Charge asymmetries in e+e- -> pi+ pi- gamma at the phi resonance

TL;DR

This paper investigates the forward-backward charge asymmetry in e+e- to pi+ pi- gamma at the phi resonance, comparing various theoretical models with experimental data to understand the underlying physics.

Contribution

It compares four different theoretical models for final state radiation at the loop level and assesses their compatibility with experimental data.

Findings

Resonance and bremsstrahlung contributions analyzed at tree level.

Kaon Loop Model needs an energy-dependent phase for data agreement.

Three models (Resonance Chiral, Unitarized Chiral, Linear Sigma) agree with experiments.

Abstract

We consider the forward-backward pion charge asymmetry for the e^{+}e^{-}\to\pi^{+}\pi^{-}\gamma process. At tree level we consider bremsstrahlung and double resonance contributions. Although the latter contribution is formally sub-leading, it is enhanced at low dipion invariant mass due to $\rho$ resonant effects. We consider also four alternative models to describe the final state radiation at the loop level: Resonance Chiral Perturbation Theory, Unitarized Chiral Perturbation Theory, Kaon Loop Model and Linear Sigma Model. The last three models yield results compatible with experimental data. The Kaon Loop Model requires an energy dependent phase to achieve the agreement.