Radiative corrections to the forward-backward asymmetry in $e^+e^-\to\pi^+\pi^-$

TL;DR

This paper calculates radiative corrections to the forward-backward asymmetry in electron-positron to pion-pair production, emphasizing model-independent methods and confirming significant effects beyond scalar QED.

Contribution

It introduces a dispersive formalism for calculating C-odd radiative corrections, incorporating a general pion form factor in a model-independent manner.

Findings

Corrections are dominated by infrared-enhanced contributions.

Results show significant deviations from scalar QED predictions.

Confirmation of recent findings in vector-meson-dominance models.

Abstract

We present a calculation of the $C$-odd radiative corrections to $e^+e^-\to \pi^+\pi^-$ in a dispersive formalism, concentrating on the leading pion-pole contribution in the virtual box diagrams. In particular, we show how the effect of a general pion vector form factor in the loop integral can be incorporated in a model-independent way and how the cancellation of infrared singularities proceeds in this case. The numerical results, dominated by the infrared enhanced contributions, indicate significant corrections beyond scalar QED, essentially confirming recent findings in generalized vector-meson-dominance models.