First study of the interference between initial and final state radiation at the Z resonance

The interference between initialand final state radiationin the processe + e −→μ + μ − at √s≈MZ has been studied by measuring the forward-backward asymmetry as a function of the acoplanarityangle between the finalstate muons. The interference is expected to be sensitive to the space-time separation of the initialand final state radiation. The measured asymmetry distribution has been compared to theoretical predictions using thekoralz generator, with and without\({\mathcal{O}}(\alpha )\) interference. The magnitude of the interference between initialand final state radiationwas found to be of the order predicted and to follow the expected distribution. Using the theoretical predictions, a value of $$\Gamma _{\rm Z} = 2.50 \pm 0.21 (stat.) \pm 0.06 (syst.) GeV.$$ has been extracted. The interpretation of this result is discussed. There is an additional uncertainty in the estimate ofΓ Z from as yet uncalculated higher order interference terms. By assuming a value ofΓ Z consistent with the world average, the data were used to estimate the size of these uncalculated corrections.