Measurement of the running of the electromagnetic coupling at large momentum-transfer at LEP

Abstract

The evolution of the electromagnetic coupling, α, in the momentum-transfer range 1800 GeV² < −Q² < 21600 GeV² is studied with about 40 000 Bhabha-scattering events collected with the L3 detector at LEP at centre-of-mass energies √s = 189–209 GeV. The running of α is parametrised as: <math><mi is="true">α</mi><mrow is="true"><mo is="true">(</mo><msup is="true"><mi is="true">Q</mi><mn is="true">2</mn></msup><mo is="true">)</mo></mrow><mo is="true">=</mo><mfrac is="true"><msub is="true"><mi is="true">α</mi><mn is="true">0</mn></msub><mrow is="true"><mn is="true">1</mn><mo is="true">−</mo><mi is="true">C</mi><mi mathvariant="normal" is="true">Δ</mi><mi is="true">α</mi><mo stretchy="false" is="true">(</mo><msup is="true"><mi is="true">Q</mi><mn is="true">2</mn></msup><mo stretchy="false" is="true">)</mo></mrow></mfrac><mo is="true">,</mo></math> where α₀ ≡ α(Q² = 0) is the fine-structure constant and C = 1 corresponds to the evolution expected in QED. A fit to the differential cross section of the e⁺e⁻ → e⁺e⁻ process for scattering angles in the range |cos θ| < 0.9 excludes the hypothesis of a constant value of α, C = 0, and validates the QED prediction with the result: C = 1.05 ± 0.07 ± 0.14, where the first uncertainty is statistical and the second systematic.