On the inclusion of the pion form factor in $e^+e^- \to \pi^+\pi^-$ beyond leading order

Abstract

The pion form factor plays a crucial role in the determination of the contribution of the hadronic vacuum polarisation to the muon anomalous magnetic moment. In order to measure this quantity, energy-scan experiments rely on Monte Carlo generator to simulate the $e^+e^- \to \pi^+\pi^-(\gamma)$ process. For the theoretical accuracy to match the experimental precision, next-to-leading order calculations and the resummation of multiple photon emissions are needed. In this context, the inclusion of the pion form factor beyond the leading order approximation is crucial to reproduce some observables, like the pion charge asymmetry. We present the impact of the inclusion of the pion form factor in loop diagrams with three approaches and the interplay with radiative corrections.