Final state emission radiative corrections to the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$. Contribution to muon anomalous magnetic moment

Abstract

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 $a_{point}=a_{point}^{(1)}+\Delta a_{point}$, $a_{point}^{(1)}=7.0866\cdot 10^{-9};\Delta a_{point}=-2.4\cdot 10^{-10}.$ Taking into account the pion form factor in the frames of the Nambu-Jona-Lasinio (NJL) approach leads to $a_{NJL}=a_{NJL}^{(1)}+\Delta a_{NJL}$, $a_{NJL}^{(1)}=5.48\cdot 10^{-8};\Delta a_{NJL}=-3.43\cdot 10^{-9}$.

Comments: 15 pages, 2 figure