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The reaction e ϩ e Ϫ → ϩ Ϫ has been measured at ͱsϭ57.77 GeV, based on 289.6Ϯ2.6 pb Ϫ1 data collected with the VENUS detector at TRISTAN. The production cross section is measured in bins of the production angle within an angular acceptance of ͉cos ͉р0.75, according to a model-independent definition. The result is consistent with the prediction of the standard electroweak theory. Although a trend in measurements at lower energies that the total cross section tends to be smaller than the prediction remains, the discrepancy is not significant. The model-independent result is converted to the differential cross section in the effective-Born scheme by unfolding photon-radiation effects. This result can be extrapolated to quantities for the full solid angle as tot EB ϭ30.05Ϯ0.59 pb and A FB EB ϭϪ0.350Ϯ0.017, by imposing an ordinary assumption on the production-angle dependence. The converted results are used to set constraints on extensions of the standard theory. S-matrix parametrization, and possible contributions from contact interactions and heavy neutral-scalar exchanges are examined. ͓S0556-2821͑98͒04309-4͔

The q 2 running of effective QED coupling a͑q 2 ͒ is measured in a spacelike region, ͑10 GeV͒ 2 # 2q 2 # ͑54 GeV͒ 2 , using Bhabha-scattering and muon-pair production data at e 1 e 2 collisions with a center-of-mass energy of 57.77 GeV. The result verifies the prediction of a theoretical estimation with a precision of better than 1% in terms of a͑q 2 ͒͞a͑t 0 ͒ with t 0 2͑10 GeV͒ 2 . [S0031-9007(98)07120-8] PACS numbers: 12.20.Fv, 13.10. + q The vacuum polarization (VP) of the photon field mediating charged-particle interactions is one of the most remarkable consequences from the quantum-field nature of the quantum electrodynamics (QED). The VP effect is expected to depend on the momentum transfer q 2 of the interaction and to be able to be interpreted in terms of a q 2 running of the effective QED coupling a͑q 2 ͒ [1]. The effective coupling equals the fine-structure constant a at the Thomson limit (q 2 0) and is expected to increase logarithmically as jq 2 j increases at large jq 2 j.The VP effect is known to be appreciable and necessary to be taken into account in calculating reliable expectations for reactions in high-energy e 1 e 2 collisions [2]. The effect leads to corrections of more than 10% to the cross sections for reactions with jq 2 j * ͑30 GeV͒ 2 . These reactions are, therefore, expected to provide good places for an experimental evaluation of the VP effect.It should be noted here that, in order to fully describe e 1 e 2 reactions at high energies, it is necessary to use the electroweak theory instead of QED. The electroweak theory predicts the participation of the Z 0 boson together with the photon. Hence, uncertainties on Z 0 properties may hide the VP effect from an experimental evaluation. 24280031-9007͞98͞81(12)͞2428(4)$15.00

Bhabha scattering at a center-of-mass energy of 57.77 GeV has been measured using the VENUS detector at KEK TRISTAN. The precision is better than 1% in scattering angle regions of ͉cos͉р0.743 and 0.822рcosр0.968. A model-independent scattering-angle distribution is extracted from the measurement. The distribution is in good agreement with the prediction of the standard electroweak theory. The sensitivity to underlying theories is examined, after unfolding the photon-radiation effect. The q 2 dependence of the photon vacuum polarization, frequently interpreted as a running of the QED fine-structure constant, is directly observed with a significance of three standard deviations. The Z 0 exchange effect is clearly seen when the distribution is compared with the prediction from QED ͑photon exchanges only͒. The agreement with the standard theory leads us to constraints on extensions of the standard theory. In all quantitative discussions, correlations in the systematic error between angular bins are taken into account by employing an error matrix technique. ͓S0556-2821͑97͒00801-1͔