The precision measurement of the $d\sigma(e^+e^- \rightarrow \mu^+\mu^- \gamma)/d\sqrt{ s}$ cross section with the photon emitted in the initial state with the KLOE detector has been used to measure the running of the QED coupling constant $\alpha(s)$ in the energy range 0.6 $< \sqrt{ s} <$ 0.975 GeV in the time-like region. We were able to achieve a significance of the hadronic contribution to the running of $\alpha(s)$ of more than 5$\sigma$ with a clear contribution of the $\rho - \omega$ resonances to the photon propagator. The real and imaginary part of the shift $\Delta\alpha$ to the running has been estracted and a fit of the real part allowed us to measure the branching fraction $BR(\omega \rightarrow \mu^+\mu^-)$ = (6.6$\pm$1.4$_{ stat}$$\pm$1.7$_{ syst}$ )$\cdot$10$^{ -5}$.
Categories: hep-ex