Final state emission radiative corrections to the process $e^+e^- \to π^+π^-(γ)$. Contribution to muon anomalous magnetic moment

Analytic calculation are presented of the contribution to the anomalous magnetic moment of a muon from the channels of annihilation of an electron-positron pair to a pair of charged pi-mesons with radiative correction connected with the final state, as well as corrections to the lowest order kernel. The result with point-like pi-meson assumptions is $a_{point}=a_{point}^{(1)}+Δa_{point}$, $a_{point}^{(1)}=7.0866 \cdot 10^{-9}; Δa_{point}= -2.4 \cdot 10^{-10} .$ Taking into account the pion form factor in the frames of the Nambu-Jona-Lasinio (NJL) approach leads to $a_{NJL}=a_{NJL}^{(1)}+Δa_{NJL}$, $a_{NJL}^{(1)}= 5.48\cdot 10^{-8}; Δa_{NJL}=-3.43\cdot 10^{-9}$.