Measurement of the running of the fine structure constant below 1 GeV with the KLOE Detector

Abstract

We have measured the running of the effective QED coupling constant $\alpha (s)$ in the time-like region $0.6<\sqrt{s}<0.975$ GeV with the KLOE detector at DA$\Phi$NE using the Initial State Radiation process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma$. It represents the first measurement of the running of $\alpha (s)$ in this energy region. Our results show a more than 5$\sigma$ significance of the hadronic contribution to the running of $\alpha (s)$, which is the strongest direct evidence both in time- and space-like regions achieved in a single measurement. By using the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section measured by KLOE, the real and imaginary part of the shift $\Delta \alpha (s)$ has been extracted. By a fit of the real part of $\Delta \alpha (s)$ and assuming the lepton universality the branching ratio $BR(\omega \to {\mu }^{+}{\mu }^{-})=(6.6\pm 1.4_{stat}\pm 1.7_{syst})\cdot 10^{-5}$ has been determined.

19 pages, 8 figures, version accepted for publication in Phys. Lett. B