Measurement of the running of the QED couplingin small-angle Bhabha scattering at LEP

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Abstract.

Using the OPAL detector at LEP, the running of the effective QED coupling α(t) is measured for space-like momentum transfer from the angular distribution of small-angle Bhabha scattering. In an almost ideal QED framework, with very favourable experimental conditions, we obtain: \( \Delta \alpha {\left( { - 6.07\;{\text{GeV}}^{2} } \right)} - \Delta \alpha {\left( { - 1.81\;{\text{GeV}}^{2} } \right)} = {\left( {440 \pm 58 \pm 43 \pm 30} \right)} \times 10^{{ - 5}} ,\) where the first error is statistical, the second is the experimental systematic and the third is the theoretical uncertainty. This agrees with current evaluations of α(t). The null hypothesis that α remains constant within the above interval of -t is excluded with a significance above 5σ. Similarly, our results are inconsistent at the level of 3σ with the hypothesis that only leptonic loops contribute to the running. This is currently the most significant direct measurement where the running α(t) is probed differentially within the measured t range.

Received: 2 March 2005, Revised: 30 August 2005, Published online: 3 November 2005