Hadronic vacuum polarization in $e^{+}e^{-}\to \mu^{+}\mu^{-}$ process bellow 3 GeV

Abstract

The interference effect between leptonic radiative corrections and hadronic polarization functions is calculated via optical theorem for $\mu-$pair productions. It is achieved within the use of the last data for $\sigma_h(e^+e^-\rightarrow hadrons)$ from SND,CMD,CMD-2,BABAR and BESSIII experimental Collaborations. The paper takes into account specific experimental conditions and the result is compared with KLOE experiment for $\mu^{-}\mu^{+}$ production at $\phi$ meson energy. Small, but non-negligible tension between theory and experiment is discussed.