At 95% confidence level the branching ratios for Z 0 decay into π 0 γ, ηψ and γγγ are below 1.5 × 10 −4 , 2.8 × 10 −4 and 1.4 × 10 −4 respectively.
A determination of the partial width Γ c c ̄ of the Z 0 boson into charm quark pairs is presented, based on a total sample of 36 900 Z 0 hadronic decays measured with the DELPHI detector at the LEP collider. The production rate of cc̄ events is derived from the inclusive analysis of charged pions coming from the decay of charmed meson D ∗+ → D 0 π + and D ∗− → D ̄ 0 π − where the π ± is constrained by kinematics to have a low p T with respect to the axis. The probability to produce these π ± from D ∗± decay in cc̄ events is taken to be 0.31 ±_0.05 as measured at √ s =10.55 GeV. The measured relative partial width Γ c c ̄ Γ h = 0.162± 0.030 ( stat. ) ±0.050 ( syst. ) is in good agreement with the standard moel value of 0.171. Together with our previous measurement of the total hadronic width Γ h this implies Γ c c ̄ = 282±53 ( stat. )±88( syst. ) MeV .
A measurement of the cross section for e + e - → hadrons using 11 000 hadronic decays of the Z boson at ten different center-of-mass energies is presented. A three-parameter fit gives the following values for the Z mass M z , the total width Γ z , the product of the electronic and hadronic partial widths Γ e Γ h , and the unfolded pole cross section σ 0 : M Z =91.171±0.030(stat)±0.030 (beam) GeV, Γ Z =2.511±0.065 GeV, Γ e Γ h =0.148±0.006 (stat.)±0.004 (syst.) GeV 2 , σ 0 =41.6±0.7(stat.)±1.1 (syst.) nb,
We have studied the energy-energy angular correlations in hadronic final states from Z 0 decay using the DELPHI detector at LEP. From a comparison with Monte Carlo calculations based on the exact second order QCD matrix element and string fragmentation we find that Λ (5) MS =104 +25 -20 ( stat. ) +25 -20( syst. ) +30 00 ) theor. ) . MeV, which corresponds to α s (91 GeV)=0.106±0.003(stat.)±0.003(syst.) +0.003 -0.000 (theor). The theoretical error stems from different choices for the renormalization scale of α s . In the Monte Carlo simulation the scale of α s as well as the fragmentation parameters have been optimized to described reasonably well all aspects of multihadron production.
Hadronic decays of Z 0 bosons are studied in the Delphi detector. Global event variables and singel particles inclusive distributions are compared with QCD-based predictions. The mean charged multiplicity is found to be 20.6±1.0 (stat+syst). The mean values of the sphericity, aplanarity, thrust, minor value, p in T and p out T are compared with values found at lower energy e + e − colliders.
The hadronic fragmentation functions of the various quark flavours and of gluons are measured in a study of the inclusive hadron production from Z 0 decays with the DELPHI detector and are compared with the fragmentation functions measured elsewhere at energies between 14 GeV and 91 GeV. A large scaling violation is observed, which is used to extract the strong coupling constant from a fit using a numerical integration of the second order DGLAP evolution equations. The result is α s ( M Z ) = 0.124 −0.007 +0.006 (exp) ± 0.009(theory) where the first error represents the experimental uncertainty and the second error is due to the factorization and renormalization scale dependence.
From the data collected by DELPHI at LEP in autumn 1995, the multiplicity of charged particles at a hadronic energy of 130 GeV has been measured to be 〈 n ch 〉 = 23.84 ± 0.51 (stat) ± 0.52 (syst). When compared to lower energy data, the value measured is consistent with the evolution predicted by QCD with corrections at next-to-leading order, for a value α s (130 GeV) = 0.105 ± 0.003 (stat) ± 0.008 (syst).
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