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

TL;DR

This paper investigates how including the pion form factor beyond leading order affects theoretical predictions of the $e^+e^- o \pi^+\pi^-$ process, crucial for precise muon g-2 calculations, using three different approaches.

Contribution

It introduces three methods to incorporate the pion form factor beyond leading order in loop diagrams, enhancing the accuracy of theoretical models for experimental comparisons.

Findings

Inclusion of the pion form factor significantly impacts loop diagram calculations.

Different approaches to including the form factor show varying effects on observables.

The study clarifies the interplay between form factor inclusion and radiative corrections.

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.