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

TL;DR

This paper analytically calculates the radiative corrections to the electron-positron annihilation into charged pions and their impact on the muon's anomalous magnetic moment, considering both point-like and form factor models.

Contribution

It provides a detailed analytic computation of final state radiative corrections to e+e- to pi+pi- processes, including form factor effects within the NJL model, for the first time.

Findings

Point-like pion correction: 7.0866 x 10^{-9} with a -2.4 x 10^{-10} correction.

NJL model correction: 5.48 x 10^{-8} with a -3.43 x 10^{-9} adjustment.

Quantifies radiative effects on muon g-2 from e+e- to pi+pi- channels.

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 $a_{NJL}=a_{NJL}^{(1)}+\Delta a_{NJL}$, $a_{NJL}^{(1)}= 5.48\cdot 10^{-8}; \Delta a_{NJL}=-3.43\cdot 10^{-9}$.