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

## TL;DR

This paper calculates the interference effects of leptonic radiative corrections and hadronic polarization in muon pair production below 3 GeV, using recent experimental data and comparing with KLOE results, revealing a small tension.

## Contribution

It introduces a detailed calculation of interference effects in $e^{+}e^{-} o \mu^{+}\mu^{-}$ below 3 GeV using latest hadronic cross-section data and experimental conditions.

## Key findings

- Interference effects are non-negligible and influence muon pair production.
- Comparison shows a small tension between theoretical calculations and KLOE experimental data.
- The analysis enhances understanding of hadronic contributions in low-energy $e^{+}e^{-}$ processes.

## 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.